Question

# If $$Z$$ is a compressibility factor, van der Waals equation at low pressure can be written as:

A
Z=1PbRT
B
Z=1+PbRT
C
Z=1+RTPb
D
Z=1aVRT

Solution

## The correct option is D $$Z=1-\displaystyle \frac{a}{VRT}$$$$\left ( P+\displaystyle \frac{n^{2}a}{V^{2}} \right )(V-nb)=nRT$$For 1 mole, $$\left ( P+\displaystyle \frac{a}{V^{2}} \right )(V-b)=RT$$           $$PV=RT+Pb-\displaystyle \frac{a}{V}+\displaystyle \frac{ab}{V^{2}}$$At low pressure, terms $$Pb$$ & $$\displaystyle \frac{ab}{V^{2}}$$ will be negligible as compared to $$RT$$.So, $$PV=RT-\displaystyle \frac{a}{V}$$$$Z=1-\displaystyle \frac{a}{RTV}$$So, the correct option is $$D$$Chemistry

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