Question

Which of the following is defined as the gas constant of a gas?
1. The reciprocal of the ratio of the universal gas constant to the molecular weight of the gas
2. The product of the universal gas constant and the molecular weight of the gas
3. The reciprocal of the product of the universal gas constant and the molecular weight of the gas
4. The ratio of the universal gas constant to the molecular weight of the gas

Answer 1

Correct Answer - Option 4 : The ratio of the universal gas constant to the molecular weight of the gas

Concept:

Ideal-gas equation is given as, PV = nRoT

The characteristic gas equation is given as, PV = mRT

where R is known as Characteristic Gas Constant (or simply Gas Constant) and Ro is Universal Gas Constant.

\(R = \frac{{{R_0}}}{M}\)

where M is the molecular weight.

∴ The gas constant is defined as the ratio of the universal gas constant to the molecular weight of the gas.

Characteristic gas constant is written as,  \(R={C_p} - {C_v}\)

where, Cp = heat capacity at constant pressure, Cv = heat capacity at constant volume.