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Chemical equilibrium
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In a chemical reaction, chemical equilibrium is the state in which both reactants and products are present in concentrations which have no further tendency to change with time.[1] Usually, this state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but equal. Thus, there are no net changes in the concentrations of the reactant(s) and product(s). Such a state is known as dynamic equilibrium.[2][3]
Contents
[hide]
1 Historical introduction
2 Thermodynamics
2.1 Addition of reactants or products
2.2 Treatment of activity
2.3 Concentration quotients
2.4 Metastable mixtures
3 Pure substances
4 Multiple equilibria
5 Effect of temperature
6 Effect of electric and magnetic fields
7 Types of equilibrium
8 Composition of a mixture
8.1 Mass-balance equations
8.1.1 Polybasic acids
8.1.2 Solution and precipitation
8.2 Minimization of Gibbs energy
9 See also
10 References
11 Further reading
Historical introduction[edit]
Burette, a common laboratory apparatus for carrying out titration, an important experimental technique in equilibrium and analytical chemistry.
The concept of chemical equilibrium was developed after Berthollet (1803) found that some chemical reactions are reversible. For any reaction mixture to exist at equilibrium, the rates of the forward and backward (reverse) reactions are equal. In the following chemical equation with arrows pointing both ways to indicate equilibrium, A and B are reactant chemical species, S and T are product species, and α, β, σ, and τ are the stoichiometric coefficients of the respective reactants and products:
α A + β B ⇌ σ S + τ T
The equilibrium concentration position of a reaction is said to lie "far to the right" if, at equilibrium, nearly all the reactants are consumed. Conversely the equilibrium position is said to be "far to the left" if hardly any product is formed from the reactants.
Guldberg and Waage (1865), building on Berthollet’s ideas, proposed the law of mass action:
forward reaction rate = k + A α B β {\displaystyle {\mbox{forward reaction rate}}=k_{+}\mathrm {A} ^{\alpha }\mathrm {B} ^{\beta }\,\!}
backward reaction rate = k − S σ T τ {\displaystyle {\mbox{backward reaction rate}}=k_{-}\mathrm {S} ^{\sigma }\mathrm {T} ^{\tau }\,\!}
where A, B, S and T are active masses and k+ and k− are rate constants. Since at equilibrium forward and backward rates are equal:
k + { A } α { B } β = k − { S } σ { T } τ {\displaystyle k_{+}\left\{\mathrm {A} \right\}^{\alpha }\left\{\mathrm {B} \right\}^{\beta }=k_{-}\left\{\mathrm {S} \right\}^{\sigma }\left\{\mathrm {T} \right\}^{\tau }\,}
and the ratio of the rate constants is also a constant, now known as an equilibrium constant.
K c = k + k − = { S } σ { T } τ { A } α { B } β {\displaystyle K_{c}={\frac {k_{+}}{k_{-}}}={\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
By convention the products form the numerator. However, the law of mass action is valid only for concerted one-step reactions that proceed through a single transition state and is not valid in general because rate equations do not, in general, follow the stoichiometry of the reaction as Guldberg and Waage had proposed (see, for example, nucleophilic aliphatic substitution by SN1 or reaction of hydrogen and bromine to form hydrogen bromide). Equality of forward and backward reaction rates, however, is a necessary condition for chemical equilibrium, though it is not sufficient to explain why equilibrium occurs.
Despite the failure of this derivation, the equilibrium constant for a reaction is indeed a constant, independent of the activities of the various species involved, though it does depend on temperature as observed by the van 't Hoff equation. Adding a catalyst will affect both the forward reaction and the reverse reaction in the same way and will not have an effect on the equilibrium constant. The catalyst will speed up both reactions thereby increasing the speed at which equilibrium is reached.[2][4]
Although the macroscopic equilibrium concentrations are constant in time, reactions do occur at the molecular level. For example, in the case of acetic acid dissolved in water and forming acetate and hydronium ions,
CH3CO2H + H2O ⇌ CH
3CO−
2 + H3O+
a proton may hop from one molecule of acetic acid on to a water molecule and then on to an acetate anion to form another molecule of acetic acid and leaving the number of acetic acid molecules unchanged. This is an example of dynamic equilibrium. Equilibria, like the rest of thermodynamics, are statistical phenomena, averages of microscopic behavior.
Le Châtelier's principle (1884) gives an idea of the behavior of an equilibrium system when changes to its reaction conditions occur. If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to partially reverse the change. For example, adding more S from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the equilibrium point backward (though the equilibrium constant will stay the same).
If mineral acid is added to the acetic acid mixture, increasing the concentration of hydronium ion, the amount of dissociation must decrease as the reaction is driven to the left in accordance with this principle. This can also be deduced from the equilibrium constant expression for the reaction:
K = { CH 3 CO 2 − } { H 3 O + } { CH 3 CO 2 H } {\displaystyle K={\frac {\ce {\{CH3CO2^{-}\}\{H3O+\}}}{\ce {\{CH3CO2H\}}}}}
If {H3O+} increases {CH3CO2H} must increase and CH
3CO−
2 must decrease. The H2O is left out, as it is the solvent and its concentration remains high and nearly constant.
A quantitative version is given by the reaction quotient.
J. W. Gibbs suggested in 1873 that equilibrium is attained when the Gibbs free energy of the system is at its minimum value (assuming the reaction is carried out at constant temperature and pressure). What this means is that the derivative of the Gibbs energy with respect to reaction coordinate (a measure of the extent of reaction that has occurred, ranging from zero for all reactants to a maximum for all products) vanishes, signalling a stationary point. This derivative is called the reaction Gibbs energy (or energy change) and corresponds to the difference between the chemical potentials of reactants and products at the composition of the reaction mixture.[1] This criterion is both necessary and sufficient. If a mixture is not at equilibrium, the liberation of the excess Gibbs energy (or Helmholtz energy at constant volume reactions) is the "driving force" for the composition of the mixture to change until equilibrium is reached. The equilibrium constant can be related to the standard Gibbs free energy change for the reaction by the equation
Δ r G ⊖ = − R T ln  K e q {\displaystyle \Delta _{r}G^{\ominus }=-RT\ln K_{\mathrm {eq} }}
where R is the universal gas constant and T the temperature.
When the reactants are dissolved in a medium of high ionic strength the quotient of activity coefficients may be taken to be constant. In that case the concentration quotient, Kc,
K c = [ S ] σ [ T ] τ [ A ] α [ B ] β {\displaystyle K_{\mathrm {c} }={\frac {[\mathrm {S} ]^{\sigma }[\mathrm {T} ]^{\tau }}{[\mathrm {A} ]^{\alpha }[\mathrm {B} ]^{\beta }}}}
where [A] is the concentration of A, etc., is independent of the analytical concentration of the reactants. For this reason, equilibrium constants for solutions are usually determined in media of high ionic strength. Kc varies with ionic strength, temperature and pressure (or volume). Likewise Kp for gases depends on partial pressure. These constants are easier to measure and encountered in high-school chemistry courses.
Thermodynamics[edit]
At constant temperature and pressure, one must consider the Gibbs free energy, G, while at constant temperature and volume, one must consider the Helmholtz free energy: A, for the reaction; and at constant internal energy and volume, one must consider the entropy for the reaction: S.
The constant volume case is important in geochemistry and atmospheric chemistry where pressure variations are significant. Note that, if reactants and products were in standard state (completely pure), then there would be no reversibility and no equilibrium. Indeed, they would necessarily occupy disjoint volumes of space. The mixing of the products and reactants contributes a large entropy (known as entropy of mixing) to states containing equal mixture of products and reactants. The standard Gibbs energy change, together with the Gibbs energy of mixing, determine the equilibrium state.[5][6]
In this article only the constant pressure case is considered. The relation between the Gibbs free energy and the equilibrium constant can be found by considering chemical potentials.[1]
At constant temperature and pressure, the Gibbs free energy, G, for the reaction depends only on the extent of reaction: ξ (Greek letter xi), and can only decrease according to the second law of thermodynamics. It means that the derivative of G with ξ must be negative if the reaction happens; at the equilibrium the derivative being equal to zero.
( d G d ξ ) T , p = 0 {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=0~} : equilibrium
In order to meet the thermodynamic condition for equilibrium, the Gibbs energy must be stationary, meaning that the derivative of G with respect to the extent of reaction: ξ, must be zero. It can be shown that in this case, the sum of chemical potentials of the products is equal to the sum of those corresponding to the reactants. Therefore, the sum of the Gibbs energies of the reactants must be the equal to the sum of the Gibbs energies of the products.
