Question

$\Delta_{ f } G ^{\circ}$ at $500\, K$ for substance ' $S$ ' in liquid state and gaseous state are $+100.7\, kcal\, mol ^{-1}$ and $+103\, kcal\, mol ^{-1}$ respectively. Vapour pressure of liquid ' $S$ ' at $500\, K$ is approximately equal to_____ atm. $\left( R =2\, cal\, K ^{-1} mol ^{-1}\right)$

Answer 1

$S _{(l)} \longrightarrow S _{( g )}$
$\Delta G ^{\circ} =\Delta f G ^{\circ}\left( S _{( g )}\right)-\Delta_{ f } G ^{\circ}\left( S _{(l)}\right)$
$=+103-100.7=2.3\, kcal\, mol ^{-1}$
$\Delta G ^{\circ} =-2.303\, RT \log _{10} K$
$2.3 =-2.303 \times 2 \times 10^{-3} \times 500 \times \log _{10} K$
$\log _{10} K =\frac{-2.3}{2.303 \times 2 \times 10^{-3} \times 500}=-1$
$\therefore K =10^{-1}=0.1$
$K = p _{ S ( g )}$
( $\because$ Partial pressure of liquid is not considered in calculating $K$ )
$\therefore $ Vapour pressure of liquid ' $S$ ' at $500\, K =0.1\, atm$