To calculate the enthalpy of combustion ([tex]\(\Delta H_{\text{comb}}\)[/tex]) of [tex]\( \mathrm{N_2H_4} \)[/tex], follow these steps:
1. Identify the given data:
- Moles of [tex]\( \mathrm{N_2H_4} \)[/tex]: [tex]\( 0.03119 \)[/tex] moles
- Heat of reaction ([tex]\( q_{\text{rxn}} \)[/tex]): [tex]\( -20,744.4 \)[/tex] Joules
2. Enthalpy of combustion formula:
The enthalpy of combustion (per mole) can be calculated by dividing the total heat of reaction by the number of moles of the substance involved.
[tex]\[
\Delta H_{\text{comb}} = \frac{q_{\text{rxn}}}{\text{moles of substance}}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\Delta H_{\text{comb}} = \frac{-20,744.4 \, \text{J}}{0.03119 \, \text{mol}}
\][/tex]
4. Perform the division to find [tex]\(\Delta H_{\text{comb}}\)[/tex] in Joules per mole:
[tex]\[
\Delta H_{\text{comb}} = \frac{-20,744.4}{0.03119}
\][/tex]
[tex]\[
\Delta H_{\text{comb}} = -665,084.572 \, \text{J/mol}
\][/tex]
5. Convert Joules to kilojoules:
Since 1 kilojoule (kJ) is equal to 1,000 Joules (J):
[tex]\[
\Delta H_{\text{comb}} = \frac{-665,084.572 \, \text{J}}{1,000}
\][/tex]
[tex]\[
\Delta H_{\text{comb}} = -665.084572 \, \text{kJ/mol}
\][/tex]
6. Apply significant figures:
The given data for moles ([tex]\(0.03119\)[/tex]) has 4 significant figures. Thus, we round the final result to 4 significant figures:
[tex]\[
\Delta H_{\text{comb}} \approx -665.1 \, \text{kJ/mol}
\][/tex]
Therefore, the enthalpy of combustion of [tex]\( \mathrm{N_2H_4} \)[/tex] is [tex]\(-665.1 \, \text{kJ/mol}\)[/tex].