α μ A + β μ B = σ μ S + τ μ T {\displaystyle \alpha \mu _{\mathrm {A} }+\beta \mu _{\mathrm {B} }=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }\,}
where μ is in this case a partial molar Gibbs energy, a chemical potential. The chemical potential of a reagent A is a function of the activity, {A} of that reagent.
μ A = μ A ⊖ + R T ln  { A } {\displaystyle \mu _{\mathrm {A} }=\mu _{A}^{\ominus }+RT\ln\{\mathrm {A} \}\,}
(where μo
A is the standard chemical potential).
The definition of the Gibbs energy equation interacts with the fundamental thermodynamic relation to produce
d G = V d p − S d T + ∑ i = 1 k μ i d N i {\displaystyle dG=Vdp-SdT+\sum _{i=1}^{k}\mu _{i}dN_{i}} .
Inserting dNi = νi dξ into the above equation gives a Stoichiometric coefficient ( ν i {\displaystyle \nu _{i}~} ) and a differential that denotes the reaction occurring once (dξ). At constant pressure and temperature the above equations can be written as
( d G d ξ ) T , p = ∑ i = 1 k μ i ν i = Δ r G T , p {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\sum _{i=1}^{k}\mu _{i}\nu _{i}=\Delta _{\mathrm {r} }G_{T,p}} which is the "Gibbs free energy change for the reaction .
This results in:
Δ r G T , p = σ μ S + τ μ T − α μ A − β μ B {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }-\alpha \mu _{\mathrm {A} }-\beta \mu _{\mathrm {B} }\,} .
By substituting the chemical potentials:
Δ r G T , p = ( σ μ S ⊖ + τ μ T ⊖ ) − ( α μ A ⊖ + β μ B ⊖ ) + ( σ R T ln  { S } + τ R T ln  { T } ) − ( α R T ln  { A } + β R T ln  { B } ) {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=(\sigma \mu _{\mathrm {S} }^{\ominus }+\tau \mu _{\mathrm {T} }^{\ominus })-(\alpha \mu _{\mathrm {A} }^{\ominus }+\beta \mu _{\mathrm {B} }^{\ominus })+(\sigma RT\ln\{\mathrm {S} \}+\tau RT\ln\{\mathrm {T} \})-(\alpha RT\ln\{\mathrm {A} \}+\beta RT\ln\{\mathrm {B} \})} ,
the relationship becomes:
Δ r G T , p = ∑ i = 1 k μ i ⊖ ν i + R T ln  { S } σ { T } τ { A } α { B } β {\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}+RT\ln {\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
∑ i = 1 k μ i ⊖ ν i = Δ r G ⊖ {\displaystyle \sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}=\Delta _{\mathrm {r} }G^{\ominus }} :
which is the standard Gibbs energy change for the reaction that can be calculated using thermodynamical tables. The reaction quotient is defined as:
Q r = { S } σ { T } τ { A } α { B } β {\displaystyle Q_{\mathrm {r} }={\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}
Therefore,
( d G d ξ ) T , p = Δ r G T , p = Δ r G ⊖ + R T ln  Q r {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }}
At equilibrium:
( d G d ξ ) T , p = Δ r G T , p = 0 {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=0}
leading to:
0 = Δ r G ⊖ + R T ln  K e q {\displaystyle 0=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln K_{\mathrm {eq} }}
and
Δ r G ⊖ = − R T ln  K e q {\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{\mathrm {eq} }}
Obtaining the value of the standard Gibbs energy change, allows the calculation of the equilibrium constant.
Addition of reactants or products[edit]
For a reactional system at equilibrium: Qr = Keq; ξ = ξeq.
If are modified activities of constituents, the value of the reaction quotient changes and becomes different from the equilibrium constant: Qr ≠ Keq
( d G d ξ ) T , p = Δ r G ⊖ + R T ln  Q r {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }~}
and
Δ r G ⊖ = − R T ln  K e q {\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{eq}~}
then
( d G d ξ ) T , p = R T ln  ( Q r K e q ) {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=RT\ln \left({\frac {Q_{\mathrm {r} }}{K_{\mathrm {eq} }}}\right)~}
If activity of a reagent i increases

Q r = ∏ ( a j ) ν j ∏ ( a i ) ν i {\displaystyle Q_{\mathrm {r} }={\frac {\prod (a_{j})^{\nu _{j}}}{\prod (a_{i})^{\nu _{i}}}}~} , the reaction quotient decreases.
then
Q r < K e q {\displaystyle Q_{\mathrm {r} }<K_{\mathrm {eq} }~} and ( d G d ξ ) T , p < 0 {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}<0~}
The reaction will shift to the right (i.e. in the forward direction, and thus more products will form).
If activity of a product j increases
then
Q r > K e q {\displaystyle Q_{\mathrm {r} }>K_{\mathrm {eq} }~} and ( d G d ξ ) T , p > 0 {\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}>0~}
The reaction will shift to the left (i.e. in the reverse direction, and thus less products will form).
Note that activities and equilibrium constants are dimensionless numbers.
Treatment of activity[edit]
The expression for the equilibrium constant can be rewritten as the product of a concentration quotient, Kc and an activity coefficient quotient, Γ.
K = [ S ] σ [ T ] τ . . . [ A ] α [ B ] β . . . × γ S σ γ T τ . . . γ A α γ B β . . . = K c Γ {\displaystyle K={\frac {[\mathrm {S} ]^{\sigma }[\mathrm {T} ]^{\tau }...}{[\mathrm {A} ]^{\alpha }[\mathrm {B} ]^{\beta }...}}\times {\frac {{\gamma _{\mathrm {S} }}^{\sigma }{\gamma _{\mathrm {T} }}^{\tau }...}{{\gamma _{\mathrm {A} }}^{\alpha }{\gamma _{\mathrm {B} }}^{\beta }...}}=K_{\mathrm {c} }\Gamma }
[A] is the concentration of reagent A, etc. It is possible in principle to obtain values of the activity coefficients, γ. For solutions, equations such as the Debye–Hückel equation or extensions such as Davies equation[7] Specific ion interaction theory or Pitzer equations[8] may be used.Software (below). However this is not always possible. It is common practice to assume that Γ is a constant, and to use the concentration quotient in place of the thermodynamic equilibrium constant. It is also general practice to use the term equilibrium constant instead of the more accurate concentration quotient. This practice will be followed here.
For reactions in the gas phase partial pressure is used in place of concentration and fugacity coefficient in place of activity coefficient. In the real world, for example, when making ammonia in industry, fugacity coefficients must be taken into account. Fugacity, f, is the product of partial pressure and fugacity coefficient. The chemical potential of a species in the gas phase is given by
μ = μ ⊖ + R T ln  ( f b a r ) = μ ⊖ + R T ln  ( p b a r ) + R T ln  γ {\displaystyle \mu =\mu ^{\ominus }+RT\ln \left({\frac {f}{\mathrm {bar} }}\right)=\mu ^{\ominus }+RT\ln \left({\frac {p}{\mathrm {bar} }}\right)+RT\ln \gamma }
so the general expression defining an equilibrium constant is valid for both solution and gas phases.
Concentration quotients[edit]
In aqueous solution, equilibrium constants are usually determined in the presence of an "inert" electrolyte such as sodium nitrate NaNO3 or potassium perchlorate KClO4. The ionic strength of a solution is given by
I = 1 2 ∑ i = 1 N c i z i 2 {\displaystyle I={\frac {1}{2}}\sum _{i=1}^{N}c_{i}z_{i}^{2}}
where ci and zi stand for the concentration and ionic charge of ion type i, and the sum is taken over all the N types of charged species in solution. When the concentration of dissolved salt is much higher than the analytical concentrations of the reagents, the ions originating from the dissolved salt determine the ionic strength, and the ionic strength is effectively constant. Since activity coefficients depend on ionic strength the activity coefficients of the species are effectively independent of concentration. Thus, the assumption that Γ is constant is justified. The concentration quotient is a simple multiple of the equilibrium constant.[9]
K c = K Γ {\displaystyle K_{\mathrm {c} }={\frac {K}{\Gamma }}}
However, Kc will vary with ionic strength. If it is measured at a series of different ionic strengths the value can be extrapolated to zero ionic strength.[8] The concentration quotient obtained in this manner is known, paradoxically, as a thermodynamic equilibrium constant.
To use a published value of an equilibrium constant in conditions of ionic strength different from the conditions used in its determination, the value should be adjustedSoftware (below).
