TITLE.PM5

GASES AND VAPOUR MIXTURES 415

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\M-therm\Th9-1.pm5

An apparent molecular weight is defined by the equation

M =

m

n

where, m = Mass of the mixture, and

n = Number of moles of mixture.

The Gas Constant

The apparent gas constant (similarly as above) is defined by the equation

R =

R

M

0

It can be assumed that a mixture of perfect gases obeys all the perfect gas laws.
In order to determine the gas constant for the mixture in terms of the gas constants of the
constituents let us consider the equation pV = mRT both for the mixture and for a constituent as
follows
pV = mRT
and piV = miRiT
Then Σ piV = Σ miRiT
∴ V Σ pi = T Σ miRi
Also p = Σ pi
∴ pV = T Σ miRi
or pV = mRT = T Σ miRi
i.e., mR = Σ miRi

or R = Σ

m

m

i R

i ...(9.12)

where
m
m

i = mass fraction of a constituent.

— From equation (9.11), piV = niR 0 T, and combining this with eqn. (9.8) V p

p

F i= iV

HG

I

KJ

applied

to the mixture (i.e., pV = nR 0 T), we have

pV

pV

i = nRT

nR T

i 0

0

or

p

p

i = n

n

i ...(9.13)

On combining this with eqn. (9.8), we get

p

p

i = n

n

i = V

V

i ...(9.14)

This means that the molar analysis is identical with the volumetric analysis, and both are
equal to the ratio of the partial pressure to the total pressure.
— The apparent molecular weight can be also be determined by the following method.
Let us apply characteristic equation to each constituent and to mixture, we have

mi =

pV

RT

i

i

m = pV

RT