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Equilibrium constant
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The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no tendency towards further change. At any given time, the reaction quotient is a number defined by taking the product of effective concentrations (chemical activities) for species appearing on the right-hand side of a chemical equation and dividing by the corresponding product for species appearing on the left-hand side. As the chemical reaction progresses, the reaction quotient changes and tends to the value of the equilibrium constant.
For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture. Thus, given the initial composition of a system, known equilibrium constant values can be used to determine the composition of the system at equilibrium. However, reaction parameters like temperature, solvent, and ionic strength may all influence the value of the equilibrium constant.
A knowledge of equilibrium constants is essential for the understanding of many chemical systems, as well as biochemical processes such as oxygen transport by hemoglobin in blood and acid-base homeostasis in the human body.
Stability constants, formation constants, binding constants, association constants and dissociation constants are all types of equilibrium constants. (See also the article on the determination of equilibrium constants for experimental and computational methods.)
Contents
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1 Basic definitions and properties
2 Types of equilibrium constants
2.1 Cumulative and stepwise formation constants
2.1.1 Competition method
2.2 Association and dissociation constants
2.3 Micro-constants
2.4 pH considerations (Brønsted constants)
2.5 Hydrolysis constants
2.6 Conditional constants
2.7 Gas-phase equilibria
3 Thermodynamic basis for equilibrium constant expressions
3.1 Equivalence of thermodynamic and kinetic expressions for equilibrium constants
4 Unknown activity coefficient values
5 Dimensionality
6 Temperature dependence
6.1 A more complex formulation
7 Pressure dependence
8 Effect of isotopic substitution
9 See also
10 References
10.1 Data sources
11 External links
Basic definitions and properties[edit]
For a system undergoing a reversible reaction described by the general chemical equation
α A + β B + ⋯ ⇌ ρ R + σ S + ⋯ {\displaystyle \alpha \,\mathrm {A} +\beta \,\mathrm {B} +\cdots \rightleftharpoons \rho \,\mathrm {R} +\sigma \,\mathrm {S} +\cdots }
a thermodynamic equilibrium constant, denoted by K ⊖ {\displaystyle \ominus } , is defined to be the value of the reaction quotient Qt when forward and reverse reactions occur at the same rate. At chemical equilibriumthe chemical composition of the mixture does not change with time and the Gibbs free energy change for the reaction is at its minimum. If the composition of a mixture at equilibrium is changed by addition of some reagent, a new equilibrium position will be reached, given enough time. An equilibrium constant is related to the composition of the mixture at equilibrium by [1] [2]
K ⊖ = { R } ρ { S } σ . . . { A } α { B } β . . . = [ R ] ρ [ S ] σ . . . [ A ] α [ B ] β . . . × Γ {\displaystyle K^{\ominus }={\frac {\mathrm {\{R\}} ^{\rho }\mathrm {\{S\}} ^{\sigma }...}{\mathrm {\{A\}} ^{\alpha }\mathrm {\{B\}} ^{\beta }...}}={\frac {{[\mathrm {R} ]}^{\rho }{[\mathrm {S} ]}^{\sigma }...}{{[\mathrm {A} ]}^{\alpha }{[\mathrm {B} ]}^{\beta }...}}\times \Gamma }
Γ = γ R ρ γ S σ . . . γ A α γ B β . . . {\displaystyle \Gamma ={\frac {\gamma _{R}^{\rho }\gamma _{S}^{\sigma }...}{\gamma _{A}^{\alpha }\gamma _{B}^{\beta }...}}}
where {X} denotes the thermodynamic activity of reagent X at equilibrium, [X] the corresponding concentration, and γ the corresponding activity coefficient. If it can be assumed that the quotient of activity coefficients, Γ {\displaystyle \Gamma } , is constant over a range of experimental conditions, such as pH, then an equilibrium constant can be derived a a quotient of concentrations.[3]
K c = K ⊖ / Γ = [ R ] ρ [ S ] σ . . . [ A ] α [ B ] β . . . {\displaystyle \mathrm {K} _{c}=K^{\ominus }/\Gamma ={\frac {{[\mathrm {R} ]}^{\rho }{[\mathrm {S} ]}^{\sigma }...}{{[\mathrm {A} ]}^{\alpha }{[\mathrm {B} ]}^{\beta }...}}} .
An equilibrium constant is related to the standard Gibbs free energy change of reaction Δ G ⊖ {\displaystyle \Delta G^{\ominus }} by
Δ G ⊖ = − R T l o g 10 K ⊖ {\displaystyle \Delta G^{\ominus }=-RT\mathrm {log} _{10}K^{\ominus }} ,
where R is the universal gas constant, and T is the temperature in Kelvins. This expression implies that K ⊖ {\displaystyle K^{\ominus }} must be a pure number and cannot have a dimension, since logarithms can only be taken of pure numbers. K c {\displaystyle K_{c}} must also be a pure number. On the other hand, the reaction quotient at equilibrium
[ R ] ρ [ S ] σ . . . [ A ] α [ B ] β . . . ( e q ) {\displaystyle {\frac {{[\mathrm {R} ]}^{\rho }{[\mathrm {S} ]}^{\sigma }...}{{[\mathrm {A} ]}^{\alpha }{[\mathrm {B} ]}^{\beta }...}}(eq)} .
does have the dimension of concentration raised to some power (see #Dimensionality, below}. Such reaction quotients are often referred to, in the biochemical literature, as equilibrium constants.
For an equilibrium mixture of gases, an equilibrium constant can be defined in terms of partial pressure or fugacity.
An equilibrium constant is related to the forward and backward rate constants, kf and kr of the reactions involved in reaching equilibrium.
K ⊖ = k f k r {\displaystyle K^{\ominus }={\frac {k_{\mathrm {f} }}{k_{\mathrm {r} }}}} .
Types of equilibrium constants[edit]
Cumulative and stepwise formation constants[edit]
A cumulative or overall constant, given the symbol β, is the constant for the formation of a complex from reagents. For example, the cumulative constant for the formation of ML2 is given by
M + 2 L ⇌ ML2; [ML2] = β12[M][L]2
The stepwise constant, K, for the formation of the same complex from ML and L is given by
ML + L ⇌ ML2; [ML2] = K[ML][L] = Kβ11[M][L]2
It follows that
β12 = Kβ11
A cumulative constant can always be expressed as the product of stepwise constants. There is no agreed notation for stepwise constants, though a symbol such as KL
ML is sometimes found in the literature. It is best always to define each stability constant by reference to an equilibrium expression.
Competition method[edit]
A particular use of a stepwise constant is in the determination of stability constant values outside the normal range for a given method. For example, EDTA complexes of many metals are outside the range for the potentiometric method. The stability constants for those complexes were determined by competition with a weaker ligand.
ML + L′ ⇌ ML′ + L [ M L ′ ] = K [ M L ] [ L ′ ] [ L ] = K β M L [ M ] [ L ] [ L ′ ] [ L ] = K β M L [ M ] [ L ′ ] ; β M L ′ = K β M L {\displaystyle [\mathrm {ML} ']=K{\frac {[\mathrm {ML} ][\mathrm {L} ']}{[\mathrm {L} ]}}=K{\frac {\beta _{\mathrm {ML} }[\mathrm {M} ][\mathrm {L} ][\mathrm {L} ']}{[\mathrm {L} ]}}=K\beta _{\mathrm {ML} }[\mathrm {M} ][\mathrm {L} '];\quad \beta _{\mathrm {ML} '}=K\beta _{\mathrm {ML} }}
The formation constant of [Pd(CN)4]2− was determined by the competition method.
