R1.3 Energy from fuels

The molar enthalpy of combustion equals the energy per gram multiplied by the molar mass: $\Delta H_c=\text{energy per gram}\times M_r$. The negative sign is included because combustion is exothermic.

$\Delta H_c=-49.5{\text{ kJ g}}^{-1}\times 58.12{\text{ g mol}}^{-1}$

$\Delta H_c=-2877{\text{ kJ mol}}^{-1}$This is consistent with typical values for alkane combustion, which increase in magnitude with chain length.

The correct answer is $-2877$ kJ mol${}^{-1}$. The negative sign confirms the reaction is exothermic, as expected for all combustion reactions.

We need to convert energy per gram (specific energy) into energy per mole (molar enthalpy) by multiplying by the molar mass (58.12 g mol${}^{-1}$).

This would be obtained by dividing 49.5 by 58.12, which is the wrong operation. Dividing specific energy by molar mass gives units of kJ g${}^{-1}$ per g mol${}^{-1}$ = kJ mol${}^{-1}$ g${}^{-2}$, which is meaningless.

This is simply the specific energy value without any conversion. The question clearly states 49.5 kJ per gram, not per mole, so no calculation has been performed.

This is $49.5\times 58.12÷10=287.7$, suggesting an arithmetic error (off by a factor of 10). The correct multiplication gives 2877, not 287.7.

Only $-2877$ kJ mol${}^{-1}$ results from the correct calculation: $49.5\times 58.12=2877$ kJ mol${}^{-1}$, with a negative sign because combustion is exothermic.

A renewable energy source can be replenished on a human timescale (years to decades) through natural processes or biological cycles. A non-renewable source took millions of years to form and cannot be replenished at the rate it is consumed.

Ethanol from sugarcane is renewable (crops regrow annually). Wind electricity is renewable (wind is a continuous natural phenomenon). Hydrogen from solar electrolysis is renewable (uses renewable electricity to split water). Crude oil took millions of years to form from ancient marine organisms under pressure — it cannot be replenished on a human timescale.

Crude oil is a fossil fuel — it is non-renewable by definition. Its extraction and combustion release carbon that has been stored underground for millions of years, unlike the other options.

We need to identify which option is non-renewable — meaning it cannot be replenished within a human lifetime.

Sugarcane is a crop that can be regrown each growing season. Ethanol is produced by fermentation of glucose from sugarcane, making it a renewable biofuel.

Wind is a continuously available natural phenomenon driven by solar heating of Earth's atmosphere. It is inherently renewable and produces no fuel depletion.

This is 'green hydrogen' — produced by splitting water using renewable solar electricity. As long as the sun shines and water is available, hydrogen can be produced indefinitely.

Crude oil formed over millions of years and exists in finite underground deposits. It is a fossil fuel and is definitively non-renewable.