"is defined in relation to the pressure increase needed to cause a given relative decrease in volume. The mass density (or just ""density"") of a material is defined as mass per unit volume and is expressed in grams per cubic centimeter (g/cm). In all three classic states of matter—gas, liquid, or solid—the density varies with a change in temperature or pressure, and gases are the most susceptible to those changes. The spectrum of densities is wide-ranging: from 10 g/cm for neutron stars, 1.00 g/cm for water to 1.2×10 g/cm for air. Also relevant here are area density which is mass"
"Molar mass In chemistry, the molar mass ""M"" is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. The base SI unit for molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol. In simple terms, molar mass of a substance is the total weight of that substance (in either kilogram or gram) for one mole of that substance. That is, the weight of a substance for 6.02214076×10^23 molecules or atoms of that substance. As an example, the molar mass of"
"101.105 – Declaration of net quantity of contents when exempt: See also 21CFR201 Part 201.51 – ""Declaration of net quantity of contents"" for general labeling and prescription labeling requirements. Mass versus weight In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. In scientific contexts, mass is the amount of ""matter"" in an object (though ""matter"" may be difficult to define), whereas weight is the force exerted on an object by gravity. In other words, an object with a mass of 1.0 kilogram will weigh approximately"
"determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: formula_2, where formula_3 is an elementary volume at position formula_4. The mass of the body then can be expressed as In practice, bulk materials such as sugar, sand, or snow contain voids. Many materials exist in nature as flakes, pellets, or granules. Voids are regions which contain something other than the considered material. Commonly the void is air, but it could also be vacuum, liquid, solid, or a different gas or"
"Mass Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does"
"specific volume of a substance is expressed in terms such as formula_6, formula_7, formula_8, or formula_9 . Specific volume is commonly applied to: Imagine a variable-volume, airtight chamber containing a certain number of atoms of oxygen gas. Consider the following four examples: Specific volume is a property of materials, defined as the number of cubic meters occupied by one kilogram of a particular substance. The standard unit is the meter cubed per kilogram (m/kg or m·kg). Sometimes specific volume is expressed in terms of the number of cubic centimeters occupied by one gram of a substance. In this case, the"
"gas law. Volume Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i. e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular,"
"Volume Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i. e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and"
"for use within SI"". SI distinguishes between mass and weight ""mass"" being a measure of the amount of material contained in an object and ""weight"" the gravitational force on that object. We normally ""weigh"" objects by comparing the gravitational force on that object with the gravitational force on an object of known mass (such as a 1 kg ""weight""). Although this concept was understood by ancient scientists (Archimedes' principle is based on it), the wording was only formalised in 1901. The SI base unit of mass is the kilogram which was originally defined in 1795 as the mass of one"
"pressure, because the resulting numbers are extremely large (on the order of 10). Using the number density of an ideal gas at and as a yardstick: is often introduced as a unit of number density, for any substances at any conditions (not necessarily limited to an ideal gas at and ). Using the number density as a function of spatial coordinates, the total number of objects ""N"" in the entire volume ""V"" can be calculated as where d""V"" = d""x"" d""y"" d""z"" is a volume element. If each object possesses the same mass ""m"", the total mass ""m"" of all"
"Mass versus weight In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. In scientific contexts, mass is the amount of ""matter"" in an object (though ""matter"" may be difficult to define), whereas weight is the force exerted on an object by gravity. In other words, an object with a mass of 1.0 kilogram will weigh approximately 9.81 newtons on the surface of the Earth (its mass multiplied by the gravitational field strength), since the newton is a unit of force, while the kilogram is a"
"volume, area, mass, and force. These may be combined to understand the concept of pressure, which is force per unit area and density, which is mass per unit volume. It has been experimentally determined that, at low enough pressures and densities, all gases behave as ideal gases. The behavior of an ideal gas is given by the ideal gas law: where ""P"" is pressure, ""V"" is volume, ""N"" is the number of particles (total mass divided by mass per particle), ""k"" is Boltzmann's constant, and ""T"" is temperature. In fact, this equation is more than a phenomenological equation, it gives"
"the total mass of all ""other"" constituents in a mixture: If formula_2 is much smaller than formula_35, the mass ratio is almost identical to the mass fraction. The SI unit is kg/kg. However, the deprecated parts-per notation is often used to describe small mass ratios. Concentration depends on the variation of the volume of the solution with temperature due mainly to thermal expansion. Concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration. A concentration"