Association and dissociation constants[edit]
In organic chemistry and biochemistry it is customary to use pKa values for acid dissociation equilibria.
p K a = − log  K d i s s = log  ( 1 K d i s s ) {\displaystyle \mathrm {p} K_{\mathrm {a} }=-\log K_{\mathrm {diss} }=\log \left({\frac {1}{K_{\mathrm {diss} }}}\right)\,}
where Kdiss is a stepwise acid dissociation constant. For bases, the base association constant, pKb is used. For any given acid or base the two constants are related by pKa + pKb = pKw, so pKa can always be used in calculations.
On the other hand, stability constants for metal complexes, and binding constants for host–guest complexes are generally expressed as association constants. When considering equilibria such as
M + HL ⇌ ML + H
it is customary to use association constants for both ML and HL. Also, in generalized computer programs dealing with equilibrium constants it is general practice to use cumulative constants rather than stepwise constants and to omit ionic charges from equilibrium expressions. For example, if NTA, nitrilotriacetic acid, N(CH2CO2H)3 is designated as H3L and forms complexes ML and MHL with a metal ion M, the following expressions would apply for the dissociation constants.
H 3 L ↽ − − ⇀ H 2 L + H ; p K 1 = − log  ( [ H 2 L ] [ H ] [ H 3 L ] ) H 2 L ↽ − − ⇀ HL + H ; p K 2 = − log  ( [ HL ] [ H ] [ H 2 L ] ) HL ↽ − − ⇀ L + H ; p K 3 = − log  ( [ L ] [ H ] [ HL ] ) {\displaystyle {\begin{array}{ll}{\ce {H3L<=>{H2L}+H}};&\mathrm {p} K_{1}=-\log \left({\frac {[{\ce {H2L}}][{\ce {H}}]}{[{\ce {H3L}}]}}\right)\\{\ce {H2L<=>{HL}+H}};&\mathrm {p} K_{2}=-\log \left({\frac {[{\ce {HL}}][{\ce {H}}]}{[{\ce {H2L}}]}}\right)\\{\ce {HL<=>{L}+H}};&\mathrm {p} K_{3}=-\log \left({\frac {[{\ce {L}}][{\ce {H}}]}{[{\ce {HL}}]}}\right)\end{array}}}
The cumulative association constants can be expressed as
L + H ↽ − − ⇀ HL ; log  β 011 = log  ( [ HL ] [ L ] [ H ] ) = p K 3 L + 2 H ↽ − − ⇀ H 2 L ; log  β 012 = log  ( [ H 2 L ] [ L ] [ H ] 2 ) = p K 3 + p K 2 L + 3 H ↽ − − ⇀ H 3 L ; log  β 013 = log  ( [ H 3 L ] [ L ] [ H ] 3 ) = p K 3 + p K 2 + p K 1 M + L ↽ − − ⇀ ML ; log  β 110 = log  ( [ ML ] [ M ] [ L ] ) M + L + H ↽ − − ⇀ MLH ; log  β 111 = log  ( [ MLH ] [ M ] [ L ] [ H ] ) {\displaystyle {\begin{array}{ll}{\ce {{L}+H<=>HL}};&\log \beta _{011}=\log \left({\frac {[{\ce {HL}}]}{[{\ce {L}}][{\ce {H}}]}}\right)=\mathrm {p} K_{3}\\{\ce {{L}+2H<=>H2L}};&\log \beta _{012}=\log \left({\frac {[{\ce {H2L}}]}{[{\ce {L}}][{\ce {H}}]^{2}}}\right)=\mathrm {p} K_{3}+\mathrm {p} K_{2}\\{\ce {{L}+3H<=>H3L}};&\log \beta _{013}=\log \left({\frac {[{\ce {H3L}}]}{[{\ce {L}}][{\ce {H}}]^{3}}}\right)=\mathrm {p} K_{3}+\mathrm {p} K_{2}+\mathrm {p} K_{1}\\{\ce {{M}+L<=>ML}};&\log \beta _{110}=\log \left({\frac {[{\ce {ML}}]}{[{\ce {M}}][{\ce {L}}]}}\right)\\{\ce {{M}+{L}+H<=>MLH}};&\log \beta _{111}=\log \left({\frac {[{\ce {MLH}}]}{[{\ce {M}}][{\ce {L}}][{\ce {H}}]}}\right)\end{array}}}
Note how the subscripts define the stoichiometry of the equilibrium product.
Micro-constants[edit]
When two or more sites in an asymmetrical molecule may be involved in an equilibrium reaction there are more than one possible equilibrium constants. For example, the molecule L-DOPA has two non-equivalent hydroxyl groups which may be deprotonated. Denoting L-DOPA as LH2, the following diagram shows all the species that may be formed (X = CH2CH(NH2)CO2H):
The first protonation constants are
[L1H] = k11[L][H], [L2H] = k12[L][H]
The concentration of LH− is the sum of the concentrations of the two micro-species. Therefore, the equilibrium constant for the reaction, the macro-constant, is the sum of the micro-constants.
K1 = k11 + k12
In the same way,
K2 = k21 + k22
Lastly, the cumulative constant is
β2 = K1K2 = k11k21 = k12k22
Thus, although there are seven micro-and macro-constants, only three of them are mutually independent. Moreover, the isomerization constant, Ki, is equal to the ratio of the microconstants.
Ki = k11/k12
In L-DOPA the isomerization constant is 0.9, so the micro-species L1H and L2H have almost equal concentrations at all pH values.
In general a macro-constant is equal to the sum of all the micro-constants and the occupancy of each site is proportional to the micro-constant. The site of protonation can be very important, for example, for biological activity.
Micro-constants cannot be determined individually by the usual methods, which give macro-constants. Methods which have been used to determine micro-constants include:
blocking one of the sites, for example by methylation of a hydroxyl group, to determine one of the micro-constants
using a spectroscopic technique, such as infrared spectroscopy, where the different micro-species give different signals.
applying mathematical procedures to 13C NMR data.[4][5]
pH considerations (Brønsted constants)[edit]
pH is defined in terms of the activity of the hydrogen ion
pH = −log10 {H+}
In the approximation of ideal behaviour, activity is replaced by concentration. pH is measured by means of a glass electrode, a mixed equilibrium constant, also known as a Brønsted constant, may result.
HL ⇌ L + H; p K = − log  ( [ L ] { H } [ H L ] ) {\displaystyle \mathrm {p} K=-\log \left({\frac {[\mathrm {L} ]\{\mathrm {H} \}}{[\mathrm {HL} ]}}\right)}
It all depends on whether the electrode is calibrated by reference to solutions of known activity or known concentration. In the latter case the equilibrium constant would be a concentration quotient. If the electrode is calibrated in terms of known hydrogen ion concentrations it would be better to write p[H] rather than pH, but this suggestion is not generally adopted.
