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Calculate the enthalpy, in [tex]$kJ / mol$[/tex], for the combustion of the hydrocarbon from the data from the previous steps.

[tex]
\begin{array}{c}
q_{\text{cal}} = 6191.78 \, \text{J} \quad n = 0.0019243682 \, \text{mol} \\
\Delta H = [?] \, \text{kJ/mol}
\end{array}
[/tex]

Enter either a "+" or "-" sign AND the magnitude. Give your answer to three significant figures.



Answer :

GinnyAnswer
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]

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