Derive ideal gas equation for n mole of gas.

Explanation:

Ideal gas equation- The volume (V) occupied by the n moles of any gas has pressure(P) and temperature (T) Kelvin,

the relationship for these variables PV=nRT where R gas constant is called the ideal gas law

Derivation of the 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,

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

i.e. v∝1p ………………………………(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 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∝nTp

or pv=nRT

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

explanation:

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