Hydrolysis constants[edit]
In aqueous solution the concentration of the hydroxide ion is related to the concentration of the hydrogen ion by
K W = [ H ] [ OH ] {\displaystyle {\ce {{\mathit {K}}_{W}=[H][OH]}}}
[ OH ] = K W [ H ] − 1 {\displaystyle {\ce {[OH]={\mathit {K}}_{W}[H]^{-1}}}}
The first step in metal ion hydrolysis[6] can be expressed in two different ways
{ M ( H 2 O ) ↽ − − ⇀ M ( OH ) + H ; [ M ( OH ) ] = β ∗ [ M ] [ H ] − 1 M + OH ↽ − − ⇀ M ( OH ) ; [ M ( OH ) ] = K [ M ] [ OH ] = K K W [ M ] [ H ] − 1 {\displaystyle {\begin{cases}{\ce {M(H2O)<=>{M(OH)}+H}};&[{\ce {M(OH)}}]=\beta ^{*}[{\ce {M}}][{\ce {H}}]^{-1}\\{\ce {{M}+OH<=>M(OH)}};&[{\ce {M(OH)}}]=K[{\ce {M}}][{\ce {OH}}]=KK_{\ce {W}}[{\ce {M}}][{\ce {H}}]^{-1}\end{cases}}}
It follows that β* = KKW. Hydrolysis constants are usually reported in the β* form and this leads to them appearing to have strange values. For example, if log K = 4 and log KW = −14, log β* = 4 + (−14) = −10. In general when the hydrolysis product contains n hydroxide groups lg β* = log K + n log KW
Conditional constants[edit]
Conditional constants, also known as apparent constants, are concentration quotients which are not true equilibrium constants but can be derived from them.[7] A very common instance is where pH is fixed at a particular value. For example, in the case of iron(III) interacting with EDTA, a conditional constant could be defined by
K c o n d = [ Total Fe bound to EDTA ] [ Total Fe not bound to EDTA ] × [ Total EDTA not bound to Fe ] {\displaystyle K_{\mathrm {cond} }={\frac {[{\mbox{Total Fe bound to EDTA}}]}{[{\mbox{Total Fe not bound to EDTA}}]\times [{\mbox{Total EDTA not bound to Fe}}]}}}
This conditional constant will vary with pH. It has a maximum at a certain pH. That is the pH where the ligand sequesters the metal most effectively.
In biochemistry equilibrium constants are often measured at a pH fixed by means of a buffer solution. Such constants are, by definition, conditional and different values may be obtained when using different buffers.
Gas-phase equilibria[edit]
For equilibria in a gas phase, fugacity, f, is used in place of activity. However, fugacity has the dimension of pressure, so it must be divided by a standard pressure, usually 1 bar, in order to produce a dimensionless quantity, f/po. An equilibrium constant is expressed in terms of the dimensionless quantity. For example, for the equilibrium 2NO2 ⇌ N2O4,
f N 2 O 4 p ⊖ = K ( f N O 2 p ⊖ ) 2 {\displaystyle {\frac {f_{\mathrm {N_{2}O_{4}} }}{p^{\ominus }}}=K\left({\frac {f_{\mathrm {NO_{2}} }}{p^{\ominus }}}\right)^{2}}
Fugacity is related to partial pressure, p, by a dimensionless fugacity coefficient ϕ: f = ϕp. Thus, for the example,
K = ϕ N 2 O 4 p N 2 O 4 / p ⊖ ( ϕ N O 2 p N O 2 / p ⊖ ) 2 {\displaystyle K={\frac {\phi _{\mathrm {N_{2}O_{4}} }p_{\mathrm {N_{2}O_{4}} }/{p^{\ominus }}}{\left(\phi _{\mathrm {NO_{2}} }p_{\mathrm {NO_{2}} }/{p^{\ominus }}\right)^{2}}}}
Usually the standard pressure is omitted from such expressions. Expressions for equilibrium constants in the gas phase then resemble the expression for solution equilibria with fugacity coefficient in place of activity coefficient and partial pressure in place of concentration.
K = ϕ N 2 O 4 p N 2 O 4 ( ϕ N O 2 p N O 2 ) 2 {\displaystyle K={\frac {\phi _{\mathrm {N_{2}O_{4}} }p_{\mathrm {N_{2}O_{4}} }}{\left(\phi _{\mathrm {NO_{2}} }p_{\mathrm {NO_{2}} }\right)^{2}}}}
Thermodynamic basis for equilibrium constant expressions[edit]
Thermodynamic equilibrium is characterized by the free energy for the whole (closed) system being a minimum. For systems at constant temperature and pressure the Gibbs free energy is minimum.[8] The slope of the reaction free energy with respect to the reaction coordinate, ξ, is zero when the free energy is at its minimum value.
( ∂ G ∂ ξ ) T , P = 0 {\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{T,P}=0}
The free energy change, δGr, can be expressed as a weighted sum of chemical potentials, the partial molar free energies of the species in equilibrium. The potential, μi, of the ith species in a chemical reaction is the partial derivative of the free energy with respect to the number of moles of that species, Ni
μ i = ( ∂ G ∂ N i ) T , P {\displaystyle \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P}}
A general chemical equilibrium can be written as
∑ j n j R e a c t a n t j ⇌ ∑ k m k P r o d u c t k {\displaystyle \sum _{j}n_{j}\mathrm {Reactant} _{j}\rightleftharpoons \sum _{k}m_{k}\mathrm {Product} _{k}}
where nj are the stoichiometric coefficients of the reactants in the equilibrium equation, and mj are the coefficients of the products. At equilibrium
∑ k m k μ k = ∑ j n j μ j {\displaystyle \sum _{k}m_{k}\mu _{k}=\sum _{j}n_{j}\mu _{j}}
The chemical potential, μi, of the ith species can be calculated in terms of its activity, ai.
μ i = μ i ⊖ + R T ln  a i {\displaystyle \mu _{i}=\mu _{i}^{\ominus }+RT\ln a_{i}}
μo
i is the standard chemical potential of the species, R is the gas constant and T is the temperature. Setting the sum for the reactants j to be equal to the sum for the products, k, so that δGr(Eq) = 0
∑ j n j ( μ j ⊖ + R T ln  a j ) = ∑ k m k ( μ k ⊖ + R T ln  a k ) {\displaystyle \sum _{j}n_{j}(\mu _{j}^{\ominus }+RT\ln a_{j})=\sum _{k}m_{k}(\mu _{k}^{\ominus }+RT\ln a_{k})}
Rearranging the terms,
∑ k m k μ k ⊖ − ∑ j n j μ j ⊖ = − R T ( ∑ k ln  a k m k − ∑ j ln  a j n j ) {\displaystyle \sum _{k}m_{k}\mu _{k}^{\ominus }-\sum _{j}n_{j}\mu _{j}^{\ominus }=-RT\left(\sum _{k}\ln {a_{k}}^{m_{k}}-\sum _{j}\ln {a_{j}}^{n_{j}}\right)}
Δ G ⊖ = − R T ln  K . {\displaystyle \Delta G^{\ominus }=-RT\ln K.}
This relates the standard Gibbs free energy change, ΔGo to an equilibrium constant, K, the reaction quotient of activity values at equilibrium.
Δ G ⊖ = ∑ k m k μ k ⊖ − ∑ j n j μ j ⊖ {\displaystyle \Delta G^{\ominus }=\sum _{k}m_{k}\mu _{k}^{\ominus }-\sum _{j}n_{j}\mu _{j}^{\ominus }}
ln  K = ∑ k ln  a k m k − ∑ j ln  a j n j ; K = ∏ k a k m k ∏ j a j n j ≡ { R } ρ { S } σ . . . { A } α { B } β . . . {\displaystyle \ln K=\sum _{k}\ln {a_{k}}^{m_{k}}-\sum _{j}\ln {a_{j}}^{n_{j}};K={\frac {\prod _{k}{a_{k}}^{m_{k}}}{\prod _{j}{a_{j}}^{n_{j}}}}\equiv {\frac {{\{\mathrm {R} \}}^{\rho }{\{\mathrm {S} \}}^{\sigma }...}{{\{\mathrm {A} \}}^{\alpha }{\{\mathrm {B} \}}^{\beta }...}}}
Equivalence of thermodynamic and kinetic expressions for equilibrium constants[edit]
At equilibrium the rate of the forward reaction is equal to the backward reaction rate. A simple reaction, such as ester hydrolysis
A B + H 2 O ⇋ A H + B ( O H ) {\displaystyle AB+H_{2}O\leftrightharpoons AH+B(OH)}
has reaction rates given by expressions
f o r w a r d r a t e = k f [ A B ] [ H 2 O ] {\displaystyle forward\ rate=k_{f}[AB][H_{2}O]}
b a c k w a r d r a t e = k b [ A H ] [ B ( O H ) ] {\displaystyle backward\ rate=k_{b}[AH][B(OH)]}
According to Guldberg and Waage. equilibrium is attained when the forward and backward reaction rates are equal to each other. In these circumstances, an equilibrium constant is defined to be equal to the ratio of the forward and backward reaction rate constants.
