Question

Establish the relation between PV=nRT.

Answer 1

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IDEAL GAS EQUATION:

Let us consider the pressure exerted by the gas to be ‘p,’

The volume of the gas be – ‘v’

Temperature be – T

n – be the number of moles of gas

Universal gas constant – R

According to Boyle’s Law,

At constant n & T, the volume bears an inverse relation with the pressure exerted by a gas.

i.e. v∝1/p ………………………………(i)

According to Charles’ Law,

When p & n are constant, the volume of a gas bears a direct relation with the Temperature.

i.e. v∝T ………………………………(ii)

According to the Avogadro’s Law,

When p & T are constant, then the volume of a gas bears a direct relation with the number of moles of gas.

i.e. v∝n ………………………………(iii)

Combining all the three equations, we have-

v∝nT/p

or pv=nRT

where R is the Universal gas constant, which has a value of 8.314 J/mol-K.

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Answer 2

Ideal gas equation can be thought of as a combination of results obtained by experiments conducted in various equations .

Boyel's law:-

V proportional to 1/p (constant - N and t )

Charle's law:-

v proportional to t (constant n and p)

Avogadro's law :-

v proportional to n( constant- .p and t)

putting these realtions together ,we get pv= nRt