Reactivity 1.3—Energy from fuels: Practice Questions

Which statement correctly describes a characteristic of renewable energy sources compared to non-renewable sources?

A liquid hydrocarbon fuel has a specific energy of \(44.0\text{ kJ g}^{-1}\) and a density of \(0.720\text{ g cm}^{-3}\). What is its energy density in \(\text{kJ dm}^{-3}\)?

Consider the combustion of methane:
\(CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l)\)
Using the following average bond enthalpies:
C-H: \(414\text{ kJ mol}^{-1}\)
O=O: \(498\text{ kJ mol}^{-1}\)
C=O: \(804\text{ kJ mol}^{-1}\)
O-H: \(463\text{ kJ mol}^{-1}\)
Calculate the specific energy of methane in \(kJ\text{ g}^{-1}\). (\(M_r\text{ of } CH_4 = 16.05\))

Which of the following is the correct definition of the specific energy of a fuel?

Hydrogen gas is considered a high-performance fuel for rockets due to its high specific energy (\(142\text{ kJ g}^{-1}\)). However, its energy density at STP is very low (\(0.0127\text{ MJ dm}^{-3}\)). If hydrogen is compressed to a liquid state (density \(0.0708\text{ g cm}^{-3}\)), what is its new energy density in \(\text{MJ dm}^{-3}\)?

Distinguish between the terms specific energy and energy density of a fuel, and explain why hydrogen (\( H_2 \)) is often stored as a liquid or under high pressure despite having a high specific energy.

Calculate the mass of \( \text{CO}_2 \) produced, in grams, for every \( 1.00 \times 10^3 \text{ kJ} \) of energy released by the complete combustion of propan-1-ol (\( C_3H_7OH \)), given its standard enthalpy of combustion is \( -2021 \text{ kJ mol}^{-1} \).

Explain why incomplete combustion of a fuel is generally more dangerous than complete combustion.

Compare the energy efficiency of two alcohols used as fuels: methanol (\(CH_3OH\)) and ethanol (\(C_2H_5OH\)).

(a) Calculate the specific energy (in \(\text{kJ g}^{-1}\)) for both fuels using the following standard enthalpy of combustion data:
\(\Delta H_c^{\circ}(\text{methanol}) = -726\text{ kJ mol}^{-1}\)
\(\Delta H_c^{\circ}(\text{ethanol}) = -1367\text{ kJ mol}^{-1}\)

(b) Based on your calculations, identify which fuel provides more energy per gram and explain why energy density is a critical factor when choosing fuels for transportation.

Using the average bond enthalpy data below, calculate the enthalpy of combustion for propane, \(C_3H_8(g)\).

Bond Enthalpies (\(\text{kJ mol}^{-1}\)):
\(C-H = 414\), \(C-C = 346\), \(O=O = 498\), \(C=O = 804\), \(O-H = 463\)

(a) Write the balanced chemical equation for the complete combustion of propane.
(b) Calculate the total energy required to break bonds and the total energy released upon forming bonds.
(c) The experimental value for \(\Delta H_c^{\circ}\) of propane is \(-2220\text{ kJ mol}^{-1}\). Suggest why your calculated value differs from the experimental value.