K = k b k f = [ A B ] [ H 2 O ] [ A H ] [ B ( O H ) ] {\displaystyle K={\frac {k_{b}}{k_{f}}}={\frac {[AB][H_{2}O]}{[AH][B(OH)]}}}
For convenience the concentration of water may be taken to be constant, resulting in the simpler expression
K c = [ A B ] [ A H ] [ B ( O H ) ] {\displaystyle K^{c}={\frac {[AB]}{[AH][B(OH)]}}}
The concentration quotient K c {\displaystyle K^{c}} has the dimension 1/concentration, but the thermodynamic equilibrium constant, K {\displaystyle K} , is dimensionless.
Unknown activity coefficient values[edit]
Variation of log Kc of acetic acid with ionic strength
It is very rare for activity coefficient values to have been determined experimentally for a system at equilibrium. There are three options for dealing with the situation where activity coefficient values are not known from experimental measurements.
Use calculated activity coefficients, together with concentrations of reactants. For equilibria in solution estimates of the activity coefficients of charged species can be obtained using Debye–Hückel theory, an extended version, or SIT theory. For uncharged species, the activity coefficient γ0 mostly follows a "salting-out" model: log10 γ0 = bI where I stands for ionic strength.[9]
Assume that the activity coefficients are all equal to 1. This is acceptable when all concentrations are very low.
For equilibria in solution use a medium of high ionic strength. In effect this redefines the standard state as referring to the medium. Activity coefficients in the standard state are, by definition, equal to 1. The value of an equilibrium constant determined in this manner is dependent on the ionic strength. When published constants refer to an ionic strength other than the one required for a particular application, they may be adjusted by means of specific ion theory (SIT) and other theories.[10]
Dimensionality[edit]
Any equilibrium constant, K, must be dimensionless. An equilibrium constant is related to the standard Gibbs free energy change for the reaction by the expression
Δ G ∘ = − R T ln  K {\displaystyle \Delta G^{\circ }=-RT\ln K}
This requires that K be a pure number from which a logarithm can be derived. In the case of a simple equilibrium
A + B ⇌ A B {\displaystyle A+B\rightleftharpoons AB}
the thermodynamic equilibrium constant is defined in terms of the activities, {AB}, {A} and {B}, of the species in equilibrium with each other.
K = { A B } { A } { B } {\displaystyle K={\frac {\{AB\}}{\{A\}\{B\}}}}
As activity is a dimensionless quantity, K is dimensionless.
Now, each activity term can be expressed as a product of a concentration [X] and a corresponding activity coefficient, γ ( X ) {\displaystyle \gamma (X)} . Therefore,
K = [ A B ] [ A ] [ B ] × γ ( A B ) γ ( A ) γ ( B ) {\displaystyle K={\frac {[AB]}{[A][B]}}\times {\frac {\gamma (AB)}{\gamma (A)\gamma (B)}}}
Since each activity coefficient has the dimension 1/concentration, K remains dimensionless. However, when the quotient of activity coefficients is set equal to 1, K appears to have the dimension of 1/concentration.
K = [ A B ] [ A ] [ B ] {\displaystyle K={\frac {[AB]}{[A][B]}}}
This is what usually happens in practice when an equilibrium constant is calculated as a quotient of concentration values. The assumption underlying this practice is that the quotient of activities is constant under the conditions in which the equilibrium constant value is determined. There conditions are usually achieved by keeping the reaction temperature constant and by using a medium of relatively high ionic strength as the solvent. It is not unusual, particularly in texts relating to biochemical equilibria, to see a value quoted with a dimension. The justification for this practice is that the concentration scale used may be either mol dm−3 or mmol dm−3, so that the concentration unit has to be stated in order to avoid there being any ambiguity.
In general equilibria between two reagents can be expressed as
p A + q B ⇌ A p B q {\displaystyle pA+qB\rightleftharpoons A_{p}B_{q}}
in which case the equilibrium constant is defined, in terms of numerical concentration values, as
K = [ A p B q ] [ A ] p [ B ] q {\displaystyle K={\frac {[A_{p}B_{q}]}{[A]^{p}[B]^{q}}}}
The apparent dimension of this K value is concentration1−p−q; this may be written as M(1−p−q) or mM(1−p−q), where the symbol M signifies a molar concentration (1 M = 1 mol dm−3)
A further complications arises from the fact that an equilibrium constant can be defined as an association constant or as a dissociation constant. For dissociation constants
A p B q ⇌ p A + q B {\displaystyle A_{p}B_{q}\rightleftharpoons pA+qB} ; K = [ A ] p [ B ] q [ A p B q ] {\displaystyle K={\frac {[A]^{p}[B]^{q}}{[A_{p}B_{q}]}}}
The apparent dimension associated with a dissociation constant is the reciprocal of the dimension associated with the corresponding association constant.
Temperature dependence[edit]
The van 't Hoff equation:
d ln  K d T = Δ H ⊖ R T 2 or d ln  K d ( T − 1 ) = − Δ H ⊖ R {\displaystyle {\frac {d\ln K}{dT}}\ ={\frac {\Delta H^{\ominus }}{RT^{2}}}{\mbox{ or }}{\frac {d\ln K}{d(T^{-1})}}\ =-{\frac {\Delta H^{\ominus }}{R}}}
shows that when the reaction is exothermic (ΔHo is negative), then K decreases with increasing temperature, in accordance with Le Chatelier's principle. It permits calculation of the reaction equilibrium constant at temperature T2 if the reaction constant at T1 is known and the standard reaction enthalpy can be assumed to be independent of temperature even though each standard enthalpy change is defined at a different temperature. However, this assumption is valid only for small temperature differences T2 − T1. In fact standard thermodynamic arguments can be used to show that
( ∂ H ∂ T ) p = C p {\displaystyle \left({\frac {\partial H}{\partial T}}\right)_{p}=C_{p}}
where Cp is the heat capacity at constant pressure. The equilibrium constant is related to the standard Gibbs energy change of reaction as
Δ G ⊖ = − R T ln  K {\displaystyle \ \Delta G^{\ominus }=-RT\ln K}
where ΔGo is the standard Gibbs free energy change of reaction, R is the gas constant, and T the absolute temperature.
If the equilibrium constant has been determined and the standard reaction enthalpy has also been determined, by calorimetry, for example, this equation allows the standard entropy change for the reaction to be derived.
A more complex formulation[edit]
The calculation of K at a particular temperature from a known K at another given temperature can be approached as follows if standard thermodynamic properties are available. The effect of temperature on equilibrium constant is equivalent to the effect of temperature on Gibbs energy because:
ln  K = − Δ r G ⊖ R T {\displaystyle \ln K={{-\Delta _{\mathrm {r} }G^{\ominus }} \over {RT}}}
where ΔrGo is the reaction standard Gibbs energy, which is the sum of the standard Gibbs energies of the reaction products minus the sum of standard Gibbs energies of reactants.
