The van der Waals equatin for `0.5` mol of a gas is

Options

A. `(P+(a)/(4V^(2))) ((V-b)/(2)) = RT`
B. `(P+ (a)/(4V ^(2))) (2V-b) = RT`
C. `(P+(a)/(4V^(2)))(2V-4b) = RT`
D. `(P+ (a)/(4V^(2)))= (2RT)/(2 (V-R))`

Answer

B

Explanation

Given,
Number of moles of a gas, `n = 0.5` mol
The van der Waal's equation is given by,
`(P+ (an ^(2))/(v ^(2)))(V- nb) = nRT`
` (P+ (a (0.5) ^(2))/( P ^(2))) (V - 0.5b) = 0.5RT`
`(P+ (a 25)/(100 v ^(2))) (V - (b )/(2)) = (RT)/(2)`
`implies (P+ (a )/(4I ^(-2))) ((2V - b)/(2)) = (RT)/(2)`
`therefore (P+ (a)/(4I^(2)) ) (2V -b) = RT`