To calculate the enthalpy change for the combustion of the hydrocarbon, follow these steps:
1. Convert the heat energy (q_{\text{cal}}) from Joules to kilojoules:
Given:
[tex]\[
q_{\text{cal}} = 6191.78 \text{ J}
\][/tex]
Since 1 kJ = 1000 J, we convert Joules to kilojoules by dividing by 1000:
[tex]\[
q_{\text{cal kJ}} = \frac{6191.78 \text{ J}}{1000} = 6.19178 \text{ kJ}
\][/tex]
2. Calculate the enthalpy change (ΔH) in [tex]\(kJ/mol\)[/tex]:
Given:
[tex]\[
n = 0.0019243682 \text{ mol}
\][/tex]
To find the enthalpy change per mole, divide the heat energy in kilojoules by the number of moles:
[tex]\[
\Delta H = \frac{q_{\text{cal kJ}}}{n} = \frac{6.19178 \text{ kJ}}{0.0019243682 \text{ mol}}
\][/tex]
3. Calculate the numerical value:
Performing the division:
[tex]\[
\Delta H = 3217.565120853691 \text{ kJ/mol}
\][/tex]
4. Round the result to three significant figures:
The significant figures determination:
[tex]\[
\Delta H \approx 3217.565 \Rightarrow 3218 \text{ kJ/mol} (\text{to three significant figures})
\][/tex]
Since the combustion process typically releases energy, the enthalpy change should be negative:
[tex]\[
\Delta H = -3218 \text{ kJ/mol}
\][/tex]
Thus, the enthalpy change for the combustion of the hydrocarbon is:
[tex]\[
\boxed{-3218 \text{ kJ/mol}}
\][/tex]