Here, the term "standard" denotes the ideal behaviour (i.e., an infinite dilution) and a hypothetical standard concentration (typically 1 mol/kg). It does not imply any particular temperature or pressure because, although contrary to IUPAC recommendation, it is more convenient when describing aqueous systems over wide temperature and pressure ranges.[11]
The standard Gibbs energy (for each species or for the entire reaction) can be represented (from the basic definitions) as:
G T 2 ⊖ = G T 1 ⊖ − S T 1 ⊖ ( T 2 − T 1 ) − T 2 ∫ T 1 T 2 C p ⊖ T d T + ∫ T 1 T 2 C p ⊖ d T {\displaystyle G_{T_{2}}^{\ominus }=G_{T_{1}}^{\ominus }-S_{T_{1}}^{\ominus }(T_{2}-T_{1})-T_{2}\int _{T_{1}}^{T_{2}}{{C_{p}^{\ominus }} \over {T}}\,dT+\int _{T_{1}}^{T_{2}}C_{p}^{\ominus }\,dT}
In the above equation, the effect of temperature on Gibbs energy (and thus on the equilibrium constant) is ascribed entirely to heat capacity. To evaluate the integrals in this equation, the form of the dependence of heat capacity on temperature needs to be known.
If the standard molar heat capacity Co
p can be approximated by some analytic function of temperature (e.g. the Shomate equation), then the integrals involved in calculating other parameters may be solved to yield analytic expressions for them. For example, using approximations of the following forms:[12]
For pure substances (solids, gas, liquid):
C p ⊖ ≈ A + B T + C T − 2 {\displaystyle C_{p}^{\ominus }\approx A+BT+CT^{-2}}
For ionic species at T < 200 °C:
C p ⊖ ≈ ( 4.186 a + b S ˘ T 1 ⊖ ) ( T 2 − T 1 ) ln  ( T 2 T 1 ) {\displaystyle C_{p}^{\ominus }\approx (4.186a+b{\breve {S}}_{T_{1}}^{\ominus }){{(T_{2}-T_{1})} \over {\ln \left({\frac {T_{2}}{T_{1}}}\right)}}}
then the integrals can be evaluated and the following final form is obtained:
G T 2 ⊖ ≈ G T 1 ⊖ + ( C p ⊖ − S T 1 ⊖ ) ( T 2 − T 1 ) − T 2 ln  ( T 2 T 1 ) C p ⊖ {\displaystyle G_{T_{2}}^{\ominus }\approx G_{T_{1}}^{\ominus }+(C_{p}^{\ominus }-S_{T_{1}}^{\ominus })(T_{2}-T_{1})-T_{2}\ln \left({\frac {T_{2}}{T_{1}}}\right)C_{p}^{\ominus }}
The constants A, B, C, a, b and the absolute entropy, S̆ o
298 K, required for evaluation of Co
p(T), as well as the values of G298 K and S298 K for many species are tabulated in the literature.
Pressure dependence[edit]
The pressure dependence of the equilibrium constant is usually weak in the range of pressures normally encountered in industry, and therefore, it is usually neglected in practice. This is true for condensed reactant/products (i.e., when reactants and products are solids or liquid) as well as gaseous ones.
For a gaseous-reaction example, one may consider the well-studied reaction of hydrogen with nitrogen to produce ammonia:
N2 + 3 H2 ⇌ 2 NH3
If the pressure is increased by an addition of an inert gas, then neither the composition at equilibrium nor the equilibrium constant are appreciably affected (because the partial pressures remain constant, assuming an ideal-gas behaviour of all gases involved). However, the composition at equilibrium will depend appreciably on pressure when:
the pressure is changed by compression of the gaseous reacting system, and
the reaction results in the change of the number of moles of gas in the system.
In the example reaction above, the number of moles changes from 4 to 2, and an increase of pressure by system compression will result in appreciably more ammonia in the equilibrium mixture. In the general case of a gaseous reaction:
α A + β B ⇌ σ S + τ T
the change of mixture composition with pressure can be quantified using:
K p = p S σ p T τ p A α p B β = X S σ X T τ X A α X B β P σ + τ − α − β = K X P σ + τ − α − β {\displaystyle K_{p}={\frac {{p_{\mathrm {S} }}^{\sigma }{p_{\mathrm {T} }}^{\tau }}{{p_{\mathrm {A} }}^{\alpha }{p_{\mathrm {B} }}^{\beta }}}={\frac {{X_{\mathrm {S} }}^{\sigma }{X_{\mathrm {T} }}^{\tau }}{{X_{\mathrm {A} }}^{\alpha }{X_{\mathrm {B} }}^{\beta }}}P^{\sigma +\tau -\alpha -\beta }=K_{X}P^{\sigma +\tau -\alpha -\beta }}
where p denote the partial pressures of the components, P is the total system pressure, X denote the mole fraction, Kp is the equilibrium constant expressed in terms of partial pressures and KX is the equilibrium constant expressed in terms of mole fractions.
The above change in composition is in accordance with Le Chatelier's principle and does not involve any change of the equilibrium constant with the total system pressure. Indeed, for ideal-gas reactions Kp is independent of pressure.[13]
Pressure dependence of the water ionization constant at 25 °C. In general, ionization in aqueous solutions tends to increase with increasing pressure.
In a condensed phase, the pressure dependence of the equilibrium constant is associated with the reaction molar volume.[14] For reaction:
α A + β B ⇌ σ S + τ T
the reaction molar volume is:
Δ V ¯ = σ V ¯ S + τ V ¯ T − α V ¯ A − β V ¯ B {\displaystyle \Delta {\bar {V}}=\sigma {\bar {V}}_{\mathrm {S} }+\tau {\bar {V}}_{\mathrm {T} }-\alpha {\bar {V}}_{\mathrm {A} }-\beta {\bar {V}}_{\mathrm {B} }}
where V̄ denotes a partial molar volume of a reactant or a product.
For the above reaction, one can expect the change of the reaction equilibrium constant (based either on mole-fraction or molal-concentration scale) with pressure at constant temperature to be:
( ∂ ln  K X ∂ P ) T = − Δ V ¯ R T . {\displaystyle \left({\frac {\partial \ln K_{X}}{\partial P}}\right)_{T}={\frac {-\Delta {\bar {V}}}{RT}}.}
The matter is complicated as partial molar volume is itself dependent on pressure.
Effect of isotopic substitution[edit]
Isotopic substitution can lead to changes in the values of equilibrium constants, especially if hydrogen is replaced by deuterium (or tritium).[15] This equilibrium isotope effect is analogous to the kinetic isotope effect on rate constants, and is primarily due to the change in zero-point vibrational energy of H–X bonds due to the change in mass upon isotopic substitution.[15] The zero-point energy is inversely proportional to the square root of the mass of the vibrating hydrogen atom, and will therefore be smaller for a D–X bond that for an H–X bond.
An example is a hydrogen atom abstraction reaction R' + H–R ⇌ R'–H + R with equilibrium constant KH, where R' and R are organic radicals such that R' forms a stronger bond to hydrogen than does R. The decrease in zero-point energy due to deuterium substitution will then be more important for R'–H than for R–H, and R'–D will be stabilized more than R–D, so that the equilibrium constant KD for R' + D–R ⇌ R'–D + R is greater than KH. This is summarized in the rule the heavier atom favors the stronger bond.[15]
Similar effects occur in solution for acid dissociation constants (Ka) which describe the transfer of H+ or D+ from a weak aqueous acid to a solvent molecule: HA + H2O = H3O+ + A− or DA + D2O ⇌ D3O+ + A−. The deuterated acid is studied in heavy water, since if it were dissolved in ordinary water the deuterium would rapidly exchange with hydrogen in the solvent.[15]
The product species H3O+ (or D3O+) is a stronger acid than the solute acid, so that it dissociates more easily and its H–O (or D–O) bond is weaker than the H–A (or D–A) bond of the solute acid. The decrease in zero-point energy due to isotopic substitution is therefore less important in D3O+ than in DA so that KD < KH, and the deuterated acid in D2O is weaker than the non-deuterated acid in H2O. In many cases the difference of logarithmic constants pKD – pKH is about 0.6,[15] so that the pD corresponding to 50% dissociation of the deuterated acid is about 0.6 units higher than the pH for 50% disssociation of the non-deuterated acid.
