madey21
Answered

Calculate [tex]\Delta H \left( kJ / \text{mol Ca(OH)}_2\right)[/tex] for the dissolving process.

[tex]\[
\begin{array}{c}
q_{\text{rxn}} = -1677 \text{ joules} \\
0.100 \text{ mol Ca(OH)}_2 \\
\Delta H = \frac{-1677 \text{ J}}{0.100 \text{ mol}} \times \frac{1 \text{ kJ}}{1000 \text{ J}}
\end{array}
\][/tex]



Answer :

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].