Question

If the slope of ‘Z’ (compressibility factor ) v/s ‘P’ curve is constant (slope = $\frac{\pi }{492.6}at{m}^{-1}$) at a particular temperature (300K) and very high pressure. Calculate diameter of the molecules. (Given: $N_A=6.023\times {10}^{23},R=0.0821atmLmo{l}^{-1}{K}^{-1}$)

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$Z=1+\frac{Pb}{RT}$ at high pressure

slope = $\frac{b}{RT}=\frac{\pi }{492.6}$

$\Rightarrow b=\frac{\pi }{492.6}\times 0.0821\times 300$ and b = $\frac{4}{3}\pi r^3\times 4N_A$

$\Rightarrow b=\frac{\pi }{492.6}\times 0.0821\times 300\times {10}^{-3}$

$\Rightarrow r=2.5A^{\circ }d=5A^{\circ }$