See also[edit]
Determination of equilibrium constants
Stability constants of complexes
Equilibrium fractionation
References[edit]
Jump up ^ IUPAC gold book
Jump up ^ Rossotti, F. J. C.; Rossotti, H. (1961). The Determination of Stability Constants. McGraw-Hill. p. 5.
Jump up ^ For reactions in aqueous solution, such as the acid neutralization reaction AH + OH- ⇋ {\displaystyle \leftrightharpoons } A- + H2O, the concentration of water may be taken as being constant. The term [H2O] is omitted from expression defining an equilibrium constant, except when solutions are very concentrated.
Jump up ^ Hague, David N.; Moreton, Anthony D. (1994). "Protonation sequence of linear aliphatic polyamines by 13C NMR spectroscopy". J. Chem. Soc., Perkin Trans. 2 (2): 265–70. doi:10.1039/P29940000265.
Jump up ^ Borkovec, Michal; Koper, Ger J. M. (2000). "A Cluster Expansion Method for the Complete Resolution of Microscopic Ionization Equilibria from NMR Titrations". Anal. Chem. 72 (14): 3272–9. doi:10.1021/ac991494p. PMID 10939399.
Jump up ^ Baes, C. F.; Mesmer, R. E. (1976). The Hydrolysis of Cations. Wiley. [page needed]
Jump up ^ Schwarzenbach, G.; Flaschka, H. (1969). Complexometric titrations. Methuen. [page needed]
Jump up ^ Denbigh, K. (1981). "Chapter 4". The principles of chemical equilibrium (4th ed.). Cambridge: Cambridge University Press. ISBN 0-521-28150-4.
Jump up ^ Butler, J. N. (1998). Ionic Equilibrium. John Wiley and Sons.
Jump up ^ "Project: Ionic Strength Corrections for Stability Constants". International Union of Pure and Applied Chemistry. Archived from the original on 29 October 2008. Retrieved 2008-11-23.
Jump up ^ Majer, V.; Sedelbauer, J.; Wood (2004). "Calculations of standard thermodynamic properties of aqueous electrolytes and nonelectrolytes". In Palmer, D. A.; Fernandez-Prini, R.; Harvey, A. Aqueous Systems at Elevated Temperatures and Pressures: Physical Chemistry of Water, Steam and Hydrothermal Solutions. Elsevier. [page needed]
Jump up ^ Roberge, P. R. (November 2011). "Appendix F". Handbook of Corrosion Engineering. McGraw-Hill. p. 1037ff.
Jump up ^ Atkins, P. W. (1978). Physical Chemistry, (6th ed.). Oxford University Press. p. 210.
Jump up ^ Van Eldik, R.; Asano, T.; Le Noble, W. J. (1989). "Activation and reaction volumes in solution. 2". Chem. Rev. 89 (3): 549–688. doi:10.1021/cr00093a005.
^ Jump up to: a b c d e Laidler K.J. Chemical Kinetics (3rd ed., Harper & Row 1987), p.428–433 ISBN 0-06-043862-2
Data sources[edit]
IUPAC SC-Database A comprehensive database of published data on equilibrium constants of metal complexes and ligands
NIST Standard Reference Database 46: Critically selected stability constants of metal complexes
Inorganic and organic acids and bases pKa data in water and DMSO
NASA Glenn Thermodynamic Database webpage with links to (self-consistent) temperature-dependent specific heat, enthalpy, and entropy for elements and molecules
External links[edit]
Science Aid: Equilibrium Constants Explanation of Kc and Kp for high-school level
[hide]
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e
Chemical equilibria
Concepts
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Buffer solution
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Equilibrium chemistry
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Hammett acidity function
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Phase diagram
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Phase rule
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values: \sum_j n_j(\mu_j^\ominus +RT\ln a_j)=\sum_k m_k(\mu_k^\ominus +RT\ln a_k)

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values: \Delta G^\ominus = \sum_k m_k\mu_k^\ominus-\sum_j n_j\mu_j^\ominus

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values: {\displaystyle \Delta G^{\circ }=-RT\ln K}

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values: \ln K = {{-\Delta_\mathrm{r} G^\ominus} \over {RT}}

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values: {\displaystyle C_{p}^{\ominus }\approx A+BT+CT^{-2}}

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values: \left(\frac{\partial \ln K_X}{\partial P} \right)_T = \frac{-\Delta \bar{V}} {RT}.

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Macintosh 128K
From Wikipedia, the free encyclopedia
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Macintosh 128K
A Macintosh 128K
Also known as
Apple Macintosh
Manufacturer
Apple Computer, Inc.
Product family
Compact Macintosh
Release date
January 24, 1984; 34 years ago (1984-01-24)[1][2]
Introductory price
US$2,495 (equivalent to $5,877 in 2017)
Discontinued
October 1, 1985 (1985-10-01)[3]
Operating system
System Software 1.0[4]
CPU
Motorola 68000 @ 7.8336 MHz (6 MHz effectively)[5]
Memory
128 KB RAM (built-in)
Dimensions
Height: 13.6 inches (35 cm)
Width: 9.6 inches (24 cm)
Depth: 10.9 inches (28 cm)
Weight
16.5 pounds (7.5 kg)
Predecessor
Apple Lisa
Successor
Macintosh 512K
The Macintosh 128K, originally released as the Apple Macintosh, is the original Apple Macintosh personal computer. Its beige case consisted of a 9 in (23 cm) CRT monitor and came with a keyboard and mouse. A handle built into the top of the case made it easier for the computer to be lifted and carried. It had an initial selling price of $2,495 (equivalent to $5,877 in 2017). The Macintosh was introduced by the now-famous $370,000 (equivalent to $871,550 in 2017) television commercial by Ridley Scott, "1984", that most notably aired on CBS during the third quarter of Super Bowl XVIII on January 22, 1984.[6] Sales of the Macintosh were strong from its initial release on January 24, 1984, and reached 70,000 units on May 3, 1984.[7] Upon the release of its successor, the Macintosh 512K, it was rebranded as the Macintosh 128K.
Contents
[hide]
1 Processor and memory
2 Peripherals
3 Storage
4 Cooling
5 Software
6 Models
7 Expansion
8 OEM upgrades
9 Credits
10 Reception
11 Timeline of compact Macintosh models
12 See also
13 References
14 External links
Processor and memory[edit]
The centerpiece of the machine was a Motorola 68000 microprocessor running at 7.8336 MHz, connected to 128 KB RAM shared by the processor and the display controller. The boot procedure and some operating system routines were contained in an additional 64 KB ROM chip. Apple did not offer RAM upgrades. Unlike the Apple II, no source code listings of the Macintosh system ROMs were offered.
The RAM in the Macintosh consisted of sixteen 4164 64k×1 DRAMs.
The 68000 and video controller took turns accessing DRAM every four CPU cycles during display of the frame buffer, while the 68000 had unrestricted access to DRAM during vertical and horizontal blanking intervals. Such an arrangement reduced the overall performance of the CPU as much as 35% for most code as the display logic often blocked the CPU's access to RAM. This made the machine run more slowly than several of its competitors, despite the nominally high clock rate.
Back case of an unaltered original Macintosh (sold January–November 1984). Those made after November 1984 have the label "Macintosh 128K" on the back of the case.
