The numerical value of the gas constant `R' depends upon the units in which pressure and volume are expressed,
R = PV / T (assuming one mole of gas)

**Numerical values of
gas constant (R)**

The
numerical value of the gas constant `R' depends upon the units in which
pressure and volume are expressed,

R
= PV / T (assuming one mole of gas)

R =
(Pressure x Volume) / Temperature

=
( Force / Area ) x ( Volume / Temperature )

Since Volume = Area x length

R
= ( Force x Length ) / Temperature

=
Work / Temperature

The dimensions of R are thus energy per degree per mole.

**i) In litre - atmosphere**

One mole
of gas at S.T.P occupies a volume of 22.4 litre and thus

At STP

P = 1 atm R = PV/T (for 1 mole)

V = 22.4 litre R = (1 x 22.4)/273

T = 273 K R = 0.0821
litre atm K^{-1}mol^{-1}

= 0.0821 dm^{3}.atm K^{-1}mol^{-1}

(_{ì} 1 litre =
1 dm^{3})

**ii) In C.G.S. System**

At STP 1 mole of gas has

P = 1 atm = 1 x 76 x 13.6 x 980 dyne cm^{-2}

= 1.013 x 10^{6} dyne cm^{-2}

V = 22400 cm^{3}; T = 273 K

R = PV / T = 1.013 x 10^{6}
x 22400 / 273

R = 8.314 x 10^{7} erg K^{-1} mol^{-1}

**iii) In M.K.S. System**

In MKS or SI units, the unit of R is joule

Since 10^{7}
erg = 1 Joule

R = 8.314 Joule K^{-1} mol^{-1}

1 calorie = 4.184 Joule

R = 1.987 cals deg^{-1} mol^{-1}

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11th 12th std standard Class Organic Inorganic Physical Chemistry Higher secondary school College Notes : Numerical values of gas constant (R) |

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