Calculating temperature after adding heat to ice

Question

If $53.2~\mathrm{kJ}$ of heat are added to $15.5~\mathrm{g}$ of ice at $-5^\circ\mathrm{C}$, what will be the resultant state of matter in which water is present and also calculate its final temperature.

I have done this:

• Step 1: Energy required to make ice at 0 Celsius
• Step 2:Energy required to make water at 0 Celsius
• Step 3: Energy required to make steam at 0 Celsius
• Step 4: Energy required to make steam at 100 Celsius
• Step 5:Energy required to make steam at 'x-100' Celsius

Please leave a comment stating if any errors are present. The answer I got is x = 808 Celsius. The correct answer is 303 Celsius.

Answer 1

It is an enthalpy balance that requires knowledge of the enthalpy change at each step: (The steps you have listed are not correct.)

1. Solid heat capacity of ice of the form e.g. $C_p^\mathrm{solid}(T)$. This allows you to calculate the amount of heat (or energy) required to warm the sub-cooled ice from $-5~^{\circ}\mathrm{C}$ to $0~^{\circ}\mathrm{C}$.
2. (Latent) heat of fusion, $\Delta H_\mathrm{fus}$ then must be added to transform the solid ice to liquid water at $0~^{\circ}\mathrm{C}$.
3. Next we must warm the liquid water from $0~^{\circ}\mathrm{C}$ to its boiling point at $100~^{\circ}\mathrm{C}$, which requires knowledge of the liquid heat capacity of water e.g. $C_p^\mathrm{liquid}(T)$.
4. Now at the boiling point, we must account for the required amount of energy to transform the liquid water into its vapor state at $100~^{\circ}\mathrm{C}$ using the (latent) heat of vaporization of water $\Delta H_\mathrm{vap}$.
5. The final step then involves super-heating the vapor from $100~^{\circ}\text{C}$ to $T_\mathrm{final} = ?~^{\circ} \mathrm{C}$, which requires knowledge of the vapor heat capacity of steam e.g. $C_p^\mathrm{vapor}(T)$.

You know the overall enthalpy change ($53.2~\mathrm{ kJ}$) and you know the starting temperature ($-5~^{\circ}\mathrm{C}$), so all you have to do is add the results from each of the steps and solve for $T_\mathrm{final}$ e.g. $303~^{\circ}\mathrm{C}$.