"volume fraction (percentage by volume, vol%) are others. For elemental analysis, mass fraction (or ""mass percent composition"") can also refer to the ratio of the mass of one element to the total mass of a compound. It can be calculated for any compound using its empirical formula or its chemical formula. ""Percent concentration"" does not refer to this quantity. This improper name persists, especially in elementary textbooks. In biology, the unit ""%"" is sometimes (incorrectly) used to denote mass concentration, also called ""mass/volume percentage."" A solution with 1 g of solute dissolved in a final volume of 100 mL of"
"of measurements to be made when they might appear ambiguous and unclear otherwise. A basic example is mass density. It is not clear how compare how much matter constitutes a variety of substances given only their masses or only their volumes. Given both for each substance, the mass ""m"" per unit volume ""V"", or mass density ""ρ"" provides a meaningful comparison between the substances, since for each, a fixed amount of volume will correspond to an amount of mass depending on the substance. To illustrate this; if two substances A and B have masses ""m"" and ""m"" respectively, occupying volumes"
"is an ""extensive property"". The symbol used to represent density in equations is ρ (rho) with SI units of kilograms per cubic meter. This term is the reciprocal of specific volume. Since gas molecules can move freely within a container, their mass is normally characterized by density. Density is the amount of mass per unit volume of a substance, or the inverse of specific volume. For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume. This variation of density is referred to as compressibility. Like"
"without reference to an exact operating volume, which may not be known (nor significant) at some stages of analysis. The specific volume of a substance is equal to the reciprocal of its mass density. Specific volume may be expressed in formula_14, formula_15, formula_16, or formula_17 . where, formula_3 is the volume, formula_20 is the mass and formula_21 is the density of the material. For an ideal gas, where, formula_23 is the specific gas constant, formula_24 is the temperature and formula_25 is the pressure of the gas. Specific volume may also refer to molar volume. The volume of gas increases proportionally"
"is given by: The values of (mass and molar) concentration different in space triggers the phenomenon of diffusion. Mass concentration (chemistry) In chemistry, the mass concentration (or ) is defined as the mass of a constituent divided by the volume of the mixture : For a pure chemical the mass concentration equals its density (mass divided by volume); thus the mass concentration of a component in a mixture can be called the density of a component in a mixture. This explains the usage of (the lower case Greek letter rho), the symbol most often used for density. The volume in"
"of carbon-12 in 0.012 kg of carbon-12. This can be expressed mathematically as Molecular masses of proteins are often expressed in kilodaltons (kDa or kD). For example, a molecule of a protein with molar mass has a mass of 64 kDa. In research and commerce, the degree of polymerization of synthetic polymers is conventionally expressed in daltons. The US Supreme Court based a major precedent of appellate law on a disputed case of counting daltons for a molecular distribution. Atomic mass unit The unified atomic mass unit or dalton (symbol: u, or Da) is a standard unit of mass that"
"""unified"" prefix is an obsolete unit based on oxygen, which was replaced in 1961. The molecular mass (abbreviated M) of a substance, formerly also called molecular weight and abbreviated as MW, is the mass of one molecule of that substance, relative to the unified atomic mass unit u (equal to 1/12 the mass of one atom of C). Due to this relativity, the molecular mass of a substance is commonly referred to as the relative molecular mass, and abbreviated to M. The average mass of a molecule is obtained by summing the average atomic masses of the constituent elements. For"
"explicitly showing the density formula_25. Pressure Pressure (symbol: ""p"" or ""P"") is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ""gage"" pressure) is the pressure relative to the ambient pressure. Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre; similarly, the pound-force per square inch (psi) is the traditional unit of pressure in the imperial and"
"containing of hydrogen atoms in it, weighing exactly 1.008 grams (same as the Ar of one hydrogen atom). The molar mass of a substance is the mass of a sample divided by the amount of substance in that sample. This is a constant for any given substance. Since the unified atomic mass unit (symbol: u, or Da) is defined as 1/12 of the mass of the C atom, it follows that the molar mass of a substance, measured in grams per mole, is numerically equal to its mean atomic or molecular mass expressed in Da. One can determine the amount"
"placed on Y. The table below displays densities and specific volumes for various common substances that may be useful. The values were recorded at standard temperature and pressure, which is defined as air at 0 °C (273.15 K, 32 °F) and 1 atm (101.325 kN/m, 101.325 kPa, 14.7 psia, 0 psig, 30 in Hg, 760 torr). <nowiki>*</nowiki> values not taken at standard temperature and pressure Specific volume In thermodynamics, the specific volume of a substance is the ratio of the substance's volume to its mass. It is the reciprocal of density and an intrinsic property of matter as well. Specific"
