Molar volume

Last updated
Molar volume
Common symbols
Vm,
SI unit m3/mol
Other units
dm3/mol, cm3/mol
Dimension L3N−1

In chemistry and related fields, the molar volume, symbol Vm, [1] or of a substance is the ratio of the volume (V) occupied by a substance to the amount of substance (n), usually at a given temperature and pressure. It is also equal to the molar mass (M) divided by the mass density (ρ):

Contents

The molar volume has the SI unit of cubic metres per mole (m3/mol), [1] although it is more typical to use the units cubic decimetres per mole (dm3/mol) for gases, and cubic centimetres per mole (cm3/mol) for liquids and solids.

Definition

Change in volume with increasing ethanol fraction. Excess Volume Mixture of Ethanol and Water-int.svg
Change in volume with increasing ethanol fraction.

The molar volume of a substance i is defined as its molar mass divided by its density ρi0: For an ideal mixture containing N components, the molar volume of the mixture is the weighted sum of the molar volumes of its individual components. For a real mixture the molar volume cannot be calculated without knowing the density: There are many liquid–liquid mixtures, for instance mixing pure ethanol and pure water, which may experience contraction or expansion upon mixing. This effect is represented by the quantity excess volume of the mixture, an example of excess property.

Relation to specific volume

Molar volume is related to specific volume by the product with molar mass. This follows from above where the specific volume is the reciprocal of the density of a substance:

Ideal gases

For ideal gases, the molar volume is given by the ideal gas equation; this is a good approximation for many common gases at standard temperature and pressure. The ideal gas equation can be rearranged to give an expression for the molar volume of an ideal gas: Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is based on the gas constant: R = 8.31446261815324 m3⋅Pa⋅K−1⋅mol−1, or about 8.20573660809596×10−5 m3⋅atm⋅K−1⋅mol−1.

The molar volume of an ideal gas at 100  kPa (1  bar) is

0.022710954641485... m3/mol at 0 °C,
0.024789570296023... m3/mol at 25 °C.

The molar volume of an ideal gas at 1 atmosphere of pressure is

0.022413969545014... m3/mol at 0 °C,
0.024465403697038... m3/mol at 25 °C.

Crystalline solids

For crystalline solids, the molar volume can be measured by X-ray crystallography. The unit cell volume (Vcell) may be calculated from the unit cell parameters, whose determination is the first step in an X-ray crystallography experiment (the calculation is performed automatically by the structure determination software). This is related to the molar volume by where NA is the Avogadro constant and Z is the number of formula units in the unit cell. The result is normally reported as the "crystallographic density".

Molar volume of silicon

Ultra-pure silicon is routinely made for the electronics industry, and the measurement of the molar volume of silicon, both by X-ray crystallography and by the ratio of molar mass to mass density, has attracted much attention since the pioneering work at NIST in 1974. [2] The interest stems from that accurate measurements of the unit cell volume, atomic weight and mass density of a pure crystalline solid provide a direct determination of the Avogadro constant. [3]

The CODATA recommended value for the molar volume of silicon is 1.205883199(60)×10−5 m3⋅mol−1, with a relative standard uncertainty of 4.9×10−8. [4]

See also

Related Research Articles

Density is a substance's mass per unit of volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume: where ρ is the density, m is the mass, and V is the volume. In some cases, density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight.

In chemistry, the mole fraction or molar fraction, also called mole proportion or molar proportion, is a quantity defined as the ratio between the amount of a constituent substance, ni, and the total amount of all constituents in a mixture, ntot :

<span class="mw-page-title-main">Specific heat capacity</span> Heat required to increase temperature of a given unit of mass of a substance

In thermodynamics, the specific heat capacity of a substance is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. It is also referred to as massic heat capacity or as the specific heat. More formally it is the heat capacity of a sample of the substance divided by the mass of the sample. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.

<span class="mw-page-title-main">Relative density</span> Ratio of two densities

Relative density, also called specific gravity, is a dimensionless quantity defined as the ratio of the density of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest ; for gases, the reference is air at room temperature. The term "relative density" is preferred in SI, whereas the term "specific gravity" is gradually being abandoned.

<span class="mw-page-title-main">Avogadro constant</span> Fundamental metric system constant defined as the number of particles per mole

The Avogadro constant, commonly denoted NA or L, is an SI defining constant with an exact value of 6.02214076×1023 mol−1 (reciprocal moles). It is defined as the number of constituent particles (usually molecules, atoms, or ions) per mole (SI unit) and used as a normalization factor in the amount of substance in a sample. The numerical value of the constant was chosen based on the number of atoms in 12 grams of carbon-12 in alignment with the historical definition of a mole. The constant is named after the physicist and chemist Amedeo Avogadro (1776–1856).