Metastable mixtures[edit]
A mixture may appear to have no tendency to change, though it is not at equilibrium. For example, a mixture of SO2 and O2 is metastable as there is a kinetic barrier to formation of the product, SO3.
2 SO2 + O2 ⇌ 2 SO3
The barrier can be overcome when a catalyst is also present in the mixture as in the contact process, but the catalyst does not affect the equilibrium concentrations.
Likewise, the formation of bicarbonate from carbon dioxide and water is very slow under normal conditions
CO2 + 2 H2O ⇌ HCO−
3 + H3O+
but almost instantaneous in the presence of the catalytic enzyme carbonic anhydrase.
Pure substances[edit]
When pure substances (liquids or solids) are involved in equilibria their activities do not appear in the equilibrium constant[10] because their numerical values are considered one.
Applying the general formula for an equilibrium constant to the specific case of a dilute solution of acetic acid in water one obtains
CH3CO2H + H2O ⇌ CH3CO2− + H3O+
K c = [ C H 3 C O 2 − ] [ H 3 O + ] [ C H 3 C O 2 H ] [ H 2 O ] {\displaystyle K_{\mathrm {c} }={\frac {\mathrm {[{CH_{3}CO_{2}}^{-}][{H_{3}O}^{+}]} }{\mathrm {[{CH_{3}CO_{2}H}][{H_{2}O}]} }}}
For all but very concentrated solutions, the water can be considered a "pure" liquid, and therefore it has an activity of one. The equilibrium constant expression is therefore usually written as
K = [ C H 3 C O 2 − ] [ H 3 O + ] [ C H 3 C O 2 H ] = K c {\displaystyle K={\frac {\mathrm {[{CH_{3}CO_{2}}^{-}][{H_{3}O}^{+}]} }{\mathrm {[{CH_{3}CO_{2}H}]} }}=K_{\mathrm {c} }} .
A particular case is the self-ionization of water itself
2 H2O ⇌ H3O+ + OH−
Because water is the solvent, and has an activity of one, the self-ionization constant of water is defined as
K w = [ H + ] [ O H − ] {\displaystyle K_{\mathrm {w} }=\mathrm {[H^{+}][OH^{-}]} }
It is perfectly legitimate to write [H+] for the hydronium ion concentration, since the state of solvation of the proton is constant (in dilute solutions) and so does not affect the equilibrium concentrations. Kw varies with variation in ionic strength and/or temperature.
The concentrations of H+ and OH− are not independent quantities. Most commonly [OH−] is replaced by Kw[H+]−1 in equilibrium constant expressions which would otherwise include hydroxide ion.
Solids also do not appear in the equilibrium constant expression, if they are considered to be pure and thus their activities taken to be one. An example is the Boudouard reaction:[10]
2 CO ⇌ CO2 + C
for which the equation (without solid carbon) is written as:
K c = [ C O 2 ] [ C O ] 2 {\displaystyle K_{\mathrm {c} }={\frac {\mathrm {[CO_{2}]} }{\mathrm {[CO]^{2}} }}}
Multiple equilibria[edit]
Consider the case of a dibasic acid H2A. When dissolved in water, the mixture will contain H2A, HA− and A2−. This equilibrium can be split into two steps in each of which one proton is liberated.
H 2 A ↽ − − ⇀ HA − + H + : K 1 = [ HA − ] [ H + ] [ H 2 A ] HA − ↽ − − ⇀ A 2 − + H + : K 2 = [ A 2 − ] [ H + ] [ HA − ] {\displaystyle {\begin{array}{rl}{\ce {H2A<=>{HA^{-}}+{H+}}}:&K_{1}={\frac {\ce {[HA-][H+]}}{\ce {[H2A]}}}\\{\ce {HA-<=>{A^{2-}}+{H+}}}:&K_{2}={\frac {\ce {[A^{2-}][H+]}}{\ce {[HA-]}}}\end{array}}}
K1 and K2 are examples of stepwise equilibrium constants. The overall equilibrium constant, βD, is product of the stepwise constants.
H 2 A ↽ − − ⇀ A 2 − + 2 H + {\displaystyle {\ce {{H2A}<=>{A^{2-}}+{2H+}}}} : β D = [ A 2 − ] [ H + ] 2 [ H 2 A ] = K 1 K 2 {\displaystyle \beta _{\ce {D}}={\frac {\ce {[A^{2-}][H^{+}]^{2}}}{\ce {[H_{2}A]}}}=K_{1}K_{2}}
Note that these constants are dissociation constants because the products on the right hand side of the equilibrium expression are dissociation products. In many systems, it is preferable to use association constants.
A 2 − + H + ↽ − − ⇀ HA − : β 1 = [ HA − ] [ A 2 − ] [ H + ] A 2 − + 2 H + ↽ − − ⇀ H 2 A : β 2 = [ H 2 A ] [ A 2 − ] [ H + ] 2 {\displaystyle {\begin{array}{ll}{\ce {{A^{2-}}+{H+}<=>HA-}}:&\beta _{1}={\frac {\ce {[HA^{-}]}}{\ce {[A^{2-}][H+]}}}\\{\ce {{A^{2-}}+{2H+}<=>H2A}}:&\beta _{2}={\frac {\ce {[H2A]}}{\ce {[A^{2-}][H+]^{2}}}}\end{array}}}
β1 and β2 are examples of association constants. Clearly β1 = 1/K2 and β2 = 1/βD; log β1 = pK2 and log β2 = pK2 + pK1[11] For multiple equilibrium systems, also see: theory of Response reactions.
Effect of temperature[edit]
The effect of changing temperature on an equilibrium constant is given by the van 't Hoff equation
d ln  K d T = Δ H m ⊖ R T 2 {\displaystyle {\frac {d\ln K}{dT}}={\frac {\Delta H_{\mathrm {m} }^{\ominus }}{RT^{2}}}}
Thus, for exothermic reactions (ΔH is negative), K decreases with an increase in temperature, but, for endothermic reactions, (ΔH is positive) K increases with an increase temperature. An alternative formulation is
d ln  K d ( T − 1 ) = − Δ H m ⊖ R {\displaystyle {\frac {d\ln K}{d(T^{-1})}}=-{\frac {\Delta H_{\mathrm {m} }^{\ominus }}{R}}}
At first sight this appears to offer a means of obtaining the standard molar enthalpy of the reaction by studying the variation of K with temperature. In practice, however, the method is unreliable because error propagation almost always gives very large errors on the values calculated in this way.
Effect of electric and magnetic fields[edit]
The effect of electric field on equilibrium has been studied by Manfred Eigen[citation needed] among others.
Types of equilibrium[edit]
Haber–Bosch process
# N2 (g) ⇌ N2 (adsorbed)
N2 (adsorbed) ⇌ 2 N (adsorbed)
H2 (g) ⇌ H2 (adsorbed)
H2 (adsorbed) ⇌ 2 H (adsorbed)
N (adsorbed) + 3 H(adsorbed) ⇌ NH3 (adsorbed)
NH3 (adsorbed) ⇌ NH3 (g)
In the gas phase: rocket engines[12]
The industrial synthesis such as ammonia in the Haber–Bosch process (depicted right) takes place through a succession of equilibrium steps including adsorption processes
Atmospheric chemistry
Seawater and other natural waters: chemical oceanography
Distribution between two phases
log D distribution coefficient: important for pharmaceuticals where lipophilicity is a significant property of a drug
Liquid–liquid extraction, Ion exchange, Chromatography
Solubility product
Uptake and release of oxygen by haemoglobin in blood
Acid–base equilibria: acid dissociation constant, hydrolysis, buffer solutions, indicators, acid–base homeostasis
Metal–ligand complexation: sequestering agents, chelation therapy, MRI contrast reagents, Schlenk equilibrium
Adduct formation: host–guest chemistry, supramolecular chemistry, molecular recognition, dinitrogen tetroxide
In certain oscillating reactions, the approach to equilibrium is not asymptotically but in the form of a damped oscillation .[10]
The related Nernst equation in electrochemistry gives the difference in electrode potential as a function of redox concentrations.
When molecules on each side of the equilibrium are able to further react irreversibly in secondary reactions, the final product ratio is determined according to the Curtin–Hammett principle.
In these applications, terms such as stability constant, formation constant, binding constant, affinity constant, association/dissociation constant are used. In biochemistry, it is common to give units for binding constants, which serve to define the concentration units used when the constant’s value was determined.
