Problem 56 - Chemistry: The Central Science

Question

A \(1.800-g\) sample of phenol \(\left(C_{6} H_{5} O H\right)\) was burned in a bomb calorimeter whose total heat capacity is \(11.66 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). The temperature of the calorimeter plus contents increased from \(21.36^{\circ} \mathrm{C}\) to \(26.37^{\circ} \mathrm{C}\). (a) Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of phenol? Per mole of phenol?

Step-by-Step Solution

Answer

The balanced chemical equation for the combustion of phenol is: $$ C_6H_5OH + \dfrac{15}{2}O_2 \rightarrow 6CO_2 + 3H_2O $$ The heat of combustion per gram of phenol is 32.415 kJ/g, and the heat of combustion per mole of phenol is 3050.25 kJ/mol.

Step 1: Write the balanced chemical equation for the combustion of phenol

Phenol \(C_6H_5OH\), when burned, will react with oxygen \(O_2\) to produce carbon dioxide \(CO_2\) and water \(H_2O\). The balanced chemical equation for this reaction is: $$ C_6H_5OH + \dfrac{15}{2}O_2 \rightarrow 6CO_2 + 3H_2O $$

Step 2: Calculate the heat released by the combusti on

To calculate the heat released by the combustion, we will use the heat capacity of the calorimeter and the change in temperature. The formula we will use is: $$ q = C \times \Delta T $$ where \(q\) is the heat released, \(C\) is the total heat capacity of the calorimeter, and \(\Delta T\) is the change in temperature. First, let's calculate the change in temperature: $$ \Delta T = T_\text{final} - T_\text{initial} = 26.37^\circ\text{C} - 21.36^\circ\text{C} = 5.01^\circ\text{C} $$ Now, we can calculate the heat released: $$ q = 11.66 \dfrac{\text{kJ}}{^\circ\text{C}} \times 5.01^\circ\text{C} = 58.347 \text{kJ} $$

Step 3: Calculate the heat of combustion per gram of phenol

We are given the mass of phenol, which is 1.8 g. To find the heat of combustion per gram of phenol, we can use the following formula: $$ \dfrac{\text{Heat of combustion}}{\text{Mass of phenol}} = \dfrac{q}{m} $$ where \(m\) is the mass of phenol. $$ \dfrac{\text{Heat of combustion}}{\text{Mass of phenol}} = \dfrac{58.347 \text{kJ}}{1.8\text{g}} = 32.415 \dfrac{\text{kJ}}{\text{g}} $$ So, the heat of combustion per gram of phenol is 32.415 kJ/g.

Step 4: Calculate the heat of combustion per mole of phenol

To find the heat of combustion per mole of phenol, we need to calculate the molar mass of phenol and use the following formula: $$ \dfrac{\text{Heat of combustion}}{\text{Moles of phenol}} = \dfrac{q}{n} $$ where \(n\) is the number of moles of phenol. First, let's calculate the molar mass of phenol: $$ \text{Molar mass of phenol} = 6 \times 12.01 + 6 \times 1.008 + 1 \times 15.999 = 94.114\text{g/mol} $$ Now, let's calculate the number of moles of phenol in the sample: $$ n = \dfrac{\text{Mass of phenol}}{\text{Molar mass of phenol}} = \dfrac{1.8\text{g}}{94.114\text{g/mol}} = 0.01912\text{mol} $$ Now, we can calculate the heat of combustion per mole of phenol: $$ \dfrac{\text{Heat of combustion}}{\text{Moles of phenol}} = \dfrac{58.347 \text{kJ}}{0.01912\text{mol}} = 3050.25 \dfrac{\text{kJ}}{\text{mol}} $$ So, the heat of combustion per mole of phenol is 3050.25 kJ/mol.

Key Concepts

Bomb Calorimeter

To understand a bomb calorimeter and its role in measuring the heat of combustion, let's start with the basics. A bomb calorimeter is a device used to measure the heat of combustion of a particular reaction. It's called a 'bomb' because it's a sealed container capable of withstanding the high pressure produced during combustion reactions.

When a substance like phenol is burned in a bomb calorimeter, the reaction is carried out in an oxygen-rich environment within the sealed container. The heat released by the combustion is absorbed by the surrounding water and the calorimeter itself. By knowing the total heat capacity, which is the amount of energy needed to raise the calorimeter's temperature by one degree Celsius, one can calculate the amount of heat released during the reaction.

This is crucial when calculating the heat of combustion per gram or per mole of a substance, which is an important quantity in thermochemistry, affecting how energy is produced and utilized in various chemical processes.

Chemical Equation Balancing

Balancing chemical equations is a fundamental skill in chemistry that ensures the law of conservation of mass is obeyed in a chemical reaction. When writing a balanced chemical equation, every element must have the same number of atoms on both the reactant and product sides of the equation.

For the combustion of phenol, the balanced equation is essential in determining the stoichiometry of the reaction, which in turn is necessary for calculating the heat of combustion. The balanced equation, \( C_6H_5OH + \dfrac{15}{2}O_2 \rightarrow 6CO_2 + 3H_2O \), indicates that one mole of phenol reacts with seven and a half moles of oxygen to produce six moles of carbon dioxide and three moles of water. Through the correct stoichiometric coefficients, we ensure accurate calculations of the energy released during the reaction.

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the energy changes during chemical and physical transformations. In this context, it involves the study of heat released or absorbed in a chemical reaction. The specific quantity of interest here is the 'heat of combustion', which is the energy released when a compound undergoes complete combustion with oxygen under standard conditions.

In the case of phenol, calculating its heat of combustion involves using the data from the bomb calorimeter and the mass or moles of the substance. This is represented by the formula \( q = C \times \Delta T \), where \( q \) is the heat released, \( C \) is the heat capacity, and \( \Delta T \) is the change in temperature. This information provides us insight into the energy content of fuels and other materials, which is fundamental in fields like material science, environmental science, and engineering.