$\begin{array}{1 1}(A)\;Z=1-\large\frac{Pb}{RT}\\(B)\;Z=1+\large\frac{Pb}{RT}\\(C)\;Z=1+\large\frac{RT}{Pb}\\(D)\;Z=1-\large\frac{a}{VRT}\end{array} $

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The van der Waals equation of state

$(P+\large\frac{a}{V_m^2})$$(V_m-b)=RT$

At low pressure, $V_m -b \approx V_m$ , the equation reduces to

$(P+\large\frac{a}{V_m^2})$$(V_m)=RT$

$\Rightarrow PV_m+\large\frac{a}{V_m}$$=RT$

$Z=\large\frac{PV_m}{RT}$$=1-\large\frac{a}{V_mRT}$

Hence (D) is the correct answer.

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