**Numerical Value of Universal Gas Constant (R)**

The numerical value of R may be calculated by determining the volume occupied by 1 mole of a gas at a given pressure and a given temperature. The dimension of R may be easily deduced from the equation: **PV = RT**

**so, R = (PxV mol ^{-1})/T**

= (force/area) x (volume mol^{-1}/temperature)

= (force/length^{2}) x (length^{3}.mol^{-1}/ temperature)

= force x length x (mol^{-1}/temperature)

= [(work x mol^{-1})/ temperature]; (here energy mol^{-1}K^{-1})

The gas constant R is 8.314 J/mol. K. Convert the numerical value of R so that its units are cal / (mol. K).

Thus, the product PV has the dimension of work, and R may be expressed in any energy unit per mole per degree Kelvin. The constant R appears in many formulas in chemistry. The numerical value of R to be used depends on the system of units employed in the equation under consideration.

**(a) Litre-atmosphere units:** In equation it was pointed out that the molar volume at S.T.P., at 1 atmosphere pressure and 0°C or 273.16`K is 22.414 L. If these values are substituted in equation PV = RT; one obtains,

R = (1 x 22.414)/273.16 = 0.0820 L atm K^{-1} mol^{-1}

**(b) C.G.S. units**: In these units pressure is expressed in dynes per square centimeter and volume in cubic centimeters.

P= 1 atm = 76 cm of Hg

=76 x13.6 x 981 dynes cm^{-2}

V = 22.414 L = 22.414 cm^{3} mol^{-1}.

R = [(76 x 13.6 x 981 x 22.414)/27316] = 8.316×10^{7} ergs K^{-1}mol^{-1}