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States Of Matter

Question
CBSEENCH11005959

What is the significance of the Vander Waal's constants? Write its units for Vander Waal's constants.

Solution

Vander Waal's equation of state for n moles of the gas is
open parentheses straight P plus an squared over straight V squared close parentheses space left parenthesis straight V minus nb right parenthesis space equals space nRT
The significance of constant 'a'. The value of constant a gives the idea of the magnitude of attractive forces between the molecules of the gas. Larger the value of a the larger will be the intermolecular forces between the molecules. Units of a. Pressure correction (β) is given by
                     straight beta space equals space an squared over straight V squared
therefore space space space straight a space equals space space fraction numerator straight beta space cross times space straight V squared over denominator straight n squared end fraction
space space space space space space space space space equals space fraction numerator Pressure space cross times space left parenthesis volume right parenthesis squared over denominator left parenthesis mole right parenthesis squared end fraction
space space space space space space space space space equals space fraction numerator atm space cross times space left parenthesis litre right parenthesis squared over denominator left parenthesis mole right parenthesis squared end fraction space equals space atm space straight L squared space mol to the power of negative 2 end exponent
The significance of constant 'b'.  The constant b is called co-volume or excluded volume per mole of a gas. It is a measure of the effective size of gas molecules.
Units of b. Units of b must be units of volume i.e. L mol–1 or dm3 mol–1.