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3.GASES eLearn.Punjab

If the pressure is expressed in mm of mercury or torr and the volume of the gas in cm3 then
values of R are,

R = 0.0821 dm3 atm K-1 mol-1
= 0.0821 x 760 dm3 mm Hg K-1 mol-1
= 62.4 dm3 mm Hg K-1 mol-1 Since, (1 mm o f Hg = 1 to rr)
= 62.4 dm3 torr K-1 mol-1
= 62400 cm3 torr K-1 mol-1 As, (1 dm3 = 1000 cm )
Using SI units of pressure, volume and temperature in the general equation, the value of R is
calculated as follows. The SI units of pressure are Nm-2 and of volume are m3. By using Avogadro’s
principle
1 atm = 760 torr = 101 325 Nm-2
lm3 = 1000 dm3
n = 1 mole
T = 273.16 K
P = 1 atm = 101325 Nm-2
V = 22.414 dm3 = 0.022414 m3
Putting their values, alongwith units.

R= PV = 101325 N m-2 x 0.0224l m3

nT 1 mol x 273.16 K

R = 8.3143 Nm K-1 mol-1 = 8.3143 J K-1 mol-1 (1 Nm = 1J)

Since 1cal. = 4.18 J

8.3143

so R= 4.18 = 1.989cal K-1 mol-1

Keep in mind that, wherever the pressure is given in Nm-2 and the volume in m3, then the value of
R used must be 8.3143 JK-1 mol-1.

3.3.2 Density of an ideal Gas

For calculating the density of an ideal gas, we substitute the value of number of moles (n) of the
gas in terms of the mass (m), and the molar mass (M) of the gas.

n= m

M

PV = m RT ................. (6)

M

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