# Universal Gas Constant

The equation of state for an ideal gas is pV = kT. The value of the constant k depends on the mass of the gas used. Keeping pressure (p) and temperature (T) constant, if the mass of a gas is doubled, the volume is also doubled, So, k is doubled. We can conclude that k is directly proportional to the mass of the gas.

When one gram-molecule or one mole of an ideal gas is taken, the constant is written as R. As per Avogadro’s law, at the same temperature and pressure, the volume of 1 gram-molecule of any gas is the same. Therefore, the value of the constant R, for all ideal gases is the same. Hence, R is called the Univeral Gas Constant or Molar Gas Constant.

Hence, for 1 mol of any gas, the equation of state reduces to

pV = RT

and for n mol, pV = nRT

Obviously, for m g of gas of molecular weight M, the number of moles, n = m/M

∴ pV = (m/M)RT

Comparing with the gas equation pV = kT

k = (m/M).R

or, k = m.(R/M)

if m = 1 g, k = R/M = r (where r is also a constant and it is called the specific gas constant)