Composition of a mixture[edit]
When the only equilibrium is that of the formation of a 1:1 adduct as the composition of a mixture, there are any number of ways that the composition of a mixture can be calculated. For example, see ICE table for a traditional method of calculating the pH of a solution of a weak acid.
There are three approaches to the general calculation of the composition of a mixture at equilibrium.
The most basic approach is to manipulate the various equilibrium constants until the desired concentrations are expressed in terms of measured equilibrium constants (equivalent to measuring chemical potentials) and initial conditions.
Minimize the Gibbs energy of the system.[13][14]
Satisfy the equation of mass balance. The equations of mass balance are simply statements that demonstrate that the total concentration of each reactant must be constant by the law of conservation of mass.
Mass-balance equations[edit]
In general, the calculations are rather complicated or complex. For instance, in the case of a dibasic acid, H2A dissolved in water the two reactants can be specified as the conjugate base, A2−, and the proton, H+. The following equations of mass-balance could apply equally well to a base such as 1,2-diaminoethane, in which case the base itself is designated as the reactant A:
T A = [ A ] + [ H A ] + [ H 2 A ] {\displaystyle T_{\mathrm {A} }=\mathrm {[A]+[HA]+[H_{2}A]} \,}
T H = [ H ] + [ H A ] + 2 [ H 2 A ] − [ O H ] {\displaystyle T_{\mathrm {H} }=\mathrm {[H]+[HA]+2[H_{2}A]-[OH]} \,}
With TA the total concentration of species A. Note that it is customary to omit the ionic charges when writing and using these equations.
When the equilibrium constants are known and the total concentrations are specified there are two equations in two unknown "free concentrations" [A] and [H]. This follows from the fact that [HA] = β1[A][H], [H2A] = β2[A][H]2 and [OH] = Kw[H]−1
T A = [ A ] + β 1 [ A ] [ H ] + β 2 [ A ] [ H ] 2 {\displaystyle T_{\mathrm {A} }=\mathrm {[A]} +\beta _{1}\mathrm {[A][H]} +\beta _{2}\mathrm {[A][H]} ^{2}\,}
T H = [ H ] + β 1 [ A ] [ H ] + 2 β 2 [ A ] [ H ] 2 − K w [ H ] − 1 {\displaystyle T_{\mathrm {H} }=\mathrm {[H]} +\beta _{1}\mathrm {[A][H]} +2\beta _{2}\mathrm {[A][H]} ^{2}-K_{w}[\mathrm {H} ]^{-1}\,}
so the concentrations of the "complexes" are calculated from the free concentrations and the equilibrium constants. General expressions applicable to all systems with two reagents, A and B would be
T A = [ A ] + ∑ i p i β i [ A ] p i [ B ] q i {\displaystyle T_{\mathrm {A} }=[\mathrm {A} ]+\sum _{i}p_{i}\beta _{i}[\mathrm {A} ]^{p_{i}}[\mathrm {B} ]^{q_{i}}}
T B = [ B ] + ∑ i q i β i [ A ] p i [ B ] q i {\displaystyle T_{\mathrm {B} }=[\mathrm {B} ]+\sum _{i}q_{i}\beta _{i}[\mathrm {A} ]^{p_{i}}[\mathrm {B} ]^{q_{i}}}
It is easy to see how this can be extended to three or more reagents.
Polybasic acids[edit]
Species concentrations during hydrolysis of the aluminium.
The composition of solutions containing reactants A and H is easy to calculate as a function of p[H]. When [H] is known, the free concentration [A] is calculated from the mass-balance equation in A.
The diagram alongside, shows an example of the hydrolysis of the aluminium Lewis acid Al3+(aq)[15] shows the species concentrations for a 5 × 10−6 M solution of an aluminium salt as a function of pH. Each concentration is shown as a percentage of the total aluminium.
Solution and precipitation[edit]
The diagram above illustrates the point that a precipitate that is not one of the main species in the solution equilibrium may be formed. At pH just below 5.5 the main species present in a 5 μM solution of Al3+ are aluminium hydroxides Al(OH)2+, AlOH+
2 and Al
13(OH)7+
32, but on raising the pH Al(OH)3 precipitates from the solution. This occurs because Al(OH)3 has a very large lattice energy. As the pH rises more and more Al(OH)3 comes out of solution. This is an example of Le Châtelier's principle in action: Increasing the concentration of the hydroxide ion causes more aluminium hydroxide to precipitate, which removes hydroxide from the solution. When the hydroxide concentration becomes sufficiently high the soluble aluminate, Al(OH)−
4, is formed.
Another common instance where precipitation occurs is when a metal cation interacts with an anionic ligand to form an electrically neutral complex. If the complex is hydrophobic, it will precipitate out of water. This occurs with the nickel ion Ni2+ and dimethylglyoxime, (dmgH2): in this case the lattice energy of the solid is not particularly large, but it greatly exceeds the energy of solvation of the molecule Ni(dmgH)2.
Minimization of Gibbs energy[edit]
At equilibrium, at a specified temperature and pressure, the Gibbs energy G is at a minimum:
d G = ∑ j = 1 m μ j d N j = 0 {\displaystyle dG=\sum _{j=1}^{m}\mu _{j}\,dN_{j}=0}
For a closed system, no particles may enter or leave, although they may combine in various ways. The total number of atoms of each element will remain constant. This means that the minimization above must be subjected to the constraints:
∑ j = 1 m a i j N j = b i 0 {\displaystyle \sum _{j=1}^{m}a_{ij}N_{j}=b_{i}^{0}}
where aij is the number of atoms of element i in molecule j and b0
i is the total number of atoms of element i, which is a constant, since the system is closed. If there are a total of k types of atoms in the system, then there will be k such equations. If ions are involved, an additional row is added to the aij matrix specifying the respective charge on each molecule which will sum to zero.
This is a standard problem in optimisation, known as constrained minimisation. The most common method of solving it is using the method of Lagrange multipliers, also known as undetermined multipliers (though other methods may be used).
Define:
G = G + ∑ i = 1 k λ i ( ∑ j = 1 m a i j N j − b i 0 ) = 0 {\displaystyle {\mathcal {G}}=G+\sum _{i=1}^{k}\lambda _{i}\left(\sum _{j=1}^{m}a_{ij}N_{j}-b_{i}^{0}\right)=0}
where the λi are the Lagrange multipliers, one for each element. This allows each of the Nj and λj to be treated independently, and it can be shown using the tools of multivariate calculus that the equilibrium condition is given by
0 = ∂ G ∂ N j = μ j + ∑ i = 1 k λ i a i j {\displaystyle 0={\frac {\partial {\mathcal {G}}}{\partial N_{j}}}=\mu _{j}+\sum _{i=1}^{k}\lambda _{i}a_{ij}}
0 = ∂ G ∂ λ i = ∑ j = 1 m a i j N j − b i 0 {\displaystyle 0={\frac {\partial {\mathcal {G}}}{\partial \lambda _{i}}}=\sum _{j=1}^{m}a_{ij}N_{j}-b_{i}^{0}}
(For proof see Lagrange multipliers.) This is a set of (m + k) equations in (m + k) unknowns (the Nj and the λi) and may, therefore, be solved for the equilibrium concentrations Nj as long as the chemical potentials are known as functions of the concentrations at the given temperature and pressure. (See Thermodynamic databases for pure substances.) Note that the second equation is just the initial constraints for minimization.
This method of calculating equilibrium chemical concentrations is useful for systems with a large number of different molecules. The use of k atomic element conservation equations for the mass constraint is straightforward, and replaces the use of the stoichiometric coefficient equations.[12]. The results are consistent with those specified by chemical equations. For example, if equilibrium is specified by a single chemical equation: [16],
∑ j = 0 m ν j R j = 0 {\displaystyle \sum _{j=0}^{m}\nu _{j}R_{j}=0}
where νj is the stochiometric coefficient for the j th molecule (negative for reactants, positive for products) and Rj is the symbol for the j th molecule, a properly balanced equation will obey:
∑ j = 1 m a i j ν j = 0 {\displaystyle \sum _{j=1}^{m}a_{ij}\nu _{j}=0}
Multiplying the first equilibrium condition by νj yields
0 = ∑ j = 1 m ν j μ j + ∑ j = 1 m ∑ i = 1 k ν j λ i a i j = ∑ j = 1 m ν j μ j {\displaystyle 0=\sum _{j=1}^{m}\nu _{j}\mu _{j}+\sum _{j=1}^{m}\sum _{i=1}^{k}\nu _{j}\lambda _{i}a_{ij}=\sum _{j=1}^{m}\nu _{j}\mu _{j}}
As above, defining ΔG
Δ G = ∑ j = 1 m ν j μ j = ∑ j = 1 m ν j ( μ j ⊖ + R T ln  ( { R j } ) ) = Δ G ⊖ + R T ln  ( ∏ j = 1 m { R j } ν j ) = Δ G ⊖ + R T ln  ( Q r ) {\displaystyle \Delta G=\sum _{j=1}^{m}\nu _{j}\mu _{j}=\sum _{j=1}^{m}\nu _{j}(\mu _{j}^{\ominus }+RT\ln(\{R_{j}\}))=\Delta G^{\ominus }+RT\ln \left(\prod _{j=1}^{m}\{R_{j}\}^{\nu _{j}}\right)=\Delta G^{\ominus }+RT\ln(Q_{r})}
which will be zero at equilibrium.
