Question

The heat liberated on complete combustion of \(7.8 \mathrm{~g}\) benzene is \(327 \mathrm{~kJ}\). This heat was measured at constant volume and at \(27^{\circ} \mathrm{C}\). Calculate the heat of combustion of benzene at constant pressure \(\left(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)\) (a) \(-3274 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(-1637 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-3270 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(-3637 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Short answer

The heat of combustion of benzene at constant pressure is approximately -3270 kJ/mol, which matches option (c).

Step-by-step solution

Calculate the Moles of Benzene Combusted

To calculate moles, use the formula: \( n = \frac{m}{M} \), where \( m \) is the mass and \( M \) is the molar mass. The molar mass of benzene (C₆H₆) is \( 78 \ g/mol \). Thus, \( n = \frac{7.8}{78} = 0.1 \ mol \).

Calculate Heat of Combustion at Constant Volume

Given that the heat liberated at constant volume is \( 327 \ kJ \) for \( 0.1 \ mol \) of benzene, we calculate it per mole: \(-Q_v = \frac{327}{0.1} = -3270 \ kJ/mol\).

Convert from Constant Volume to Constant Pressure

Use the formula: \( Q_p = Q_v + \Delta nRT \). For combustion, the balanced equation is: \( 2C_6H_6 + 15O_2 \rightarrow 12CO_2 + 6H_2O \), leading to \( \Delta n = (12 + 6) - (2 + 15) = 1 \) per 2 moles, or 0.5 per mole of C₆H₆. So, \( \Delta nRT = 0.5 \times 8.3 \times 300 = 1245 \ J/mol = 1.245 \ kJ/mol \).

Calculate Heat of Combustion at Constant Pressure

Combine the results: \( Q_p = -3270 + 1.245 = -3,268.755 \ kJ/mol \). Thus, rounding off to the nearest integer, the heat of combustion at constant pressure is approximately \(-3270 \ kJ/mol\).

Select the Closest Option

From the choices given, option (c) \(-3270 \ kJ/mol\) is the direct match with the calculated heat of combustion at constant pressure.

Key concepts

Heat of Combustion

The heat of combustion refers to the energy released when a substance burns completely in the presence of oxygen. It is usually expressed in kilojoules per mole (kJ/mol). This value is crucial when studying the energy characteristics of fuels and other combustible substances. During combustion, chemical bonds are broken and new bonds are formed, releasing energy. The heat of combustion can vary based on whether the process occurs at constant volume or constant pressure. In calorimetric experiments, the heat released under these conditions helps determine the efficiency and energy content of fuels.

• The heat of combustion at constant volume (denoted as \(Q_v\)) is the energy released per mole of substance during combustion in a closed container.


• The heat of combustion at constant pressure (denoted as \(Q_p\)) considers any work done by gases expanding or compressing, which often accounts for a slight variation from \(Q_v\).

Constant Volume Calorimetry

Constant volume calorimetry involves measuring the heat of reaction at constant volume, typically in a bomb calorimeter. This technique assumes no gas expansion work occurs since the volume does not change, making it a simpler calculation.

• The calorimeter contains a small chamber where the sample is burned, releasing heat that changes the temperature of surrounding water.


• By knowing the heat capacity of the calorimeter, the total energy output can be calculated.

In the provided exercise, the heat liberated at constant volume was calculated to better understand the energy released from burning benzene. This measurement forms a starting point because it doesn't account for pressure changes, allowing for straightforward energy determination.

Molar Mass Calculation

Molar mass calculation is a fundamental step in stoichiometric analyses involving chemical reactions. It is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). Calculating the molar mass allows you to convert between grams of a substance and the number of moles, establishing a vital link to assess chemical equations quantitatively.

• The formula for calculating molar mass is the sum of the atomic masses of all atoms in a molecule. For example, benzene (\(C_6H_6\)) has a molar mass of 78 g/mol, which is calculated as \(6\times12.01 + 6\times1.008\).


• In the original exercise, determining the moles of benzene combusted was critical to calculating the heat of combustion.

Understanding molar mass calculation enables predictions about how much reactant will be needed or how much product will be created, underpinning many chemical processes.