Question

A mole of $CC{l}_4$ vapours at ${77}^{\circ }C$ occupies a volume of 36.0 L.If vanderwaals constants are $a=20.39L^{2}atmmo{l}^{-2}$ and $b=0.1383Lmo{l}^{-1}$ calculate the compressibility factor Z under (a) low pressure region and (b) high pressure region.
The values of compressibility factor Za and Zb respectively are:

• A. Za = 0.82,Zb = 1.12
• B. Za= 0.98, Zb =1.004
• C. Za=0.90,Zb=1.12
• D. Za=0.90,Zb=1.22

Answer 1

The correct option is B

Za= 0.98, Zb =1.004

Under (a) Za= 0.98
Under (b) Zb= 1.004

Option b

a)Under low pressure region,the molar volume is high, so $V_m-b\approx V_m$.The following equation.

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

Then becomes $p{V}_m+\frac{a}{V_m}=RT$

So the compressibility factor is

b)Under high pressure p is high , so
$P(V_m-b)=RT\Rightarrow p=\frac{RT}{V_m-b}$
Now, the compressibility factor is
$Z=\frac{p{V}_m}{RT}=\frac{V_m}{V_m-b}=\frac{1}{1-\left(\frac{b}{V_m}\right)}=\frac{1}{1-\left(\frac{0.138}{35}\right)}=1.004$