[Physics Class Notes] on Molar Gas Constant Pdf for Exam

Molar gas constant also known as gas constant, the universal gas constant, or the ideal gas constant is a fundamental physical constant that arises in the formulation of general gas laws. The molar gas constant is denoted by the symbol R. It is equivalent to the Boltzmann Constant. R can also be defined as Avogadro Number multiplied by Boltzmann Constant. However, instead of the energy per temperature increment of a particle, it is expressed in terms of energy per temperature increment per mole which is also equivalent to the pressure-volume product. This constant features in fundamental equations of physics like the ideal gas laws equations, the Arrhenius Equation and the Nernst equation.

The origin of the symbol R for the ideal gas constant is probably in honour of French chemist Henry Regnault who is known for his measurements of thermal properties of gases.

Units of Ideal Gas Constant

The SI unit of the ideal gas constant is Pascal or Newton per metre. It can also be written as joule per mole per Kelvin.

Molar Gas Constant Value

The molar gas constant is a combination of Boyle’s law, Charles law, Gay-Lussac’s law and Avogadro’s number. It relates the energy scale to the temperature scale in physics. The value of gas constant:

R = 8.3144598(48)J.mol^-1. K^-1

Dimension of Gas Constant

We find the dimensions of the ideal gas constant from the ideal gas equation which is given by:

PV=nRT, Here P is the pressure of the gas, V is the volume of the gas, T is the temperature of the gas on an absolute scale and n is the number of moles of the given gas. 

Hence, gas constant formula can be written as:

$R= frac{PV}{nt}$

Now substitute pressure as force per unit area for deriving the dimensions of R. 

Now, $R= frac{frac{text{Force}}{text{Area}}times text{volume}}{text{Mole} times text{Temperature}}$ ……(i)

For volume, we take it as the cube of length and for the area, we take it as length square. We substitute n as the mole. Force can be written as mass per unit acceleration which is equal to mass into length per unit square of time. 

$R= frac{frac{text{mass} times text{length}}{{text{length}^{2}}times text{time}^{2}}times text{(length)}^3}{text{mole} times text{temperature} }$

$R = frac{[ML^{-1}T^{-2}]times[L^3] }{mole} times K$

Hence the dimensions of R is [ML²T^-2K^-1mol^-1]

Also, from equation (i) we can see that, 

$R= frac{frac{text{force}}{text{length}^{2}}times text{length}^3}{text{mole} times text{temperature}}$

$R= frac{text{force}times text{length}}{text{mole}times text{temperature}}$

$R = frac{text{work}}{text{mole}}times text{temperature}$

Thus, the universal gas constant can be defined also in terms of work. It is work per unit mole per degree. Hence the expression of gas constant in Joules per mole per Kelvin is justified.

Specific Gas Constant

The Specific Gas Constant of a particular gas or a mixture of gases is calculated by dividing the molar gas constant by the molar mass of the gas or the mixture. The application of specific gas constants is in the field of engineering especially. 

R[_{specific} = frac{R}{M}]

The specific gas constant can be related to the Boltzmann constant just like the Universal gas constant, by dividing it with the molecular mass of the gas or the mixture. 

R[_{specific} = frac{k_{b}}{m}]

Well, another important thermodynamic equation related to the specific gas constant is Mayer’s relation. 

R[_{specific} = c_{p} – c_{v}]

Here cp is the specific heat capacity of gas at constant pressure whereas cv is the specific heat capacity of the gas at constant volume. 

The knowledge of the universal gas constant is indispensable for various calculations related to the ideal gas formula and other applications in physical sciences.

Did You Know?

In 2006, the most precise measurement of R was done by measuring the speed of sound Cₐ(P, T)  in  room temperature of the triple point of water at various pressures and on extrapolating the value of R obtained was 

Cₐ(0,T)= (Y₀RT/AR (Ar) Mᵤ)[^{frac{1}{2}}]

Here, Y₀ is the heat capacity ratio which is 5/3 for monoatomic gases like argon. T is the temperature which is the triple point of water, AR (Ar) is the relative atomic mass of argon and Mᵤ  is 10⁻³ kg per mole. 

This equation gives the exact precise value of R.