Question

Calculate $\Delta S$ for following process.
$\underset{\text{at 100 K}}{X\left(s\right)}⟶\underset{\text{at 200 K}}{X\left(l\right)}$
Given : Melting point of $X_{\left(s\right)}=100K;\Delta H_{fusion}=20kJ/mol;C_{p,m}(X,l)=10J/mol.K$

• A. $26.93J/K$
• B. $206.93J/K$
• C. $203J/K$
• D. $206.93kJ/K$

Answer 1

The correct option is B $206.93J/K$

$X_{\left(s\right)}\to X_{\left(l\right)}$

100k 200 k

$\Delta S=\frac{\Delta H}{T}$

$\Delta S=\frac{\Delta H_{fusion}}{T_{melt}}+{\int }_{100k}^{200k}\frac{C_{p_1}m(X,l)}{T}dT$

$\Delta S=\frac{20\times {10}^3}{100}+10ln\left(\frac{200}{100}\right)$

$=200+10\left(2.303\right)\left(0.3\right)$

$=200+6.9$

$=206.93J/k$