The dalton or unified atomic mass unit is a non-SI unit of mass defined as 1/12 of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. The atomic mass constant, denoted mu, is defined identically, giving mu = 1/12m(12C) = 1 Da.

<span class="mw-page-title-main">Gas constant</span> Physical constant equivalent to the Boltzmann constant, but in different units

The molar gas constant is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.

<span class="mw-page-title-main">Molar mass</span> Mass per amount of substance

In chemistry, the molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of the compound. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities.

In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. It was formulated by the English chemist William Henry, who studied the topic in the early 19th century. In simple words, we can say that the partial pressure of a gas in vapour phase is directly proportional to the mole fraction of a gas in solution.

Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular, of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol/dm3 in SI units. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M or 1 M. Molarity is often depicted with square brackets around the substance of interest; for example, the molarity of the hydrogen ion is depicted as [H+].

The density of air or atmospheric density, denoted ρ, is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variations in atmospheric pressure, temperature and humidity. At 101.325 kPa (abs) and 20 °C, air has a density of approximately 1.204 kg/m3 (0.0752 lb/cu ft), according to the International Standard Atmosphere (ISA). At 101.325 kPa (abs) and 15 °C (59 °F), air has a density of approximately 1.225 kg/m3 (0.0765 lb/cu ft), which is about 1800 that of water, according to the International Standard Atmosphere (ISA). Pure liquid water is 1,000 kg/m3 (62 lb/cu ft).

Molar refractivity, , is a measure of the total polarizability of a mole of a substance and is dependent on the temperature, the index of refraction, and the pressure.

<span class="mw-page-title-main">Collision theory</span> Chemistry principle

Collision theory is a principle of chemistry used to predict the rates of chemical reactions. It states that when suitable particles of the reactant hit each other with the correct orientation, only a certain amount of collisions result in a perceptible or notable change; these successful changes are called successful collisions. The successful collisions must have enough energy, also known as activation energy, at the moment of impact to break the pre-existing bonds and form all new bonds. This results in the products of the reaction. The activation energy is often predicted using the Transition state theory. Increasing the concentration of the reactant brings about more collisions and hence more successful collisions. Increasing the temperature increases the average kinetic energy of the molecules in a solution, increasing the number of collisions that have enough energy. Collision theory was proposed independently by Max Trautz in 1916 and William Lewis in 1918.

In thermodynamics, the specific volume of a substance is a mass-specific intrinsic property of the substance, defined as the quotient of the substance's volume to its mass. It is the reciprocal of density ρ (rho) and it is also related to the molar volume and molar mass:

The number density is an intensive quantity used to describe the degree of concentration of countable objects in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional linear number density. Population density is an example of areal number density. The term number concentration is sometimes used in chemistry for the same quantity, particularly when comparing with other concentrations.

In chemistry and fluid mechanics, the volume fraction is defined as the volume of a constituent Vi divided by the volume of all constituents of the mixture V prior to mixing:

In physics and engineering, mass flux is the rate of mass flow per unit of area. Its SI units are kg m−2 s−1. The common symbols are j, J, q, Q, φ, or Φ, sometimes with subscript m to indicate mass is the flowing quantity. Mass flux can also refer to an alternate form of flux in Fick's law that includes the molecular mass, or in Darcy's law that includes the mass density.

In chemistry, the mass fraction of a substance within a mixture is the ratio of the mass of that substance to the total mass of the mixture. Expressed as a formula, the mass fraction is:

<span class="mw-page-title-main">Volume (thermodynamics)</span> Extensive parameter used to describe a thermodynamic systems state

In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law. The physical region covered by a system may or may not coincide with a control volume used to analyze the system.

In chemistry, the mass concentrationρi is defined as the mass of a constituent mi divided by the volume of the mixture V.

References

  1. 1 2 International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry , 2nd edition, Oxford: Blackwell Science. ISBN   0-632-03583-8 . p. 41. Electronic version.
  2. Deslattes, R. D.; Henins, A.; Bowman, H. A.; Schoonover, R. M.; Carroll, C. L.; Barnes, I. L.; Machlan, L. A.; Moore, L. J.; Shields, W. R. (1974). "Determination of the Avogadro Constant". Phys. Rev. Lett. 33 (8): 463–66. Bibcode:1974PhRvL..33..463D. doi:10.1103/PhysRevLett.33.463.
  3. Mohr, Peter J.; Taylor, Barry N. (1999). "CODATA recommended values of the fundamental physical constants: 1998" (PDF). Journal of Physical and Chemical Reference Data . 28 (6): 1713–1852. Bibcode:1999JPCRD..28.1713M. doi:10.1063/1.556049. Archived from the original (PDF) on 2017-10-01.
  4. "2022 CODATA Value: molar volume of silicon". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.