CHEMISTRY, M4 EQ-Bank 38v2

Methane (\(\ce{CH4}\)) is a hydrocarbon fuel which combusts completely according to the following equation:

\[\ce{CH4 (g) + 2O2 (g) -> CO2 (g) + 2H2O (g)}\]

A chemist burns 0.30 g of methane in excess oxygen during a calorimetry study, and the heat energy is used to heat 75.0 g of water. The initial temperature of the water in the calorimeter is 22.0 °C, which rises to a maximum of 36.5 °C after absorbing the energy from the combustion reaction. Based on these results, calculate the experimental molar heat of combustion (\(\Delta H^\circ_{\text{comb}}\)) for methane. (4 marks)

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The experimental molar heat of combustion (\(\Delta H^\circ_{\text{comb}}\)) for methane is \( -240 \, \text{kJ/mol} \). (2 sig.fig)

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Calculate the energy absorbed by the water:

\[q = mc\Delta T = (75.0 \, \text{g})(4.18 \, \text{J/g}^\circ\text{C})(36.5^\circ\text{C} – 22.0^\circ\text{C}) = 4545.75 \, \text{J}\]

Calculate the number of moles of methane burned:

\[n = \frac{m}{M} = \frac{0.30 \, \text{g}}{16.042 \, \text{g/mol}} = 0.0187 \, \text{mol}\]

Calculate the molar heat of combustion:

\[\Delta H^\circ_{\text{comb}} = -\frac{q}{n} = -\frac{4545.75 \, \text{J}}{0.0187 \, \text{mol}} = -243088.24 \, \text{J/mol} = -240 \, \text{kJ/mol}\]

→ The experimental molar heat of combustion (\(\Delta H^\circ_{\text{comb}}\)) for methane is \( -240 \, \text{kJ/mol} \). (2 sig.fig)