Question

The enthalpy of vaporisation of liquid diethyl ether $(C_2{H}_5{)}_{2}O$ is $26{\text{kJ mol}}^{-1}$ at its boiling point $35{}^o\text{C}.$ Calculate $△S^o$ for conversion of vapour to liquid (condensation) at $35{}^o\text{C}.$

• A. $-84.41{\text{J K}}^{-1}{\text{mol}}^{-1}$
• B. $+84.41{\text{J K}}^{-1}{\text{mol}}^{-1}$
• C. $-48.41{\text{J K}}^{-1}{\text{mol}}^{-1}$
• D. $+48.41{\text{J K}}^{-1}{\text{mol}}^{-1}$

Answer 1

The correct option is A $-84.41{\text{J K}}^{-1}{\text{mol}}^{-1}$

Entropy change for the phase transformation is given as:

$△S_{\text{vaporisation}}=\frac{△H_{\text{vaporisation}}}{T_b}$

where boiling point i.e, $T_b=35+273=308\text{K}$
and $H_{\text{vaporisation}}=26\text{kJ/mol}$

putting the values we get,

$△S_{\text{vap}}=\frac{26000{\text{J mol}}^{-1}}{308\text{K}}$

$=84.42{\text{J K}}^{-1}{\text{mol}}^{-1}$

And we know
$△H_{\text{condensation}}=-△H_{\text{vaporisation}}$
so,
$△S_{\text{condensation}}=-△S_{\text{vaporisation}}$

$△S_{\text{condensation}}=-84.42{\text{J K}}^{-1}{\text{mol}}^{-1}$