A) \[2.64\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\]
B) \[9.26\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\]
C) \[7.90\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}~\]
D) \[8.49\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\]
Correct Answer: B
Solution :
\[\underset{273K}{\mathop{{{H}_{2}}O}}\,(s)\to \underset{273K}{\mathop{{{H}_{2}}O(\ell )}}\,\Delta {{S}_{1}}=\frac{\Delta {{H}_{fusion}}}{T}=\frac{334}{273}=1.22\] \[\underset{273K}{\mathop{{{H}_{2}}O}}\,(\ell )\to \underset{373K}{\mathop{{{H}_{2}}O}}\,(\ell )\Delta {{S}_{2}}=4.2\times \ell n=\left( \frac{373}{273} \right)=1.31\] \[\underset{373K}{\mathop{{{H}_{2}}O}}\,(\ell )\to \underset{373K}{\mathop{{{H}_{2}}O}}\,(g)\Delta {{S}_{3}}=\frac{\Delta {{H}_{vap}}}{T}=\frac{2491}{373}=6.67\] \[\underset{373K}{\mathop{{{H}_{2}}O}}\,(g)\to \underset{383K}{\mathop{{{H}_{2}}O}}\,(g)\Delta {{S}_{4}}=2\ell n\frac{383}{373}=0.529\] \[\Delta \,{{S}_{total}}\,\,=\,\,9.26\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\]
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