When two or more gases, which do not react chemically, are mixed together in a vessel, the total pressure of the mixture is given by Dalton's law of partial pressures which states that, "At constant temperature, the total pressure exerted by the gaseous mixture is equal to the sum of the individual pressures which each gas would exert if it occupies the same volume of mixture fully by itself.

**Dalton's law of
partial Pressures**

When two or more gases, which do not react chemically, are mixed together in a vessel, the total pressure of the mixture is given by Dalton's law of partial pressures which states that,

"At constant temperature, the total pressure exerted by the gaseous
mixture is equal to the sum of the individual pressures which each gas would
exert if it occupies the same volume of mixture fully by itself. Partial
pressure is the measure of the pressure of an individual gas in a mixture of
same volume and temperature.

Thus, if p1, p2, p3 .... are the partial pressures of the various gases
present in a mixture, then the total pressure P of the gaseous mixture is given
by

P = p1 + p2 + p3 ..., provided the volume and temperature of mixture and
that of the individual gases are the same.

**Equation of state of a
Gaseous mixture**

Let a
gaseous mixture consists of n_{A}, n_{B} and n_{C}
moles of three ideal gases A, B and C respectively, subjected to constant T and
V, then, according to ideal gas equation.

p_{A} = n_{A}RT
/ V

p_{B} = n_{B} RT / V

pc = n_{c} RT / V

where pA, pB, pC are the partial pressures of A,B,C gases respectively.
Hence the total pressure of the mixture is given as

P = p_{A} + p_{B} + pc

P = n_{A}RT/ V + n_{B}RT/V + n_{C}RT/V

PV = (n_{A} + n_{B} + n_{C})
RT

This equation is known as **equation
of state of gaseous mixture.**

**Calculation of Partial Pressure**

In order to calculate the pressure (p_{A}) of the individual
component say A, in a mixture (A and B), which is equal to the partial pressure
of A, according to the equation of state of gaseous mixture it is seen that,

P = Total pressure of the mixture

P
= (n_{A} + n_{B}) x (RT/V)

But p_{A} = ( n_{A} /V ) RT and
pB = (n_{B}/V)
x RT

The ratio
is given by

p_{A} / P = n_{A} / (n_{A}
+ n_{B}) . V/RT . RT/V

x_{A} =
mole fraction of A.

Or p_{A}
= X_{A}P

i.e:- Partial pressure, p_{A} = mole fraction of A x total pressure.
Similarly;

p_{B} = X_{B}
P

Thus, the
partial pressure of the individual component in the mixture can be calculated
by the product of its mole fraction and total pressure.

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