Peripherals[edit]
The built-in display was a one-bit black-and-white, 9 in (23 cm) CRT with a fixed resolution of 512×342 pixels, establishing the desktop publishing standard of 72 PPI.[8] Expansion and networking were achieved using two non-standard RS-422 DE-9 serial ports named "printer" and "modem"; they did not support hardware handshaking. An external floppy disk drive could be added using a proprietary connector (19-pin D-sub). The keyboard and mouse used simple proprietary protocols, allowing some third-party upgrades. The original keyboard had no arrow keys, numeric keypad or function keys. This was an intentional decision by Apple, as these keys were common on older platforms and it was thought that the addition of these keys would encourage software developers to simply port their existing applications to the Mac, rather than design new ones around the GUI paradigm.[9] Later, Apple would make a numeric keypad available for the Macintosh 128K. The keyboard sold with the newer Macintosh Plus model would include the numeric keypad and arrow keys, but still no function keys. As with the Apple Lisa before it, the mouse had a single button. Standard headphones could also be connected to a monaural jack. Apple also offered their 300 and 1200 bit/s modems originally released for the Apple II line. Initially, the only printer available was the Apple ImageWriter, a dot matrix printer which was designed to produce 144 dpi WYSIWYG output from the Mac's 72 dpi screen. Eventually, the LaserWriter and other printers were capable of being connected using AppleTalk, Apple's built-in networking system.
Storage[edit]
The Macintosh contained a single 400 KB, single-sided 3.5-inch floppy disk drive, dedicating no space to other internal mechanical storage. The Mac OS was disk-based from the beginning, as RAM had to be conserved, but this "Startup Disk" could still be temporarily ejected. (Ejecting the root filesystem remained an unusual feature of the classic Mac OS until System 7.) One floppy disk was sufficient to store the System Software, an application and the data files created with the application. Indeed, the 400 KB drive capacity was larger than the PC XT's 360 KB 5.25-inch drive. However, more sophisticated work environments of the time required separate disks for documents and the system installation. Due to the memory constraints (128 KB) of the original Macintosh, and the fact that the floppies could hold 400 KB, users frequently had to swap disks in and out of the floppy drive. For this reason, external floppy drives were frequently used. The Macintosh External Disk Drive (mechanically identical to the internal one, piggybacking on the same controller) was a popular add-on at US $495. Third-party hard drives were considerably more expensive and usually connected to the slower serial port (as specified by Apple), though a few manufacturers chose to use the faster non-standard floppy port. The 128K can only use the original Macintosh File System for storage.
Macintosh motherboard
Cooling[edit]
The unit did not include a fan, relying instead on convection cooling, which made it quiet while in operation. Steve Jobs insisted that the Macintosh ship without a fan, which persisted until the introduction of the Macintosh SE in 1987. This was allegedly a source of many common, costly component failures in the first four Macintosh models. This was enough of a problem to prompt the introduction of a third-party, external cooling fan. This fan unit fitted inside the Macintosh's carrying-handle slot and produced a forced draft through the computer's existing ventilation holes.[10]
Software[edit]
The Macintosh shipped with the very first System and Finder application, known to the public as "System 1.0" (formally known as System 0.97 and Finder 1.0). The original Macintosh saw three upgrades to both before it was discontinued. Apple recommends System 2.0 and Finder 4.2, with System 3.2 and Finder 5.3 as the maximum. System 4.0 officially dropped support for the Macintosh 128K because it was distributed on 800 KB floppy disks, which could not be used by the 128K.
The applications MacPaint and MacWrite were bundled with the Mac. Other programs available included MacProject, MacTerminal and Microsoft Word. Programming languages available at the time included MacBASIC, MacPascal[11] and the Macintosh 68000 Development System.[12] The Macintosh also came with a manual and a unique guided tour cassette tape which worked together with the guided tour diskette as a tutorial for both the Macintosh itself and the bundled applications, since most new Macintosh users had never used a mouse before, much less manipulated a graphical user interface.
Back case label of a Macintosh made after November 1984
Models[edit]
The computer was released in January 1984 as simply the Apple Macintosh. Following the release of the Macintosh 512K in September, which expanded the memory from 128 KB to 512 KB, the original Macintosh was re-branded Macintosh 128K and nicknamed the "thin Mac." The new 512K model was nicknamed the "fat Mac." While functionally the same, as closed systems, the Macintosh and Macintosh 128K were technically two different computers, with the re-badged 128K containing a completely redesigned logic board to easily accommodate both 128 KB and 512 KB RAM configurations during manufacturing. Though the RAM was still permanently soldered to the logic board, the new design allowed for easier (though unsanctioned) third-party upgrades to 512 KB. In addition, most of the newer models contained the 1984 revision B of the ROM to accommodate changes in the 400 KB floppy disk drive.[13] System software contains support for an unreleased Macintosh 256K.[14]
The increased RAM of the 512K was vitally important for the Macintosh as it finally allowed for more powerful software applications, such as the then-popular program Microsoft Multiplan. However, Apple continued to market the 128K for over a year as an entry-level computer, the mid-level 512K and high-end Lisa (and claiming that it could be easily expanded should the user ever need more RAM).
Expansion[edit]
Jobs stated that because "customization really is mostly software now ... most of the options in other computers are in Mac", unlike the Apple II the Macintosh 128K did not need slots, which he described as costly and requiring larger size and more power.[15] It was not upgradable by the user and only Apple service centers were permitted to open the case.[16] All accessories were external, such as the MacCharlie that added IBM PC compatibility.[17] There was no provision for adding internal storage, more RAM or any upgrade cards, however some of the Macintosh engineers objected to Jobs's ideas and secretly developed workarounds for them. As an example, the Macintosh was supposed to have only 17 address lines on the motherboard, enough to support 128k of system RAM, but the design team added an additional two address lines without Jobs's knowledge, making it possible to expand the computer to 512k, although the actual act of upgrading system RAM was difficult and required piggybacking additional RAM chips overtop the onboard 4164 chips. In September 1984, after months of complaints over the Mac's inadequate RAM, Apple released an official 512k machine. Although this had always been planned from the beginning, Steve Jobs maintained if the user desired more RAM than the Mac 128 provided, he should simply pay extra money for a Mac 512 rather than upgrade the computer himself. When the Mac 512 was released, Apple rebranded the original model as "Macintosh 128k" and modified the motherboard to allow easier RAM upgrades. Improving on the hard-wired RAM thus required a motherboard replacement (which was priced similarly to a new computer), or a third-party chip replacement upgrade, which was not only expensive but would void Apple's warranty. The difficulty of fitting software into its limited free memory, coupled with the new interface and event driven programming model, discouraged software vendors from supporting it, leaving the 128K with a relatively small software library. Whereas the Macintosh Plus, and to a lesser extent the Macintosh 512K, are compatible with much later software, the 128K is limited to specially crafted programs. A stock Mac 128K with the original 64K ROM is neither compatible with Apple's external 800 KB drive with HFS nor with Apple's Hard Disk 20. A Mac 128K that has been upgraded with the newer 128K ROM (called a Macintosh 128Ke) can use internal and external 800 KB drives with HFS, as well as the HD20. Both can print on an AppleShare network, but neither can do file sharing because of their limited RAM.
