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If Z is a compressibility factor, van de...

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

A

`Z = 1 + (RT)/(pb)`

B

`Z =1 - (a)/(VRT)`

C

`Z =1 - (pb)/(RT)`

D

`Z = 1 + (pb)/(RT)`

Text Solution

Verified by Experts

The correct Answer is:
B
PLAN To solve this problem, the stepwise approach required, i.e.
(i) Write the van der Waals’ equation, then apply the condition that at low pressure, volume become high,
i.e. `V-b, V`
(ii) Now calculate the value of compressibility factor (Z). ` [Z = pV//RT]`
According to van der Waals’ equation, `(p + (a)/(V^(2))) (V-b) = RT`
At low pressure, `(p + (a)/(V^(2))) V= RT rArr pV + (a)/(V) = RT or pV = RT - (a)/(V)`
Divide both side by RT, `(pV)/(RT) = 1 - (a)/(RTV)`
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