See also[edit]
Acidosis
Alkalosis
Arterial blood gas
Benesi–Hildebrand method
Determination of equilibrium constants
Equilibrium constant
Henderson–Hasselbalch equation
Michaelis–Menten kinetics
pCO2
pH
pKa
Redox equilibria
Steady state (chemistry)
Thermodynamic databases for pure substances
References[edit]
^ Jump up to: a b c Atkins, Peter; De Paula, Julio (2006). Atkins' Physical Chemistry (8th ed.). W. H. Freeman. pp. 200–202. ISBN 0-7167-8759-8.
^ Jump up to: a b Atkins, Peter W.; Jones, Loretta. Chemical Principles: The Quest for Insight (2nd ed.). ISBN 0-7167-9903-0.
Jump up ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "chemical equilibrium".
Jump up ^ Brady, James E. Chemistry: Matter and Its Changes (4th ed.). Fred Senese. ISBN 0-471-21517-1.
Jump up ^ Schultz, Mary Jane (1999). "Why Equilibrium? Understanding Entropy of Mixing". Journal of Chemical Education. 76 (10): 1391. Bibcode:1999JChEd..76.1391S. doi:10.1021/ed076p1391.
Jump up ^ Clugston, Michael J. (1990). "A mathematical verification of the second law of thermodynamics from the entropy of mixing". Journal of Chemical Education. 67 (3): 203. Bibcode:1990JChEd..67Q.203C. doi:10.1021/ed067p203.
Jump up ^ Davies, C. W. (1962). Ion Association. Butterworths.
^ Jump up to: a b Grenthe, I.; Wanner, H. "Guidelines for the extrapolation to zero ionic strength" (PDF).
Jump up ^ Rossotti, F. J. C.; Rossotti, H. (1961). The Determination of Stability Constants. McGraw-Hill.
^ Jump up to: a b c Concise Encyclopedia Chemistry. 1994. ISBN 0-89925-457-8.
Jump up ^ Beck, M. T.; Nagypál, I. (1990). Chemistry of Complex Equilibria (2nd ed.). Budapest: Akadémiai Kaidó.
^ Jump up to: a b "Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications" (PDF). NASA Reference publication 1311. NASA. 1994.
Jump up ^ Smith, W. R.; Missen, R. W. (1991). Chemical Reaction Equilibrium Analysis: Theory and Algorithms (Reprinted ed.). Malabar, FL: Krieger Publishing.
Jump up ^ "Mathtrek Systems".
Jump up ^ The diagram was created with the program HySS
Jump up ^ C. Kittel, H. Kroemer (1980). "9". Thermal Physics (2 ed.). W. H. Freeman Company. ISBN 0-7167-1088-9.
Further reading[edit]
Library resources about
Chemical equilibrium
Resources in your library
Van Zeggeren, F.; Storey, S. H. (1970). The Computation of Chemical Equilibria. Cambridge University Press. Mainly concerned with gas-phase equilibria.
Leggett, D. J., ed. (1985). Computational Methods for the Determination of Formation Constants. Plenum Press.
Martell, A. E.; Motekaitis, R. J. (1992). The Determination and Use of Stability Constants. Wiley-VCH.
Gans, P. (2004). Stability Constants: Determination and Uses (CD-ROM)|format= requires |url= (help). Leeds: Protonic Software.
[hide]
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Chemical equilibria
Concepts
Acid dissociation constant
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Dynamic equilibrium
Equilibrium chemistry
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Henry's law
Liquid–liquid extraction
Macrocycle effect
Phase diagram
Predominance diagram
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The West Wing (season 7)
From Wikipedia, the free encyclopedia
Jump to: navigation, search
"Mr. Frost" redirects here. For the film, see Mister Frost.
The West Wing (season 7)
DVD box cover. Cast from top to bottom and left to right: Jed, Leo, Charlie, Annabeth, Abbey, Josh, Matt, Donna, Will, Kate, Sen. Vinick, Toby and C. J.
Country of origin
United States
No. of episodes
22
Release
Original network
NBC
Original release
September 25, 2005 (2005-09-25) – May 14, 2006 (2006-05-14)
Season chronology
← Previous
Season 6
List of The West Wing episodes
The seventh and final season of the American political drama television series The West Wing aired in the United States on NBC from September 25, 2005 to May 14, 2006 and consisted of 22 episodes. The series changed time slots from Wednesdays at 8:00 pm to Sundays at 8:00 pm, and the series struggled in its new time slot against ABC's Extreme Makeover: Home Edition and CBS's Cold Case.[1][2]
The season was released on DVD as a six-disc boxed set under the title The West Wing: The Complete Seventh Season by Warner Home Video being released first in Region 2 on September 11, 2006 and then in Region 1 on November 7, 2006. All episodes from the season are available to purchase and download to registered users of iTunes Stores in certain countries[3][4][5][6] and in the US through Amazon Video on Demand.[7] In Canada, the seventh season was due to be simulcast on CTV;[8] however, CTV dropped the series.[9] In the United Kingdom the season premiered on March 10, 2006 on More4.[10]
Contents
[hide]
1 Crew
2 Cast
2.1 Main cast
2.2 Recurring cast
3 Reception
4 Plot
5 Episodes
6 DVD release
7 References
Crew[edit]
The season was produced by John Wells Productions in association with Warner Bros. Television.[11] The executive producers were the production company's namesake and founder John Wells, Christopher Misiano, Alex Graves, political analyst Lawrence O'Donnell and Peter Noah;[12][13] Noah was previously a supervising producer in the sixth season,[14] and O'Donnell, who is a former Democratic chief of staff on the Senate Committee on Finance, provided insight into political life.[15] The West Wing was created by Aaron Sorkin. For the seventh season, regular staff writers were Wells, O'Donnell, Noah, Eli Attie, Debora Cahn, Josh Singer and Lauren Schmidt, while cast member Bradley Whitford wrote his second episode of the series. The regular directors were Misiano, Graves, Andrew Bernstein and Lesli Linka Glatter.
Cast[edit]
The seventh season had star billing for thirteen major roles, with twelve of these filled by returning main cast members from the sixth season. Martin Sheen receives the "and" credit for his role as President Josiah Bartlet, while Jimmy Smits receives a "with" credit. The rest of the ensemble, including Kristin Chenoweth, are credited alphabetically.
