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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.

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    $\begingroup$ You don't make steam at 0°C. You heat water to 100°C and only then evaporate it. $\endgroup$ – Ivan Neretin Apr 18 '16 at 14:45
  • $\begingroup$ So i have to make water from 0 Celsius to 100 Celsius to 100 Celsius steam and then continue step 5? $\endgroup$ – J_B892 Apr 18 '16 at 14:50
  • $\begingroup$ Yeah, like that. $\endgroup$ – Ivan Neretin Apr 18 '16 at 14:58
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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. $303~^{\circ}\mathrm{C}$.

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  • $\begingroup$ Welcome to Chemistry.SE! Take the tour to get familiar with this site. Mathematical expressions and equations can be formatted using $\LaTeX$ syntax. For more information in general have a look at the help center. $\endgroup$ – Martin - マーチン Apr 19 '16 at 5:53

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