if Z is a compressibility factor, van der waals equation at low pressures can be written as

Options

A. `Z=1+(Pb)/(RT)`
B. `Z=1+(RT)/(Pb)`
C. `Z=1-(a)/(RTV)`
D. `Z=1-(Pb)/(RT)`

Answer

C

Explanation

For 1 mol of a real gas `(P+(a)/(V^(2)))(V-b)=RT`
At low pressures, V is large enough compared with b. so,
`V-b~~V`.
`therefore (P+(a)/(V^(2)))V=RT" or",PV+(a)/(V)=RT`
or, `(PV)/(RT)=1-(a)/(RTV)" "therefore Z=1-(a)/(RTV)`