"Mass flow rate In physics and engineering, mass flow rate is the mass of a substance which passes per unit of time. Its unit is kilogram per second in SI units, and slug per second or pound per second in US customary units. The common symbol is formula_1 (ṁ, pronounced ""m-dot""), although sometimes ""μ"" (Greek lowercase mu) is used. Sometimes, mass flow rate is termed ""mass flux"" or ""mass current"", see for example ""Fluid Mechanics, Schaum's et al"". In this article, the (more intuitive) definition is used. Mass flow rate is defined by the limit: The reason for the dot"
"Amount of substance Amount of substance is a standard-defined quantity that measures the size of an ensemble of particles, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount. The International System of Units (SI) defines the amount of substance to be proportional to the number of entities present. The SI unit for amount of substance is the mole. It has the unit symbol mol. The proportionality constant is the inverse of the Avogadro constant. The mole is defined as the amount of substance that contains an equal number of elementary entities as there"
"Molecular mass Relative molecular mass or molecular weight is the mass of a molecule. It is calculated as the sum of the relative atomic masses of each constituent element multiplied by the number of atoms of that element in the molecular formula. The molecular mass of small to medium size molecules, measured by mass spectrometry, determines stoichiometry. For large molecules such as proteins, methods based on viscosity and light-scattering can be used to determine molecular mass when crystallographic data are not available. Both atomic and molecular masses are usually obtained relative to the mass of the isotope C (carbon 12),"
"is assigned the average of the properties of atoms in a small region nearby. In particular, it has a density and velocity that depend on time and position . The momentum per unit volume is . Consider a column of water in hydrostatic equilibrium. All the forces on the water are in balance and the water is motionless. On any given drop of water, two forces are balanced. The first is gravity, which acts directly on each atom and molecule inside. The gravitational force per unit volume is , where is the gravitational acceleration. The second force is the sum"
"the extensive quantities such as energy, volume, or entropy (versus intensive quantities of temperature and pressure) are placed on a unit mass basis, and so too are the calculations, making those more general and therefore of more general use. Hence, each term involving an extensive quantity could be divided by the mass, giving the terms units of joules/kg (specific energy), meters/kg (specific volume), or joules/(kelvin·kg) (specific entropy, heat capacity) etc. and would be represented using lower case letters, u, v, s, etc. Equation 1 can now be related to the specific heat equation for constant volume. The specific heats are"
"Bulk density Bulk density is a property of powders, granules, and other ""divided"" solids, especially used in reference to mineral components (soil, gravel), chemical substances, (pharmaceutical) ingredients, foodstuff, or any other masses of corpuscular or particulate matter. It is defined as the mass of many particles of the material divided by the total volume they occupy. The total volume includes particle volume, inter-particle void volume, and internal pore volume. Bulk density is not an intrinsic property of a material; it can change depending on how the material is handled. For example, a powder poured into a cylinder will have a"
"Relative atomic mass Relative atomic mass (symbol: ""A"") or atomic weight is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to one unified atomic mass unit. The unified atomic mass unit (symbol: ""u"" or ""Da"") is defined as being of the atomic mass of a carbon-12 atom. Since both values in the ratio are expressed in the same unit (""u""), the resulting value is dimensionless; hence the value is said to be ""relative"". For a single given sample, the relative atomic mass of a given element"
"Atomic mass unit The unified atomic mass unit or dalton (symbol: u, or Da) is a standard unit of mass that quantifies mass on an atomic or molecular scale (atomic mass). One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1g/mol. It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest, and has a value of , or approximately 1.66 yoctograms. The CIPM has categorised it as a non-SI unit"
"mass. This was clear at the beginning of the 20th century, before the advent of the theory of relativity. Mass, ""m"", denoted something like an amount of substance or quantity of matter. At the same time, mass was the quantitative measure of inertia of a body. The mass of a body determines the momentum, formula_1, of the body at given velocity, formula_2; it is a proportionality factor in the formula: The factor ""m"" is referred to as inertial mass. But mass, as related to the ""inertia"" of a body, can also be defined by the formula: where ""F"" is the"
"these is a different concept. In scientific contexts, mass refers loosely to the amount of ""matter"" in an object (though ""matter"" may be difficult to define), whereas weight refers to the force experienced by an object due to gravity. An object with a mass of 1.0 kilogram will weigh approximately 9.81 newtons (newton is the unit of force, while kilogram is the unit of mass) on the surface of the Earth (its mass multiplied by the gravitational field strength). Its weight will be less on Mars (where gravity is weaker), more on Saturn, and negligible in space when far from"