This season saw every cast member appear in a diminished role, with the exception of Jimmy Smits who appeared in all 22 episodes. The other most appearing cast members were Janney (17 episodes) and Whitford (20 episodes). Alda, McCormack and Sheen appeared in 12 episodes each, Malina and Moloney in 13, Chenoweth in 10, Schiff in 11, Spencer, who died of a heart-attack in December 2005, appeared in 7, Hill appeared in 5 and Channing appeared in 4 episodes.[16]
Main cast[edit]
Alan Alda as Arnold Vinick
Stockard Channing as Abbey Bartlet
Kristin Chenoweth as Annabeth Schott
Dulé Hill as Charlie Young
Allison Janney as C. J. Cregg
Joshua Malina as Will Bailey
Mary McCormack as Kate Harper
Janel Moloney as Donna Moss
Richard Schiff as Toby Ziegler
John Spencer as Leo McGarry
Bradley Whitford as Josh Lyman
Jimmy Smits as Matt Santos
Martin Sheen as Josiah Bartlet
Recurring cast[edit]
Janeane Garofalo initially contracted to join the show in a three-episode arc as Louise Thornton, a media strategist hired by Matt Santos;[11][17] however, she became a regular recurring cast member.[18] Other characters that returned in recurring roles were Ron Silver as Bruno Gianelli, campaign manager for Sen. Vinick.[19][20] Other guest stars returning to recurring roles include Teri Polo as Helen Santos,[21] Patricia Richardson as Sen. Vinick's chief of staff Sheila Brooks,[22] Lily Tomlin as Presidential secretary Debbie Fiderer,[23] Karis Campbell as Santos' secretary Ronna,[24] Allison Smith as Leo's daughter, Mallory,[21] Kathleen York as Andrea Wyatt, Melissa Fitzgerald as Carol, Renée Estevez as Nancy,[25] and Peter James Smith and William Duffy as Ed and Larry and all White House staff. Oliver Platt returned in his recurring role as Oliver Babish,[26] having previously appeared back in 2001.[27] In March 2006, it was announced that a number of former cast members would be reprising the roles of previous characters. These included Rob Lowe as political official Sam Seaborn, Mary-Louise Parker as women's right advocate Amy Gardner, Anna Deavere Smith as National Security Advisor Nancy McNally, Emily Procter as Republican attorney Ainsley Hayes, Marlee Matlin as pollster Joey Lucas, Gary Cole as Vice President Bob Russell, Tim Matheson as former Vice President John Hoynes, Timothy Busfield as journalist Danny Concannon, and Annabeth Gish as Liz Bartlet Westin, eldest daughter of President Bartlet.[28]
Reception[edit]
The season was nominated for six Primetime Emmy Awards in 2006, winning two. The show was nominated for Outstanding Drama Series for the seventh year running. Alan Alda, as Senator Vinick, won in the award for Outstanding Supporting Actor in a Drama Series. Martin Sheen, as President Bartlet, was nominated for Outstanding Lead Actor in a Drama Series and Allison Janney, as C.J., was nominated in the Outstanding Lead Actress in a Drama Series category.[29] Mimi Leder was nominated for Outstanding Directing in a Drama Series for the episode "Election Day" and Audio mixer Edward J. Greene and EFX mixer Andrew Strauber won the award for Outstanding Multi-camera Sound Mixing for a Series or Special for "The Debate".[29][30] Eli Attie and John Wells received a Writers Guild of America Award nomination in the Episodic Drama category for "Election Day Part II".[31] Attie and Wells were nominated for the $15,000 Humanitas Prize in the 60-minute category for the same episode, which was also the submission that won the show an AFI Award that year.[32] The show won the Hallmark Hall of Fame Heritage Award at the Television Critics Association Awards[33] and Alda received a nomination for Individual Achievement in Drama.[34] Alda was also nominated for a Screen Actors Guild Award for Outstanding Performance by a Male Actor in a Drama Series,[35] The Guild nominated the whole ensemble for the Outstanding Performance in a Drama Series award.[35] Supervising sound editors Walter Newman and Thomas A. Harris, supervising dialogue editor Catherine Flynn, and dialogue and ADR editors Virginia Cook and Steffan Falesitch were nominated for a Golden Reel Award in the Best Sound Editing in Television: Short Form – Dialogue and Automated Dialogue Replacement with the episode "The Ticket".[36] At the ALMA Awards, a Latino awards ceremony, the show won Best TV Series and Jimmy Smits (as Matt Santos) as Best Actor in a TV Series.[37] At another Latino ceremony, the Imagen Awards, the show won Best Primetime Series[38] with Smits nominated for Best Actor in Television.[39]
PopMatters said the final season "recovered its sense of humor".[40] David Hinckley of the Daily News praised the character of Bruno Gianelli as a "brilliant (...) shark of a campaign manager" and commended the series for never rushing the romantic character arc of Josh and Donna.[20] As the fictional Election Day approached, Aleksandra Stankovic of The Harvard Crimson said that "a more complex, more mature West Wing, but one with no clear narrative resolution in sight" was evolving and that she welcomed the "restoration of narrative tension".[41] Bill Brioux from the Toronto Sun agreed, stating that the seventh series was "enjoying a creative renaissance" and had been "enlivened by the election storyline".[42] Mike Duffy of the Detroit Free Press said that The West Wing had "rediscovered the vivid political zing in its farewell season";[43] however, Jeffrey Robinson from DVD Talk commented that the shift away from daily issues and operations in the White House meant "season seven did not feel like The West Wing".[44]
One episode, "The Debate", was aired as live television. Rob Owen of the Pittsburgh Post-Gazette wrote that "real-life issues were brought to a prime-time national audience," but the first half was "boring back-and-forth [with] not much revealed about the characters" and had it not been live it could have been "stronger, better produced and with a less dull first half."[45] Janet Daley of The Daily Telegraph called the episode "riveting, and astonishingly brave" with "dazzling exposition of the central political argument of our time: whether free markets deliver better life chances, and a more virtuous society, than economies controlled by government."[46]
Despite slipping ratings and a fear the show would be axed, NBC announced in March 2005 that The West Wing would be returning for a seventh season.[47] The change from Wednesdays to Sundays cost the show approximately 30 percent of its audience;[42] the first two episodes of the season garnered the series' lowest ever ratings and Deseret News said the move of time slot sealed the show's fate.[48][49] In January 2006, it was announced that the seventh would be the final season. Kevin Reilly, entertainment president for NBC, said that after poor viewing figures for the "last couple of seasons [they reached] a point where you look at the ratings and you just say, 'it's time.'"[50]
Plot[edit]
The seventh and final season mainly follows Santos and Vinick on the campaign trail, while also addressing the aftermath of the shuttle leak investigation. The Bartlet administration's last year in office is featured, but not prominently. Toby admits to leaking the story about a military spacecraft and President Bartlet is forced to fire him. Later, he refuses to name his recently deceased brother as the source of the classified information, despite being urged to by his ex-wife, his lawyer and a federal prosecutor, as he feels it would be wrong to dishonor his memory. Also, C.J.'s tenure as Chief of Staff becomes more stressful as she deals with the war between Russia and China over Kazakhstan. The presidential race tightens up when Vinick's lead is dampened by an accident at a nuclear plant he had championed. Leo suffers a heart attack, and dies on the night of the election — reflecting the death of portrayer John Spencer — which Santos eventually wins. The last few episodes show the final days of the Bartlet administration and Santos' transition; in the series finale, Santos is sworn in as President.
Episodes[edit]
No.
overall
No. in
season
Title
Directed by
Written by
Original air date
Prod.
code
U.S. viewers
(millions)
133
1 "The Ticket" Christopher Misiano Debora Cahn September 25, 2005 (2005-09-25) 2T6201 8.90[51]
The season opener starts with a scene from three years in the future; a reunion of main characters at the opening of Bartlet's Presidential library and Josh introducing the President, whose identity is not revealed. C.J. and Danny are together and have had a baby, Will Bailey is a Congressman, and Kate Harper has written a book; Toby Ziegler is also present and received warmly by President Bartlet. Leo McGarry is not present at the reunion (coincidentally actor John Spencer died three months after the airing of this episode). The show then returns to the main timeline with the Santos/McGarry campaign getting off to a rough start with tensions between Santos and Leo and between the campaign and the White House, despite poll numbers which show the campaign doing better than expected. C.J. is questioned by the White House counsel as to her involvement with the leak about a secret military space shuttle.
134
2 "The Mommy Problem" Alex Graves Eli Attie October 2, 2005 (2005-10-02) 2T6202 7.66[52]
The Santos campaign takes a media hit on security issues because of the Bartlet administration's handling of the leak investigation. A White House reporter, Greg Brock, is sent to jail for failing to disclose his sources, and Josh clashes with both the White House and with a new communications director (Janeane Garofalo). The campaign debates whether Santos should respond to a summons to a weekend of military reserve training.
135
3 "Message of the Week" Christopher Misiano Lawrence O'Donnell, Jr. October 9, 2005 (2005-10-09) 2T6203 7.95[53]
The episode follows the ups and downs of the Vinick campaign as Santos gains momentum on national security, then loses momentum as Vinick presses him on immigration issues, although this prompts the resignation of a top Vinick aide. The religious right tries to corner Vinick into promising to appoint pro-life judges. Vinick's deception to appease them backfires before Governor Sullivan saves the day.
136
4 "Mr. Frost" Andrew Bernstein Alex Graves October 16, 2005 (2005-10-16) 2T6204 8.15[54]
The Santos campaign's "education week" is derailed by a controversy over teaching intelligent design, however, the Santos campaign turns the issue around, playing off Vinick's vulnerability as a pro-choice Republican on religious issues. In the White House, subpoenas are being handed down. Palestinian Chairman Farad is murdered by a suicide bomber. As Bartlet is determined to attend the funeral despite security concerns, C.J. is hounded by a lone intelligence agent who believes Farad's death was part of a larger conspiracy. She then finds out another foreign leader has also been assassinated. In the closing moments of the episode, Toby reveals to C.J. that he was responsible for the security leak.
