Questions: Consider the reaction below: CH4(g) + O2(g) → CO2(g) + 2 H2O(g) ΔH=-890.4 kJ Calculate the amount of heat (q) produced by the combustion of 7.74 g of methane. Include your sign indicating if heat is absorbed or released. kJ

Solution Steps

The chemical formula for methane is \(\mathrm{CH}_4\). To find its molar mass, we sum the atomic masses of its constituent atoms:

• Carbon (C): \(12.01 \, \text{g/mol}\)
• Hydrogen (H): \(1.008 \, \text{g/mol} \times 4 = 4.032 \, \text{g/mol}\)

Thus, the molar mass of methane is: \[ 12.01 \, \text{g/mol} + 4.032 \, \text{g/mol} = 16.042 \, \text{g/mol} \]

Given the mass of methane is 7.74 g, we calculate the number of moles using the molar mass: \[ \text{moles of } \mathrm{CH}_4 = \frac{7.74 \, \text{g}}{16.042 \, \text{g/mol}} = 0.4823 \, \text{mol} \]

The reaction enthalpy \(\Delta H\) is given as \(-890.4 \, \text{kJ/mol}\), indicating that 890.4 kJ of heat is released per mole of methane combusted. Therefore, the heat produced by 0.4823 moles of methane is: \[ q = 0.4823 \, \text{mol} \times (-890.4 \, \text{kJ/mol}) = -429.3 \, \text{kJ} \]

Final Answer