TITLE.PM5

414 ENGINEERING THERMODYNAMICS

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In general therefore,

Vi =

p

p

iV ...(9.8)

i.e., ΣVi =
pV
p

V
p
∑ i = Σpi
Now from eqn. (9.4), p = Σ pi, therefore,
Σ Vi = V ...(9.9)
Thus, the volume of a mixture of gases is equal to the sum of the volumes of the individual
constituents when each exists alone at the pressure and temperature of the mixture.
This is the statement of another empirical law, the law of partial volumes, sometimes called
Amagat’s law or Leduc’s law.
— The analysis of mixtures, oftenly, is simplified if it is carried out in moles. The mole is
given by the equation
n = m
M
where, n = Number of moles,
m = Mass of gas, and
M = Molecular weight.
According to Avogadro’s law, the number of moles of any gas is proportional to the volume of
the gas at a given pressure and temperature. Referring to Fig. 9.2 (a), the volume V contains n moles
of the mixture at p and T. In Fig. 9.2 (b), the gas A occupies a volume VA at p and T, and this volume
contains nA moles. Similarly there are nB moles of gas B in volume VB and nC moles of gas C in
volume VC.
From eqn. (9.9), Σ Vi = V
or VA + VB + VC = V
∴ The total number of moles in the vessel must equal the sum of the moles of the individual
constituents,
n = nA + nB + nC = Σ ni ...(9.10)

9.4. The Apparent Molecular Weight and Gas Constant

The Apparent Molecular Weight
In a gas mixture if a gas occupies a total volume of V at a temperature T, then from the
definition of partial pressure and equation pV = nR 0 T, we have
piV = niR 0 T ...(9.11)
(where R 0 is the universal gas constant)
∴Σ piV = Σ niR 0 T
i.e., V Σ pi = R 0 T Σ ni
Also p = Σ pi [from eqn. (9.4)]
∴ pV = R 0 T Σ ni
Also n = Σ ni [from eqn. (9.10)]
∴ pV = nR 0 T
The mixture therefore acts as a perfect gas, and this is the characteristic equation for
mixture.