Questions: Nitromethane (CH3NO2) burns in air to produce significant amounts of heat. 2 CH3NO2(l) + 3 / 2 O2(g) -> 2 CO2(g) + 3 H2O(l) + N2(g) ΔHrnn^ρ = -1418 kJ How much heat is produced by the complete reaction of 5.56 kg of nitromethane?

Solution Steps

Calculate the molar mass of nitromethane (\(\mathrm{CH}_{3} \mathrm{NO}_{2}\)):

• Carbon (C): \(12.01 \, \text{g/mol}\)
• Hydrogen (H): \(1.01 \, \text{g/mol} \times 3 = 3.03 \, \text{g/mol}\)
• Nitrogen (N): \(14.01 \, \text{g/mol}\)
• Oxygen (O): \(16.00 \, \text{g/mol} \times 2 = 32.00 \, \text{g/mol}\)

Add these values together: \[ \text{Molar mass of } \mathrm{CH}_{3} \mathrm{NO}_{2} = 12.01 + 3.03 + 14.01 + 32.00 = 61.05 \, \text{g/mol} \]

Convert the given mass of nitromethane to moles using its molar mass: \[ \text{Mass of nitromethane} = 5.56 \, \text{kg} = 5560 \, \text{g} \] \[ \text{Moles of } \mathrm{CH}_{3} \mathrm{NO}_{2} = \frac{5560 \, \text{g}}{61.05 \, \text{g/mol}} \]

Use the stoichiometry of the reaction to find the heat produced. The reaction shows that 2 moles of \(\mathrm{CH}_{3} \mathrm{NO}_{2}\) release \(-1418 \, \text{kJ}\): \[ \text{Heat produced per mole of } \mathrm{CH}_{3} \mathrm{NO}_{2} = \frac{-1418 \, \text{kJ}}{2} = -709 \, \text{kJ/mol} \]

Calculate the total heat produced: \[ \text{Total heat} = \text{Moles of } \mathrm{CH}_{3} \mathrm{NO}_{2} \times (-709 \, \text{kJ/mol}) \]

Final Answer