If the slope of “Z' (compressibility factor) v/s “p'curve is constant (slope = `(pi)/(492.6) "atm"^(-1))` at a particular temperature (300K) and very high pressure, then calculate diameter of the molecules (Given: `N_(A) = 6.0 x 10^(23)`, R=0.0821 atm. lit `mol^(-1) K^(-1)`)

Options

A. 7.5 Å
B. 5 Å
C. 2.5 Å
D. 1.25 Å

Answer

B

Explanation

`Z = 1 + (Pb)/(RT)` at high pressure , slope = `(b)/(RT) = (pi)/(492.6) implies b = (pi)/(492.6) xx 0.0821 xx 300` and `b = (4)/(3) pi r^(3) xx 4 N_(A) = (pi)/(492.6) xx 0.0821 xx 300 xx 10^(-3) implies r = 2.5` Å or d = 5 Å