Gas constant

Values of R	Units (V·P·T-1·n-1)
8.314472	J·K-1·mol-1
0.0820574587	L·atm·K-1·mol-1
8.20574587 × 10-5	m3·atm·K-1·mol-1
8.314472	cm3·MPa·K-1·mol-1
8.314472	L·kPa·K-1·mol-1
8.314472	m3·Pa·K-1·mol-1
62.36367	L·mmHg·K-1·mol-1
62.36367	L·Torr·K-1·mol-1
83.14472	L·mbar·K-1·mol-1
1.987	cal·K-1·mol-1
6.132440	lbf·ft·K-1·g-mol-1
10.73159	ft3·psi· °R-1·lb-mol-1
0.7302413	ft3·atm·°R-1·lb-mol-1
998.9701	ft3·mmHg·K-1·lb-mol-1
8.314472 × 107	erg·K-1·mol-1

The gas constant (also known as the molar, universal, or ideal gas constant) is a physical constant that is featured in a number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is expressed in units of energy (that is, the pressure-volume product) per kelvin per mole. It is equivalent to the Boltzmann constant, except that the latter is expressed in units of energy per kelvin per particle.

Denoted by the symbol R, the value of the gas constant is:

R = 8.314472(15) J · K^-1 · mol^-1

The two digits in parentheses indicate the uncertainty (standard deviation) in the last two digits of the value.

Ideal gas law

An ideal gas (or "perfect" gas) is a hypothetical gas consisting of a very large number of identical particles, each of zero volume, uniformly distributed in density, with no intermolecular forces. Additionally, the molecules or atoms of the gas have complete randomness of direction and velocity, and they undergo perfectly elastic collisions with the walls of the container.

The gas constant occurs in the ideal gas law (the simplest equation of state) as follows:

$P={\frac {nRT}{V}}={\frac {RT}{V_{\rm {m}}}}$

where:

$P\,\!$ is the absolute pressure

$T\,\!$ is absolute temperature

$V\,\!$ is the volume the gas occupies

$n\,\!$ is the amount of gas (in terms of the number of moles of gas)

$V_{\rm {m}}\,\!$ is the molar volume

The gas constant has the same units as specific entropy.

Individual gas constant

Whereas the universal gas constant is the same for all ideal gases, the individual gas constant is applicable to a particular gas (or mixture of gases such as air) and is related to the molecular weight of that gas (or mixture). Its value is independent of temperature.

In the SI system, the units for the individual gas constant are J·kg^-1·K^-1; and in the imperial system, the units are ft·lb·°R^-1·slug^-1. The values of the individual gas constant for air and some other common gases are given below.

Gas	Individual Gas Constant SI Units (J·kg-1·K-1)	Individual Gas Constant Imperial Units (ft·lb·°R-1·slug-1)
Air	286.9	1,716
Carbon dioxide (CO2)	188.9	1,130
Helium (He)	2,077	12,420
Hydrogen (H2)	4,124	24,660
Methane (CH4)	518.3	3,099
Nitrogen (N2)	296.8	1,775
Oxygen (O2)	259.8	1,554
Water vapor (H2O)	461.5	2,760

As seen from the above table, the individual gas constant varies considerably, depending on the gas being studied.

Relationship with the Boltzmann constant

The Boltzmann constant k_B (often abbreviated k) has the value 1.3807 x 10^-23 J.K^-1. It may be used in place of the universal gas constant by working in pure particle count, N, rather than number of moles, n, since

$\qquad R=N_{A}k_{B}\,\!$,

where $N_{A}$ is Avogadro's number (= 6.022 x 10²³ particles per mole).

In terms of Boltzmann's constant, the ideal gas law may be written as:

$PV=Nk_{B}T\,\!$

where N is the number of particles (atoms or molecules) of the ideal gas.

Given its relationship with the Boltzmann constant, the ideal gas constant also appears in equations unrelated to gases.

Specific gas constant

The specific gas constant of a gas or a mixture of gases (R) is given by the universal gas constant, divided by the molar mass ($M$) of the gas or mixture.

$R={\frac {\bar {R}}{M}}$

It is common to represent the specific gas constant by the symbol $R$. In such cases, the context and/or units of $R$ should make it clear as to which gas constant is being referred to. For example, the equation for the speed of sound is usually written in terms of the specific gas constant.

The specific gas constant of dry air is

$R_{\mathrm {dry\,air} }=287.05{\frac {\mbox{J}}{{\mbox{kg}}\cdot {\mbox{K}}}}$

US Standard Atmosphere

The US Standard Atmosphere, 1976 (USSA1976) defines the Universal Gas Constant as:

${\bar {R}}=8.31432\times 10^{3}{\frac {\mathrm {N\cdot m} }{\mathrm {kmol\cdot K} }}$

The USSA1976 does recognize, however, that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant. This disparity is not a significant departure from accuracy, and USSA1976 uses this value of R for all the calculations of the standard atmosphere. When using the ISO value of R, the calculated pressure increases by only 0.62 pascals at 11,000 meters (the equivalent of a difference of only 0.174 meters, or 6.8 inches) and an increase of 0.292 pascals at 20,000 meters (the equivalent of a difference of only 0.338 meters, or 13.2 inches).

See also

• Earth's atmosphere
• Gas
• Mole (unit)
• Pressure
• Temperature
• Volume

References

ISBN links support NWE through referral fees

• American Institute of Chemical Engineers. 1984. Ideal Gas Law, Enthalpy, Heat Capacity, Heats of Solution and Mixing. New York: American Institute of Chemical Engineers. ISBN 0816902607.

• Atkins, Peter, and Loretta Jones. 2008. Chemical Principles: The Quest for Insight. 4th ed. New York: W.H. Freeman. ISBN 0716799030.

• Chang, Raymond. 2006. Chemistry. 9th ed. New York: McGraw-Hill Science/Engineering/Math. ISBN 0073221031.

• Cotton, F. Albert, and Geoffrey Wilkinson. 1980. Advanced Inorganic Chemistry. 4th ed. New York: Wiley. ISBN 0471027758.

• McMurry, J., and R.C. Fay. 2004. Chemistry. 4th ed. Upper Saddle River, NJ: Prentice Hall. ISBN 0131402080.

External links

• Molar Gas Constant R. NIST. Retrieved July 15, 2008.
• Boltzmann Constant k. NIST. Retrieved July 15, 2008.
• The Individual and Universal Gas Constant. The Engineering ToolBox. Retrieved July 15, 2008.
• The Ideal Gas Constant. Retrieved July 16, 2008.

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