Sure, let's calculate the enthalpy change for each reaction step-by-step using the provided formula:
[tex]\[
\Delta H = \frac{-q}{\text{moles}} \times \frac{1 \text{ kJ}}{1000 \text{ J}}
\][/tex]
### Reaction 1
Given data:
- [tex]\( q_1 = -50000 \)[/tex] joules
- [tex]\( \text{moles}_1 = 2 \)[/tex]
1. Substitute the values into the formula:
[tex]\[
\Delta H_1 = \frac{-(-50000) \text{ J}}{2 \text{ moles}} \times \frac{1 \text{ kJ}}{1000 \text{ J}}
\][/tex]
2. Simplify the equation:
[tex]\[
\Delta H_1 = \frac{50000 \text{ J}}{2 \text{ moles}} \times \frac{1 \text{ kJ}}{1000 \text{ J}}
\][/tex]
3. Calculate the intermediate values:
[tex]\[
\frac{50000 \text{ J}}{2 \text{ moles}} = 25000 \text{ J/mol}
\][/tex]
4. Convert joules to kilojoules:
[tex]\[
25000 \text{ J/mol} \times \frac{1 \text{ kJ}}{1000 \text{ J}} = 25 \text{ kJ/mol}
\][/tex]
5. Record to 2 significant figures:
[tex]\[
\Delta H_1 = 25.00 \text{ kJ/mol}
\][/tex]
### Reaction 2
Given data:
- [tex]\( q_2 = -100000 \)[/tex] joules
- [tex]\( \text{moles}_2 = 3 \)[/tex]
1. Substitute the values into the formula:
[tex]\[
\Delta H_2 = \frac{-(-100000) \text{ J}}{3 \text{ moles}} \times \frac{1 \text{ kJ}}{1000 \text{ J}}
\][/tex]
2. Simplify the equation:
[tex]\[
\Delta H_2 = \frac{100000 \text{ J}}{3 \text{ moles}} \times \frac{1 \text{ kJ}}{1000 \text{ J}}
\][/tex]
3. Calculate the intermediate values:
[tex]\[
\frac{100000 \text{ J}}{3 \text{ moles}} = 33333.33 \text{ J/mol}
\][/tex]
4. Convert joules to kilojoules:
[tex]\[
33333.33 \text{ J/mol} \times \frac{1 \text{ kJ}}{1000 \text{ J}} = 33.3333 \text{ kJ/mol}
\][/tex]
5. Record to 2 significant figures:
[tex]\[
\Delta H_2 = 33.33 \text{ kJ/mol}
\][/tex]
### Final Results
- Reaction 1: [tex]\( 25.00 \)[/tex] kJ/mol
- Reaction 2: [tex]\( 33.33 \)[/tex] kJ/mol
