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Question

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


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