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Calculate the enthalpy change (ΔH) of the reactant using the formula below, which also converts joules to kilojoules. Record to 2 significant figures.

[tex]\[
\Delta H = \frac{-q}{\text{moles}} \times \frac{\text{kJ}}{1000 \text{J}}
\][/tex]

Reaction 1: [tex]\(\square \, \text{kJ/mol}\)[/tex]

Reaction 2: [tex]\(\square \, \text{kJ/mol}\)[/tex]


Sagot :

Let's solve the problem step-by-step to find the enthalpy change (ΔH) for both reactions using the given formula:

[tex]\[ \Delta H = \frac{-q}{\text {moles}} \times \frac{\text{kJ}}{1000 \text{J}} \][/tex]

where:
- [tex]\( q \)[/tex] is the heat energy in joules,
- "moles" is the number of moles of the substance.

### Reaction 1

1. Given data:
- [tex]\( q_{\text{reaction1}} = -30000 \)[/tex] J (energy in joules)
- moles of reactants for reaction 1 = 2

2. Convert energy from joules to kilojoules:
[tex]\[ q_{\text{reaction1 (kJ)}} = \frac{-30000}{1000} \text{ kJ} = -30 \text{ kJ} \][/tex]

3. Calculate ΔH for reaction 1:
[tex]\[ \Delta H_{\text{reaction1}} = \frac{q_{\text{reaction1 (kJ)}}}{\text{moles reaction 1}} = \frac{-30}{2} = -15 \text{ kJ/mol} \][/tex]

4. Round ΔH to 2 significant figures:
[tex]\[ \Delta H_{\text{reaction1}} \approx -15.0 \text{ kJ/mol} \][/tex]

### Reaction 2

1. Given data:
- [tex]\( q_{\text{reaction2}} = -45000 \)[/tex] J (energy in joules)
- moles of reactants for reaction 2 = 3

2. Convert energy from joules to kilojoules:
[tex]\[ q_{\text{reaction2 (kJ)}} = \frac{-45000}{1000} \text{ kJ} = -45 \text{ kJ} \][/tex]

3. Calculate ΔH for reaction 2:
[tex]\[ \Delta H_{\text{reaction2}} = \frac{q_{\text{reaction2 (kJ)}}}{\text{moles reaction 2}} = \frac{-45}{3} = -15 \text{ kJ/mol} \][/tex]

4. Round ΔH to 2 significant figures:
[tex]\[ \Delta H_{\text{reaction2}} \approx -15.0 \text{ kJ/mol} \][/tex]

### Summary:

- Reaction 1: [tex]\(-15.0\)[/tex] [tex]\( \text{kJ/mol} \)[/tex]
- Reaction 2: [tex]\(-15.0\)[/tex] [tex]\( \text{kJ/mol} \)[/tex]

So, the enthalpy changes for both reactions, recorded to 2 significant figures, are as follows:

- Reaction 1: [tex]\( -15.0 \text{ kJ/mol} \)[/tex]
- Reaction 2: [tex]\( -15.0 \text{ kJ/mol} \)[/tex]
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