The compresibility factor (Z) of one mole of a van der waals gas of negligible 'a' value is-

Options

A. 1
B. `(bP)/(RT)`
C. `1+(bP)/(RT)`
D. `1-(bP)/(RT)`

Answer

C

Explanation

For 1 mol of a gas, van der waals equation,
`(P+(a)/(V^(2)))(v-b)=RT`
If the value of 'a' is negligible, then `P+(a)/(V^(2))~~P`
`therefore P(V-b)=RT`
or, `PV=RT+Pb or, (PV)/(RT)=1+(Pb)/(RT) or, Z=1+(Pb)/(RT)`.