To calculate \(\Delta H\) (in \(\text{kJ/mol}\)) for the dissolving process of \(\text{Ca(OH)}_2\), we can follow these steps:
1. Identify the given values:
- The heat of the reaction, \(q_{\text{rxn}}\), is given as \(-1677 \text{ joules}\).
- The amount of \(\text{Ca(OH)}_2\) is \(0.100 \text{ mol}\).
2. Set up the expression to calculate \(\Delta H\):
[tex]\[
\Delta H = \frac{q_{\text{rxn}}}{\text{amount of } \text{Ca(OH)}_2}
\][/tex]
3. Insert the given values into the expression:
[tex]\[
\Delta H = \frac{-1677 \text{ J}}{0.100 \text{ mol}}
\][/tex]
4. Convert the units from joules to kilojoules:
- Recall that \(1 \text{ kJ} = 1000 \text{ J}\).
- Therefore, we multiply by the conversion factor \(\frac{1 \text{ kJ}}{1000 \text{ J}}\).
Now, the full expression is:
[tex]\[
\Delta H = \left(\frac{-1677 \text{ J}}{0.100 \text{ mol}}\right) \times \left(\frac{1 \text{ kJ}}{1000 \text{ J}}\right)
\][/tex]
5. Simplify the expression:
[tex]\[
\Delta H = \frac{-1677}{0.100} \times \frac{1}{1000} \text{ kJ/mol}
\][/tex]
Calculating the numerical part:
[tex]\[
\frac{-1677}{0.100} = -16770
\][/tex]
Therefore,
[tex]\[
-16770 \times \frac{1}{1000} = -16.77 \text{ kJ/mol}
\][/tex]
6. Conclusion:
[tex]\(\Delta H\)[/tex] for the dissolving process of [tex]\(\text{Ca(OH)}_2\)[/tex] is [tex]\(-16.77 \text{ kJ/mol}\)[/tex].