137
5 "Here Today" Alex Graves Peter Noah October 23, 2005 (2005-10-23) 2T6205 7.85[55]
C.J. deals with the immediate repercussions of Toby's confession, including co-opting Will Bailey into his job, and White House Counsel Oliver Babish questions Toby until his lawyer intervenes. Josh struggles with the necessity to "clean house" on the Santos campaign, firing dozens of inexperienced staffers, including one close to the candidate. Kate Harper tangles with both the National Security Council and intelligence agent Frost as tensions rise between Russia and China. Ellie Bartlet reveals that she is engaged and lets her parents know she should get married very soon because otherwise she'll be a visibly pregnant bride. The president fires Toby and addresses the nation as Toby is led from the White House.
138
6 "The Al Smith Dinner" Lesli Linka Glatter Eli Attie October 30, 2005 (2005-10-30) 2T6206 8.51[56]
An ad by a 527 group attacking Santos for his pro-choice stand has both campaigns up in arms, trying to avoid the campaign going negative or diving into the abortion issue — a touchy subject for both candidates: Vinick because his pro-choice position risks alienating pro-life conservatives, Santos because his risks alienating pro-choice liberals, including a major pro-choice interest group who are considering endorsing Vinick. Back at the White House, Will struggles with dealing with the press as the new Communications Director, settling into Toby's old office. Josh struggles with Lou Thornton's decision to bring Donna into the campaign as a spokesperson. In the final moments, as both candidates wait backstage at the Alfred E. Smith Memorial Foundation Dinner, Santos and Vinick agree to an unexpected deal: a live debate the following Sunday.
139
7 "The Debate" Alex Graves Lawrence O'Donnell, Jr. November 6, 2005 (2005-11-06) 2T6207 9.58[57]
Candidates Matthew Santos and Arnold Vinick debate live in a forum moderated by Forrest Sawyer. During Vinick's opening statement, he proposes dropping the negotiated rules and having a freer debate format. During the hour-long debate (originally broadcast live in two tapings for East and West Coast audiences), the two candidates cover topics ranging from immigration to job creation to health care to African debt relief.
140
8 "Undecideds" Christopher Misiano Debora Cahn December 4, 2005 (2005-12-04) 2T6208 7.26[58]
Santos must face the challenge of visiting a black family in Los Angeles whose child was shot by a Latino police officer. C.J. must manage a crisis between China and Kazakhstan. And Will must go through Ellie's wedding guest list in a painful, protracted negotiation.
141
9 "The Wedding" Max Mayer Josh Singer December 11, 2005 (2005-12-11) 2T6209 8.13[59]
Wedding plans for the Bartlets' daughter move forward as Josh tries to pay for a windfall in the polls with a dwindling campaign war chest. Meanwhile, the President must balance his daughter's most important day with a potential war between two nuclear powers. Democratic Party leaders want Leo to be campaign manager rather than Josh, but Josh has the trust of Leo and that carries through to Santos.
142
10 "Running Mates" Paul McCrane Peter Noah January 8, 2006 (2006-01-08) 2T6210 11.74[60]
At the beginning of the episode, Martin Sheen directly addresses the viewers out of character to pay tribute to co-star John Spencer, who played Leo and had died three weeks prior to this episode's broadcast. In the episode, Leo does poorly in Vice Presidential debate practice, making Lou and Josh nervous, and the media catches wind. Will and Kate set up a date, which turns out to be watching the VP debate in Will's office. Santos takes time off from the campaign trail to visit his family, finding himself out-of-sync with domestic issues amid a flurry of invasive media coverage. Josh calls Toby, who is currently between arraignments, about the VP debate. In the end, Leo performs unexpectedly well, and reveals he leaked stories of his poor practice sessions to lower expectations.
143
11 "Internal Displacement" Andrew Bernstein Bradley Whitford January 15, 2006 (2006-01-15) 2T6211 6.36[61]
C.J. realizes that she barely has any time left in office and decides to try to solve the crisis in Darfur, Sudan, along with the crisis between Russia and China over Kazakhstan. Adding more to her stress level, the President's son-in-law, Doug Westin, is rumored to be having an affair with his kids' nanny; Danny makes his first appearance (outside of the season opener flash forward) since the fifth season to go on a date with C.J.
144
12 "Duck and Cover" Christopher Misiano Eli Attie January 22, 2006 (2006-01-22) 2T6212 7.71[62]
Elections are underway in Kazakhstan, but Russia and China teetering on the brink of an oil war in Central Asia is the least of Bartlet and C.J.'s concerns as they face a nuclear reactor in California on the verge of a meltdown. While agonizing over whether to evacuate nearby citizens and release radioactive steam into the atmosphere, the Santos and Vinick campaigns stare each other down, trying to avoid being the first to turn the crisis into a political issue – all the more complex as, decades ago, Vinick lobbied for the plant's construction. When the news comes out, the election becomes, in Josh's words, "too close to call."
145
13 "The Cold" Alex Graves Story by : Debora Cahn & Lauren Schmidt
Teleplay by : Debora Cahn March 12, 2006 (2006-03-12) 2T6213 7.02[63]
When new polling puts Santos and Vinick neck-and-neck nationwide, the Santos campaign staff are elated – Josh and Donna so much so that they end up sharing a kiss, which forces them to confront their feelings for each other. Vinick, on the other hand, has a cold, and is feeling pressure from the RNC to make a rightward turn in his campaign and play to the Republican base. This makes Bruno nervous and afraid he's going to be fired. President Bartlet summons both candidates to the White House so he can advise them that he's ordering tens of thousands of U.S. troops into Kazakhstan. Before he meets with either Presidential candidate, he meets with Leo McGarry, whom he has also called to the White House. Bartlet's meeting with Leo is more personal as he shares his concerns about the consequences of his decisions, with Leo back in his old role as the President's closest confidant. This would be John Spencer's last appearance.
146
14 "Two Weeks Out" Laura Innes Lawrence O'Donnell, Jr. March 19, 2006 (2006-03-19) 2T6214 8.07[64]
With the election two weeks out and both candidates polling even in California, both the Santos and Vinick campaigns scramble to the state to try to gain free media from public events. Toby advises Josh that California is the big issue and that Santos should head there immediately. Santos' press coverage in California is trumped by Vinick holding a til-they-drop press conference outside the nuclear plant. Vinick, whose hand is broken by constant handshakes, has a stroke of luck when Bruno discovers Santos' briefcase in a holding room. Vinick and Bruno must make a difficult decision: do they use its contents against Santos, or take the high road and return it? The briefcase contains evidence that suggests that the Congressman may be supporting an illegitimate child. Vinick asks to meet with Santos, whereupon the Congressman denies the allegation, saying that he is making up for the mistakes of his brother.
147
15 "Welcome to Wherever You Are" Matia Karrell Josh Singer March 26, 2006 (2006-03-26) 2T6215 7.90[65]
It's 5 days before the election – Halloween – and the Santos campaign's stress levels rise as they kick off a whirlwind tour of battleground states, with Jon Bon Jovi along for the ride. Among the crises of the day: Helen Santos makes provocative statements about felons voting, Donna can't work out a sketch for The Tonight Show, Santos is irked that his security briefings are cut short, and Josh is receiving campaign tips from Toby – who is himself facing a federal prosecutor who threatens new indictments which could derail the Santos campaign. Toby gets a brief respite from visits to the prosecutor's office to see his kids (Molly and Huck) and his ex-wife, Andie, who urges Toby to blame his late brother for the sake of their children.
148
16 "Election Day Part I" Mimi Leder Lauren Schmidt April 2, 2006 (2006-04-02) 2T6216 7.27[66]
The episode opens late at night on the day before election day. Josh finally relaxes long enough to see various campaign staff hooking up, and he and Donna sleep together – twice. Election day brings stress in both campaigns: Josh is convinced he is finding problems in exit poll data, while the Vinick campaign worries the data shows them losing in key places. West Virginia is unexpectedly called for Vinick and the traditionally Republican South Carolina is called for Santos. The episode closes with Annabeth finding Leo in his room, her screaming for help, and Secret Service agents closing in calling over their radio, "He's down, he's down!"
