MCQ 11 Mark
Calculate the enthalpy change on freezing of 1.0 mol of water at $10.0^{\circ} C$ to the ice at $-10.0^{\circ} C . \Delta_{\text {fus }} H =6.03 kJ$ $\operatorname{mol}^{-1}$ at $0^{\circ} C$.
a. $C _{ P }\left[ H _2 O ( l )\right]=75.3 Jmol ^{-1} K^{-1}$
b. $C _{ P }\left[ H _2 O ( s )\right]=36.8 Jmol ^{-1} K^{-1}$
a. $C _{ P }\left[ H _2 O ( l )\right]=75.3 Jmol ^{-1} K^{-1}$
b. $C _{ P }\left[ H _2 O ( s )\right]=36.8 Jmol ^{-1} K^{-1}$
- A$\Delta H =-5.231 kJmol ^{-1}$
- ✓$\Delta H =-7.151 kJ mol ^{-1}$
- C$\Delta H =-6.114 kJmol ^{-1}$
- D$\Delta H =-7.415 kJ mol ^{-1}$
Answer
View full question & answer→Correct option: B.
$\Delta H =-7.151 kJ mol ^{-1}$
(b) $\Delta H =-7.151 kJ mol ^{-1}$
Explanation: Water $\left(10.0^{\circ} C \right) \rightarrow$ ice $\left(-10.0^{\circ} C \right) \Delta H=$ ?
The enthalpy change for the conversion of 1 mole liquid water at $10.0^{\circ} C$ into 1 mole liquid water $0^{\circ} C$, water $\left(10.0^{\circ} C \right)$ $\rightleftharpoons \operatorname{water}\left(0^{\circ} C \right)$.
$
\Delta H_1=C_p \times H_2 O(l) \times \Delta T=-75.3 Jmol^{-1} K^{-1}=-753 J mol^{-1}
$
Enthalpy of fusion, water $\left(0^{\circ} C \right) \rightleftharpoons \operatorname{ice}\left(0^{\circ} C \right), \Delta H_2=\Delta_{\text {fus }} H$
$
l \triangle H_2=\triangle H_{\text {freezing }}=-\triangle H_{\text {fusion }}=-6.06 kJ mol^{-1}
$
Enthalpy change for conversion of 1 mole of ice at $0^{\circ} C$ to 1 mole of ice at $10^{\circ} C$, Ice $\left(0^{\circ} C \right) \rightleftharpoons$ ice $\left(10.0^{\circ} C \right)$;
$
\begin{aligned}
& \Delta H_3=C_p\left[H_2 O(s)\right] \Delta T=-36.8 Jmol^{-1} K^{-1} \times 10 K=-368 J mol^{-1} \\
& \Delta H=\Delta H_1+\Delta H_2+\Delta H_3=-(0.753+6.03+0.368) kJ mol^{-1}=-7.151 kJml^{-1}
\end{aligned}
$
Explanation: Water $\left(10.0^{\circ} C \right) \rightarrow$ ice $\left(-10.0^{\circ} C \right) \Delta H=$ ?
The enthalpy change for the conversion of 1 mole liquid water at $10.0^{\circ} C$ into 1 mole liquid water $0^{\circ} C$, water $\left(10.0^{\circ} C \right)$ $\rightleftharpoons \operatorname{water}\left(0^{\circ} C \right)$.
$
\Delta H_1=C_p \times H_2 O(l) \times \Delta T=-75.3 Jmol^{-1} K^{-1}=-753 J mol^{-1}
$
Enthalpy of fusion, water $\left(0^{\circ} C \right) \rightleftharpoons \operatorname{ice}\left(0^{\circ} C \right), \Delta H_2=\Delta_{\text {fus }} H$
$
l \triangle H_2=\triangle H_{\text {freezing }}=-\triangle H_{\text {fusion }}=-6.06 kJ mol^{-1}
$
Enthalpy change for conversion of 1 mole of ice at $0^{\circ} C$ to 1 mole of ice at $10^{\circ} C$, Ice $\left(0^{\circ} C \right) \rightleftharpoons$ ice $\left(10.0^{\circ} C \right)$;
$
\begin{aligned}
& \Delta H_3=C_p\left[H_2 O(s)\right] \Delta T=-36.8 Jmol^{-1} K^{-1} \times 10 K=-368 J mol^{-1} \\
& \Delta H=\Delta H_1+\Delta H_2+\Delta H_3=-(0.753+6.03+0.368) kJ mol^{-1}=-7.151 kJml^{-1}
\end{aligned}
$