OEM upgrades[edit]
By early 1985 much Macintosh software required 512K of memory. Apple sold an official memory upgrade for the Macintosh 128K, which included a motherboard replacement effectively making it a Macintosh 512K, for the price of US $995.[18][19][20] Additionally, Apple offered an 800 KB floppy disk drive kit, including updated 128K ROMs. Finally, a Mac 128K could be upgraded to a Macintosh Plus by swapping the logic board as well as the case back (to accommodate the slightly different port configuration) and optionally adding the Macintosh Plus extended keyboard. Any of the kits could be purchased alone or together at any time, for a partial or full upgrade for the Macintosh 128K. All upgrades were required to be performed by professional Apple technicians,[21] who reportedly refused to work on any Macintosh upgraded to 512K without Apple's official upgrade, which at US$700 was much more expensive than about $300 for third-party versions.[22]
Credits[edit]
Signatures inside the Macintosh 128K case
The original Macintosh was unusual in that it included the signatures of the Macintosh Division as of early 1982 molded on the inside of the case. The names were Peggy Alexio, Colette Askeland, Bill Atkinson, Steve Balog, Bob Belleville, Mike Boich, Bill Bull, Matt Carter, Berry Cash, Debi Coleman, George Crow, Donn Denman, Christopher Espinosa, Bill Fernandez, Martin Haeberli, Andy Hertzfeld, Joanna Hoffman, Rod Holt, Bruce Horn, Hap Horn, Brian Howard, Steve Jobs, Larry Kenyon, Patti King, Daniel Kottke, Angeline Lo, Ivan Mach, Jerrold Manock, Mary Ellen McCammon, Vicki Milledge, Mike Murray, Ron Nicholson Jr., Terry Oyama, Benjamin Pang, Jef Raskin, Ed Riddle, Brian Robertson, Dave Roots, Patricia Sharp, Burrell Smith, Bryan Stearns, Lynn Takahashi, Guy "Bud" Tribble, Randy Wigginton, Linda Wilkin, Steve Wozniak, Pamela Wyman and Laszlo Zidek.
The Macintosh 128/512K models also included an Easter egg in the OS ROM. If the user went to the system debugger and typed G 4188A4, a graphic reading "Stolen from Apple Computers" would appear in the upper left corner of the screen. This was designed to prevent unauthorized cloning of the Macintosh after numerous Apple II clones appeared, many of which simply stole Apple's copyrighted system ROMs. Steve Jobs allegedly planned that if a Macintosh clone appeared on the market and a court case happened, he could access this Easter egg on the computer to prove that it was using pirated Macintosh ROMs.[citation needed]
Reception[edit]
Erik Sandberg-Diment of The New York Times in January 1984 stated that Macintosh "presages a revolution in personal computing". Although preferring larger screens and calling the lack of color a "mistake", he praised that the "refreshingly crisp and clear" display and lack of fan noise.[23] While unsure whether it would become "a second standard to Big Blue", Ronald Rosenberg of The Boston Globe wrote in February of "a euphoria that Macintosh will change how America computes. Anyone that tries the pint-size machine gets hooked by its features".[24] Gregg Williams of BYTE that month found the h ardware and software design (which it predicted would be "imitated but not copied") impressive, but criticized the lack of a standard second disk drive. He predicted that the computer would popularize the 3½-inch floppy disk drive standard, that the Macintosh would improve Apple's reputation, and that it "will delay IBM's domination of the personal computer market." Williams concluded that the Macintosh was "the most important development in computers in the last five years. [It] brings us one step closer to the ideal of computer as appliance."[16] In a follow-up article in the May 1984 issue of BYTE, Williams added, "Initial reaction to the Macintosh has been strongly, but not overpoweringly, favorable. A few traditional computer users see the mouse, the windows, and the desktop metaphor as silly, useless frills, and others are outraged at the lack of color graphics, but most users are impressed by the machine and its capabilities. Still, some people have expressed concern about the relatively small 128K-byte RAM (randomaccess read/write memory) size, the lack of any computer language sent as part of the basic unit, and the inconvenience of the single disk drive."[25]
Jerry Pournelle, also of BYTE, added that "The Macintosh is a bargain only if you can get it at the heavily discounted price offered to faculty and students of the favored 24 universities in the Macintosh consortium." He noted, however, that the Macintosh attracted people "who previously hated computers ... There is, apparently, something about mice and pull-down menus and icons that appeal to people previously intimidated by A> and the like".[26]
Timeline of compact Macintosh models
See also: Timeline of Macintosh models
See also: Compact Macintosh
See also[edit]
Technical information on the Mac 128K
References[edit]
Jump up ^ Linzmayer, Owen W. (2004). Apple Confidential 2.0. No Starch Press. p. 113. ISBN 1-59327-010-0.
Jump up ^ "The Macintosh Product Introduction Plan". Stanford University Libraries & Academic Information Resources. Archived from the original on July 21, 2010.
Jump up ^ "Macintosh 128K: Technical Specifications". apple.com. Retrieved March 27, 2015.
Jump up ^ "Official Apple Support". apple.com.
Jump up ^ "Byte Magazine Volume 09 Number 02 - Benchmarks". Internet Archive.
Jump up ^ Burnham, David (March 4, 1984). "The computer, the consumer and privacy". The New York Times. Washington, D.C. Retrieved March 27, 2015.
Jump up ^ Polsson, Ken (July 29, 2009). "Chronology of Apple Computer Personal Computers". Archived from the original on July 10, 2009. Retrieved August 27, 2009.
Jump up ^ "Macintosh / Macintosh 128K". The Mac 512. Retrieved 20 December 2016.
Jump up ^ "History of computer design: Apple Macintosh". landsnail.com.
Jump up ^ "The Fanny Mac System Saver fan for 1984 Macintosh 128k 512k Plus M0001 Rare!". Worthpoint.com. Retrieved February 1, 2014.
Jump up ^ "Mac GUI". macgui.com.
Jump up ^ "Mac GUI". macgui.com.
Jump up ^ "400K Drive Problem/Cure: Fails to Read/Write or MacTest". apple.com.
Jump up ^ Small, David (1989). Spectre GCR. Gadgets by Small. p. 75.
Jump up ^ "An Interview: The Macintosh Design Team". BYTE. Interview with Lemmons, Phil. February 1984. pp. 58–80. Retrieved 7 July 2016.
^ Jump up to: a b Williams, Gregg (February 1984). "The Apple Macintosh Computer". BYTE. p. 30. Retrieved October 22, 2013.
Jump up ^ Sandberg-Diment, Erik (September 24, 1985). "Linking Mac to the IBM PC". The New York Times (review). Retrieved October 27, 2013.
Jump up ^ Sandberg-Diment, Erik (1985-03-19). "Apple Might Learn a Thing or Two from I.B.M." The New York Times. p. C4. ISSN 0362-4331. Retrieved 2017-07-03.
Jump up ^ "Mac GUI". macgui.com.
Jump up ^ "Mac GUI". macgui.com.
Jump up ^ Macintosh Plus: Description (Discontinued) The Macintosh Plus Logic Board Kit
Jump up ^ Webster, Bruce (September 1985). "West Coast Faire, Mac Stuff, and the Amiga". BYTE. p. 401. Retrieved 20 March 2016.
Jump up ^ Sandberg-Diment, Erik (1984-01-24). "Personal Computers; Hardware Review: Apple Weighs in with Macintosh". The New York Times.
Jump up ^ Rosenberg, Ronald (1984-02-28). "Doubts Raised About PCjr". The Boston Globe.
Jump up ^ "Update on Apple Macintosh and Lisa 2" (PDF).
Jump up ^ Pournelle, Jerry (Aug 1984). "Between Conventions". BYTE. p. 313. Retrieved 24 February 2016.
External links[edit]
Wikimedia Commons has media related to Macintosh 128K.
Full Macintosh 128K specifications (Apple Computer) at the Wayback Machine (archived May 14, 2008)
Macintosh 128K profile, Low End Mac.
Mac 128K Information page at Mac512.com
Original Review of the Macintosh by Lawrence J. Magid (January 29, 1984) at the Wayback Machine (archived September 20, 2008)
Online attempt at simulating Macintosh System 1
Mac Essentials, Lost 1984 Videos
"The Vintage Mac Museum: Mac 128K Slideshows". Archived from the original on November 13, 2013. Retrieved 2016-01-06.
Apple Macintosh before System 7 Macintosh 128K Hardware
Tips For the 128K Support For 128K Diehard Users
The M0001 Registry Owners of Vintage Macintosh
Inside the Macintosh 128K
The Original Macintosh, anecdotes and the people who made it
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