A light fuel oil with an average chemical composition of C10 H18 is burned with oxygen in a bomb

step 1 The amount of heat evolved in the calorimeter is proportional to the amount of isoctane that is

A light fuel oil with an average chemical composition of C10...

A light fuel oil with an average chemical composition of $\mathrm{C}_{10} \mathrm{H}_{18}$ is burned with oxygen in a bomb calorimeter. The heat evolved is measured as $43960 \mathrm{~J} \mathrm{~g}^{-1}$ for the reaction at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$. Calculate the standard heat of combustion of the fuel oil at $298.15 \mathrm{~K}$ $\left(25^{\circ} \mathrm{C}\right)$ with $\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ and $\mathrm{CO}_2(\mathrm{~g})$ as products. Note that the reaction in the bomb occurs at constant volume, produces liquid water as a product, and goes to completion.

Key Concepts

Phase Change Correction

When the physical state of the products in a reaction differs from that defined by the standard conditions—such as water produced as a liquid in the reaction but required as vapor in the standard state—a correction must be applied. This correction accounts for the additional energy associated with changing the phase, such as the enthalpy of vaporization.

Relation Between Internal Energy and Enthalpy

The relationship between the change in internal energy (?U) measured in a bomb calorimeter and the enthalpy change (?H) of the reaction is given by ?H = ?U + ?n_gas·RT, where ?n_gas represents the change in the number of moles of gas. This relation is essential for converting the calorimetric data into the standard heat of combustion when standard states differ from the measurement conditions.

Standard Heat of Combustion

This is the energy released when one mole of a substance burns completely in oxygen under standard conditions. It reflects the intrinsic energy content of the fuel and is expressed as an enthalpy change (?H) for the reaction.

Bomb Calorimetry

Bomb calorimetry is a technique used to measure the heat evolved by a reaction at constant volume. Since the measurement is made at constant volume, it directly provides the change in internal energy (?U), which may require adjustments to obtain the standard enthalpy change (?H) at constant pressure.

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