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The '''molar volume''' (symbol ''V''<sub>m</sub>) is the [[volume (science)|volume]] occupied by one [[mole (unit)|mole]] of a substance | The '''molar volume''' (symbol ''V''<sub>m</sub>) is the [[volume (science)|volume]] occupied by one [[mole (unit)|mole]] of a substance at a given [[temperature]] and [[pressure]].<ref name="GreenBook">[http://www.iupac.org/publications/books/gbook/green_book_2ed.pdf International Union of Pure and Applied chemistry (IUPAC): Quantities, Units and Symbols in Physical Chemistry] 2nd Edition, 1993</ref><ref name="NIST">[http://physics.nist.gov/Pubs/SP811/sec08.html NIST Guide to SI] Item 8.6.3 in Section 8</ref> It is equal to the [[molecular mass]] (''M'') of the subtance divided by its [[density (chemistry)|density]] (''ρ'') at the given temperature and pressure: | ||
::<math>V_{\rm m} = {M\over\rho}</math> | ::<math>V_{\rm m} = {M\over\rho}</math> | ||
It has an [[SI unit]] of cubic [[metre]]s per mole (m<sup>3</sup>/mol).<ref name="GreenBook"/> However, molar volumes are often expressed as cubic metres per 1,000 moles (m<sup>3</sup>/kmol) or cubic decimetres per mol (dm<sup>3</sup>/mol) for gases and as centimetres per mole (cm<sup>3</sup>/mol) for liquids and solids. | It has an [[SI unit]] of cubic [[metre]]s per mole (m<sup>3</sup>/mol).<ref name="GreenBook"/><ref name="NIST"/> However, molar volumes are often expressed as cubic metres per 1,000 moles (m<sup>3</sup>/kmol) or cubic decimetres per mol (dm<sup>3</sup>/mol) for gases and as centimetres per mole (cm<sup>3</sup>/mol) for liquids and solids. | ||
If a substance is a mixture containing ''N'' components, the molar volume is calculated using: | If a substance is a mixture containing ''N'' components, the molar volume is calculated using: | ||
::<math>V_{\rm m} = \frac{\displaystyle\sum_{i=1}^{N}x_{i}M_{i}}{\rho_{mixture}}</math> | ::<math>V_{\rm m} = \frac{\displaystyle\sum_{i=1}^{N}x_{i}M_{i}}{\rho_{mixture}}</math> | ||
where ''x<sub> i</sub>'' is the [[mole fraction]] of the ith component, ''M<sub> i</sub>'' is the molecular mass of the ith component and ''ρ<sub>mixture</sub> is the mixture density at the given temperature and pressure. | where ''x<sub> i</sub>'' is the [[mole fraction]] of the ith component, ''M<sub> i</sub>'' is the molecular mass of the ith component and ''ρ<sub>mixture</sub> is the mixture density at the given temperature and pressure. | ||
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== Ideal gases == | == Ideal gases == | ||
The [[ideal gas law]] equation can be rearranged to give this expression for the molar volume of an ideal gas: | The [[ideal gas law]] equation can be rearranged to give this expression for the molar volume of an ideal gas: | ||
::<math>V_{\rm m} = {V\over{n}} = {{RT}\over{P}}</math> | |||
::<math>V_{\rm m} = {V\over{n}} = {{RT}\over{P}}</math> | |||
'''where in [[SI unit]]s:''' | '''where in [[SI unit]]s:''' |
Revision as of 01:46, 11 January 2010
The molar volume (symbol Vm) is the volume occupied by one mole of a substance at a given temperature and pressure.[1][2] It is equal to the molecular mass (M) of the subtance divided by its density (ρ) at the given temperature and pressure:
It has an SI unit of cubic metres per mole (m3/mol).[1][2] However, molar volumes are often expressed as cubic metres per 1,000 moles (m3/kmol) or cubic decimetres per mol (dm3/mol) for gases and as centimetres per mole (cm3/mol) for liquids and solids.
If a substance is a mixture containing N components, the molar volume is calculated using:
where x i is the mole fraction of the ith component, M i is the molecular mass of the ith component and ρmixture is the mixture density at the given temperature and pressure.
When stating molar volume numerical values, it is important to also state the given conditions of temperature and pressure. Otherwise, the numerical values are meaningless.
Ideal gases
The ideal gas law equation can be rearranged to give this expression for the molar volume of an ideal gas:
where in SI units:
P | = the gas absolute pressure, in Pa |
---|---|
n | = number of moles, in mol |
Vm | = the gas molar volume, in m3/mol |
T | = the gas absolute temperature, in K |
R | = the universal gas law constant of 8.314472 m3·Pa·mol-1·K-1 |
or where in U.S. customary units:
P | = the gas absolute pressure, in psia |
---|---|
n | = number of moles, in lb-mol |
Vm | = the gas molar volume, in ft3/lb-mol |
T | = the gas absolute temperature, in degrees Rankine (°R) |
R | = the universal gas law constant of 10.7316 ft3·psia·lb-mol-l·°R-1 |
The molar volume of any ideal gas may be calculated at various standard reference conditions as shown below:
- In SI metric units:
- Vm = 8.314472 × 273.15 / 101,325 = 0.022414 m3/mol at 0 °C and 101,325 Pa absolute pressure = 22.414 kmol at 0 °C (273.15 K) and 101.325 kPa absolute pressure
- Vm = 8.314472 × 273.15 / 100,000 = 0.022711 m3/kmol at 0 °C and 100,000 Pa absolute pressure = 22.711 kmol at 0 °C (273.15 K) and 100 kPa absolute pressure
- In customary USA units:
- Vm = 10.7316 × 519.67 / 14.696 = 379.48 ft3/lb-mol at 60 °F (519.67 °R) and 14.696 psia
The technical literature can be confusing because some authors fail to state whether they are using the universal gas law constant R, which applies to any ideal gas, or whether they are using the specific gas law constant Rs, which only applies to a specific individual gas. The relationship between the two constants is Rs = R / M, where M is the molecular mass of the gas.
Notes:
- lb-mol is an abbreviation for pound-mol
- °R is degrees Rankine (an absolute temperature scale) and °F is degrees Fahrenheit (a temperature scale).
- °R = °F + 459.67
Non-ideal gases
References
- ↑ 1.0 1.1 International Union of Pure and Applied chemistry (IUPAC): Quantities, Units and Symbols in Physical Chemistry 2nd Edition, 1993
- ↑ 2.0 2.1 NIST Guide to SI Item 8.6.3 in Section 8