Ideal Gas Constant

28th May 2019 @ 5 min read

The ideal gas constant is also known as the universal gas constant or the molar gas constant or simply the gas constant. It is a very important constant in chemistry and physics. It is denoted as R. The dimension of the gas constant is expressed in energy per unit mole per unit temperature. The value of the gas constant in SI unit is 8.314 J mol⁻¹ K⁻¹. The gas constant has the same unit as of entropy and molar heat capacity.

The origin of the symbol R for the ideal gas constant is still obscure. Some say the symbol for the gas constant is named in honour of French chemist Henri Regnault. He is known for his work on measurements of thermal properties of gases.

Definition of Ideal Gas Constant

The ideal gas constant is the proportionality constant in the ideal gas equation. It is the ratio of the product of pressure and volume to the product of mole and temperature.

Formula of Gas Constant

The formula of the gas constant from the ideal gas law equation is

$R=\frac{PV}{nT}$

where P is the pressure of an ideal gas,
V is the volume the gas occupies,
n is the number of moles of the gas,
and the T is the temperature in the kelvin.

SI unit of Ideal Gas Constant

The SI unit of the ideal gas constant can be determined as:

$[R]=\frac{[P][V]}{[n][T]}=\frac{\text{Pa}\times \text{m}^3}{\text{mol}\times \text{K}}$

The SI unit of pressure is Pa or N m⁻².

$[R] =\frac{\left(\text{N}\big/ \text{m}^2\right)\times \text{m}^3}{\text{mol}\times \text{K}} =\frac{\text{N}\,\text{m}}{\text{mol}\, \text{K}}$

Now, N m is the equivalent to the joule, which is the SI unit of energy.

$[R] =\frac{\text{N}\,\text{m}}{\text{mol}\, \text{K}} =\frac{\text{J}}{\text{mol}\, \text{K}}$

Value of Ideal Gas Constant in SI unit

At STP (P = 101 325 Pa, T = 273.15 K), the molar volume or volume per mole is 22.414 × 10⁻³ m³ mol⁻¹. Therefore, we can calculate the value of R as

$R =\frac{PV}{nT} & =\frac{101\,325 \times 22.414 \times 10^{-3}}{1 \times 273.15}\\ &=8.314 \, \text{J}\,\text{mol}^{-1}\,\text{K}^{-1}$

This is an approximate value of the ideal gas constant.

With the 26^th General Conference on Weights and Measures (CGPM), the revised and exact value of the gas constant is 8.314 462 618 153 24 J mol⁻¹ K⁻¹.

Values of Ideal Constant in Different Units

The value of R in different units is presented in the table below.

The value of the ideal gas constant in different units
Value	Unit
8.314 462 618 153 24	J mol⁻¹ K⁻¹
8 314.462 618 153 24	J kmol ⁻¹ K⁻¹
8.314 462 618 153 24 × 10⁷	erg mol⁻¹ K⁻¹
8.314 462 618 153 24 × 10³	amu m² s⁻² K⁻¹
8.205 733 8(47) × 10⁻⁵	m³ atm mol⁻¹ K⁻¹
0.082 057 338(47)	L atm mol⁻¹ K⁻¹
1.987 203 6(11)	cal mol⁻¹K⁻¹
62.363 577(36)	mmHg L mol⁻¹ K⁻¹
62.363 577(36)	torr L mol⁻¹ K⁻¹
1 545.348 96(3)	ft lb_f lbmol⁻¹ K⁻¹
1.985 88	Btu lbmol⁻¹R⁻¹
998.970 1(17)	ft³ mmHg lbmol⁻¹K⁻¹
10.731 59(2)	ft³ psi lbmol⁻¹ R⁻¹

Specific Gas Constant

The specific gas constant is a version of the ideal gas constant in mass form instead of molar form. It is defined as the ratio of the ideal gas constant to the molar gas of the gas. It has the dimension of the energy per unit mass per unit absolute temperature. The SI unit is J kg⁻¹ K⁻¹. It is denoted as R_sp.

$R_\text{sp} =\frac{R}{M_\text{w}}$

where M_w is the molar mass or molecular weight of the gas.

The molecular weight of hydrogen gas is 2 g mol⁻¹. So, R_sp for hydrogen is calculated as:

$R_\text{sp}=\frac{8.314}{2} &=4.157 \,\text{J}\,\text{g}^{-1}\,\text{K}^{-1}\\ &=4157 \,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}$

Similarly, for air of molecular weight of 28.84 g mol⁻¹.

$R_\text{sp} =\frac{8.314}{28.84} &=0.288\,3 \,\text{J}\,\text{g}^{-1}\,\text{K}^{-1}\\ &=288.3 \,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}$

Also, the specific gas constant is found in Mayer's relation.

$R_\text{sp} =c_p-c_v$

where c_p is the specific gas constant at constant pressure, and c_v is the specific heat capacity at constant volume.

The specific gas constant is very useful in engineering applications of thermodynamics.

Boltzmann's Constant and Ideal Gas Constant

The ideal gas constant and the Boltzmann constant (k_B) are related by Avogadro's constant (N_A). The Boltzmann constant is the ratio of the ideal gas constant to the Avogadro's constant.

$k_\text{B} =\frac{R}{N_\text{A}}$

Using equation $R_\text{sp} =\frac{R}{M_\text{w}}$ ,

$k_\text{B} =\frac{R_\text{sp}M_\text{w}}{N_\text{A}} =R_\text{sp}m$

where m is the mass per molecule of the gas.

Gas Constant in other important equations

Apart from the above equations, the gas constant is also found in many other important equations of chemistry. Some of these equations are discussed below.

Nernst Equation

The Nernst equation is an equation in electrochemistry that relates the potential of an electrochemical reaction to the standard electrode potential. The equation is named after German chemist Walther Nernst. For an electrochemical half-cell, the Nernst equation is

$E_\text{red}=E_\text{red}^\ominus-\frac{RT}{zF}\ln\frac{\alpha_\text{red}}{\alpha_\text{ox}}$

where:
E_red is the reduced potential of the half-cell at temperature T,
E^⊖
_red is the standard potential of the half-cell,
α_red and α_ox are activities of reduced and oxidised species,
and z and F are the number of electrons transferred and the Faraday constant.

Arrhenius Equation

The Arrhenius equation is an important equation use in chemical kinetics. It is used to determine the rate constant k.

$k =Ae^{-\frac{E_\text{a}}{RT}}$

where A is the Arrhenius constant and E_a is the activation energy.

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