149
17 "Election Day Part II" Christopher Misiano Eli Attie & John Wells April 9, 2006 (2006-04-09) 2T6217 8.39[67]
During an exhausting and adrenaline-filled night, the electoral votes come in as the Santos and Vinick campaigns wait anxiously. C.J. breaks the news of Leo's death to President Bartlet, and the news hits the airwaves less than an hour before polls close on the West Coast. After Santos and Vinick win their home states of Texas and California respectively, the two campaigns agonize over whether to mount legal challenges before final results are announced in Nevada and Oregon. In the end, both states break for Santos, who gives his election night speech as the President-elect.
150
18 "Requiem" Steve Shill Eli Attie, Debora Cahn & John Wells April 16, 2006 (2006-04-16) 2T6218 8.29[68]
Leo's funeral brings back fond memories and old friends, including Amy Gardner, who urges Josh to consider appointing a Congresswoman from Florida Vice President; Ainsley Hayes, who approaches C.J. about a job in the Santos administration; Danny Concannon, who tries to rekindle his relationship with C.J.; and Bob Russell, who offers himself as a vice presidential prospect. Meanwhile, Santos and Josh clash over Barry Goodwin's place in the transition, Santos eyes numerous Speaker of the House candidates, and Bartlet and the staff reminisce about Leo in the Residence.
151
19 "Transition" Nelson McCormick Peter Noah April 23, 2006 (2006-04-23) 2T6219 8.42[69]
Josh's astoundingly hectic schedule begins to catch up to him, and friends and co-workers worry that if he doesn't take some time off very soon, he won't be able to function as chief of staff in the long run. Meanwhile, Josh has his hands full, acting as liaison between the President-Elect and the White House, and trying to staff the West Wing for the new administration. Top of his list is former Deputy Communications Director Sam Seaborn (Rob Lowe), who is reluctant to leave his happy life working in the private sector. Sam decides to stay on the condition that Josh take a week's vacation. In the end, Josh flies off with Donna who had previously given Josh an ultimatum to define their relationship. Meanwhile, Santos enrages C.J. by undermining Bartlet's military agenda with a phone call to the President of China.
152
20 "The Last Hurrah" Tim Matheson Lawrence O'Donnell, Jr. April 30, 2006 (2006-04-30) 2T6220 8.34[70]
The transition is speeding ahead, and Matt and Helen Santos are overwhelmed by almost everything about their new lives – including Secret Service protection, choosing a DC school for their kids, and dealing with the White House household staff. Vinick slips back into anonymity with too much time on his hands, and his staffers come to realize he's plotting another run for the presidency. Santos is trying to figure out how to get his vice-presidential choice confirmed, and makes a surprising offer to Vinick: be the new administration's Secretary of State.
153
21 "Institutional Memory" Lesli Linka Glatter Debora Cahn May 7, 2006 (2006-05-07) 2T6221 7.94[71]
The episode is set two weeks before the inauguration and the Bartlet administration staff is preparing to leave the White House. Most are seeking jobs in the Santos administration or elsewhere. C.J. is offered two jobs she is interested in - one to manage a philanthropic foundation and one as a high-ranking counselor in the Santos administration. C.J.'s relationship with Danny is suffering because he feels she is not taking it seriously. C.J. also visits Toby for the first time since his dismissal and considers whether she should urge President Bartlet to pardon him before leaving office. Will Bailey is offered a job with the DCCC to help get Democrats elected but finds himself becoming interested in one apparently unwinnable Congressional seat in Oregon.
154
22 "Tomorrow" Christopher Misiano John Wells May 14, 2006 (2006-05-14) 2T6222 10.11[72]
President Santos is inaugurated and President Bartlet leaves office. It is revealed that Santos plans to try to make Governor Eric Baker the vice-president through the Twenty-fifth Amendment and Bartlet pardons Toby in the last hours of his presidency.
DVD release[edit]
The DVD release of season seven was released by Warner Bros. first in the UK on September 11, 2006 and then in the US on November 7, 2006 after the season had completed broadcasting on television. As well as every episode from the season, the DVD release features bonus material including a two featurettes on "The Debate" – an episode that was broadcast live. Two live episodes of "The Debate" were produced, one for the East Coast and another for the West Coast.[73] The West Coast version of "The Debate" is the one used on the DVD.[74]
The West Wing: The Complete Seventh Season
Set details[74] Special features[75]
22 episodes
6-disc set
1.78:1 aspect ratio
English (Dolby Surround 2.0)
Subtitles: French, Spanish
Featurettes:
Live from the Director's Chair
Countdown to West Wing Live
Release dates[74][76][77]
United States Canada United Kingdom Australia
November 7, 2006 September 11, 2006 August 8, 2007
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Jump up ^ "West Wing wins seventh season". BBC News. March 18, 2005. Retrieved September 17, 2010.
Jump up ^ "West Wing is going live next month". RTÉ Ten. October 7, 2005. Archived from the original on October 26, 2012. Retrieved September 17, 2010.
Jump up ^ Pierce, Scott D. (May 12, 2006). "Term limits — 'West Wing' ends a remarkable 7-year run Sunday". Deseret News. Retrieved September 18, 2010.
Jump up ^ "Seventh season is West Wing's last". RTÉ Ten. January 23, 2006. Archived from the original on October 26, 2012. Retrieved September 17, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. September 27, 2005. Archived from the original on June 1, 2009. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. October 4, 2005. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. October 11, 2005. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. October 18, 2005. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. October 25, 2005. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. November 1, 2005. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. November 8, 2005. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. December 6, 2005. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. December 13, 2005. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. January 11, 2006. Archived from the original on December 15, 2014. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. January 18, 2006. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. January 24, 2006. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. March 14, 2006. Archived from the original on October 11, 2014. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. March 21, 2006. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. March 28, 2006. Archived from the original on March 11, 2015. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. April 4, 2006. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. April 11, 2006. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. April 18, 2006. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. April 25, 2006. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. May 2, 2006. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. May 9, 2006. Archived from the original on July 28, 2014. Retrieved September 16, 2010.
Jump up ^ "Weekly Program Rankings Report". ABC Medianet. May 16, 2006. Archived from the original on May 28, 2010. Retrieved September 16, 2010.
Jump up ^ "The West Wing: The Complete Seventh Season". DVD Verdict. Retrieved September 27, 2010.
^ Jump up to: a b c "The West Wing: The Complete Seventh Season". Warner Bros. Retrieved October 11, 2010.
Jump up ^ "The West Wing: The Complete Seventh Season". Warner Bros. Retrieved September 18, 2010.
Jump up ^ "The West Wing - Complete Season 7 [DVD] [2001]". Amazon.co.uk. Retrieved September 18, 2010.
Jump up ^ "The West Wing Season 7 DVD". dvdorchard Pty Limited. Retrieved July 3, 2008.
General references
"The West Wing Episodes on NBC". TV Guide. Retrieved January 7, 2012.
"Shows A-Z - west wing, the on nbc". the Futon Critic. Retrieved January 7, 2012.
"The West Wing - Episode Guide". MSN TV. Retrieved January 7, 2012.
"The West Wing: Episode Guide". Zap2it. Retrieved January 7, 2012.
"The West Wing Episode Guides". NBC. Archived from the original on August 3, 2006. Retrieved January 7, 2012.
[hide]
v
t
e
The West Wing
List of characters
List of politicians
Main characters
Josiah Bartlet
Leo McGarry
Josh Lyman
Toby Ziegler
Sam Seaborn
C. J. Cregg
Charlie Young
Donna Moss
Abbey Bartlet
Will Bailey
Matt Santos
Arnold Vinick
Mandy Hampton
Annabeth Schott
Recurring characters
Ellie Bartlet
Zoey Bartlet
Debbie Fiderer
Amy Gardner
John Hoynes
Dolores Landingham
Joey Lucas
Robert Ritchie
Bob Russell
Andrea Wyatt
Episodes
Season 1
"Pilot"
"Five Votes Down"
"The Crackpots and These Women"
"In Excelsis Deo"
"He Shall, from Time to Time..."
"Let Bartlet Be Bartlet"
"What Kind of Day Has It Been"
Season 2
"The Lame Duck Congress"
"Noël"
"Two Cathedrals"
Season 3
"Manchester, Part I"
"Manchester, Part II"
"Ways and Means"
"On the Day Before"
Season 4
"20 Hours in America"
"Twenty Five"
Season 5
"The Warfare of Genghis Khan"
"An Khe"
"Full Disclosure"
"Eppur Si Muove"
Season 6
Season 7
Retrieved from "https://en.wikipedia.org/w/index.php?title=The_West_Wing_(season_7)&oldid=820270228"
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