Numerical value of ‘R’ L-atm, SI & C.G.S unit.

Determine the numerical value of ‘R’ in L-atm unit.

Liter-atmosphere unit: In this system, pressure is expressed in atmosphere and me is expressed in liter. At S.T.P. the volume of one mole of any gas is 22.4L & pressure 1 atm.

Hence,   P = 1 atm

              V = 22.4 L

              T = 273K

              n  =  1 mol

From the ideal gas equation,

(ii) Determine the numerical value of  ‘R’ in SI unit.

Ans.: S.I. unit: In this system, pressure is expressed in Pascal (Pa/Nm^-2) and volume is expressed in cubic meter (m³)

Hence,   P = 101325 Nm^-2

              V = 0.0224 m³

              T = 273K

              n  =  1 mol

From the ideal gas equation,

(iii) Determine the numerical value of ‘R’ in C.G.S. unit.

Ans.: C.G.S unit: In this system, pressure is expressed in dyne cm^-2 and volume is expressed in cubic cm (cm³)  

Hence,   P = hρg

                 = 76 cm ⨯ 13.6 gcm^-3⨯ 981 cms^-2

                 = (76 ⨯ 13.6 ⨯ 981) gcms^-2  cm^-2

                 = (76 ⨯ 13.6 ⨯ 981) dyne cm^-2      [1gcms^-2  =  1 dyne] 

                 = 1013961.6 dyne cm^-2

              V = 22400 cm³

              T = 273K

              n  =  1 mol

From the ideal gas equation,