Problem 58 - Chemistry: The Central Science in SI Units, Global Edition

Question

A 2.20-g sample of phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) was burned in a bomb calorimeter whose total heat capacity is \(11.90 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} .\) The temperature of the calorimeter plus contents increased from 21.50 to \(27.50^{\circ} \mathrm{C} .(\mathbf{a})\) Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of phenol and per mole of phenol?

Step-by-Step Solution

Answer

The balanced chemical equation for the combustion of phenol is: \(C_6H_5OH + 7O_2 \rightarrow 6CO_2 + 3H_2O\). The heat of combustion per gram of phenol is 32.45 kJ/g, and the heat of combustion per mole of phenol is 3053.35 kJ/mol.

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

Combustion reactions involve the reaction of a substance with oxygen gas, producing carbon dioxide and water as the products. For phenol, the chemical equation for its combustion can be written as: C6H5OH + O2 → CO2 + H2O To balance the equation, we need to adjust the coefficients of each element so that the number of atoms on each side of the equation is equal. The balanced chemical equation is: C6H5OH + 7O2 → 6CO2 + 3H2O

Step 2: Calculate the total heat gained by the calorimeter.

The total heat capacity of the calorimeter is 11.90 kJ/°C. The temperature increased from 21.50°C to 27.50°C, a difference of 6.00°C. To find the total heat gained by the calorimeter, we use the formula: Total heat gained = Heat capacity * Temperature change Total heat gained = 11.90 kJ/°C * 6.00°C = 71.40 kJ

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

We are given that 2.20 g of phenol was burned. To find the heat of combustion per gram of phenol, we divide the total heat by the mass of phenol: Heat of combustion per gram = Total heat gained / Mass of phenol Heat of combustion per gram = 71.40 kJ / 2.20 g = 32.45 kJ/g

Step 4: Determine the molar mass of phenol.

To find the molar mass of phenol (C6H5OH), we can sum up the molar masses of the individual atoms in the molecule: Molar mass of phenol = 6 * (Molar mass of C) + 5 * (Molar mass of H) + 1 * (Molar mass of O) + 1 * (Molar mass of H) Molar mass of phenol = 6 * (12.01 g/mol) + 5 * (1.01 g/mol) + 1 * (16.00 g/mol) + 1 * (1.01 g/mol) = 94.11 g/mol

Step 5: Calculate the heat of combustion per mole of phenol.

Now that we have the molar mass of phenol and the heat of combustion per gram, we can find the heat of combustion per mole: Heat of combustion per mole = Heat of combustion per gram * Molar mass of phenol Heat of combustion per mole = 32.45 kJ/g * 94.11 g/mol = 3053.35 kJ/mol The heat of combustion per gram of phenol is 32.45 kJ/g, and the heat of combustion per mole of phenol is 3053.35 kJ/mol.

Key Concepts

Phenol Combustion

Phenol, a chemical compound with the formula \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH} \), undergoes a combustion reaction when it reacts with oxygen in the air. This process is crucial in the study of calorimetry, as it helps us understand how energy is released. During combustion, phenol reacts with oxygen to form carbon dioxide \( \mathrm{CO}_{2} \) and water \( \mathrm{H}_{2}\mathrm{O} \). The equation for this reaction is initially unbalanced:

• \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH} + \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O}\)

To balance it, we need to ensure that there are equal numbers of each type of atom on both sides of the equation. The balanced equation is then written as:

• \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH} + 7\mathrm{O}_{2} \rightarrow 6\mathrm{CO}_{2} + 3\mathrm{H}_{2}\mathrm{O}\)

This balanced equation now represents complete phenol combustion, which is essential to accurately calculate the energy released in this exothermic reaction.

Heat Capacity

When studying calorimetry, understanding heat capacity is vital. Heat capacity is a measure of the amount of heat needed to change the temperature of a system by one degree Celsius. In the context of this exercise, the bomb calorimeter, used to study the combustion of phenol, has a heat capacity of \( 11.90 \mathrm{~kJ}/{ }^{\circ} \mathrm{C} \).

• It's an extensive property, meaning it depends on the size or amount of the material in the system.
• The calorimeter absorbs the heat released during phenol combustion, causing its temperature to change.

To calculate the total heat gained by the calorimeter, use the formula:

• Total heat gained = Heat capacity × Temperature change

Here, the temperature change is \( 6.00 \mathrm{~^{\circ}C} \) (from \( 21.50^{\circ} \mathrm{C} \) to \( 27.50^{\circ} \mathrm{C} \)), resulting in a calculated heat gain of \( 71.40 \mathrm{~kJ} \). This information helps us determine the energetic properties of phenol when burned.

Balanced Chemical Equation

Writing a balanced chemical equation is a fundamental skill in chemistry, necessary for accurately describing chemical reactions. When working on the combustion of phenol, balancing the equation ensures that the law of conservation of mass applies, meaning the same number of each type of atom appears on both sides.

• Start with the skeleton equation: \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH} + \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O}\).
• Identify the number of each atom on both sides, then adjust coefficients to balance them.

For phenol combustion, balancing results in:

• \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH} + 7\mathrm{O}_{2} \rightarrow 6\mathrm{CO}_{2} + 3\mathrm{H}_{2}\mathrm{O}\).

It's crucial for subsequent calculations, like determining reactant quantities and the energy involved. Ensure accuracy in balancing to get reliable results in calorimetry assessments.

Molar Mass Calculation

Calculating molar mass involves determining the mass of one mole of a substance, expressed in grams per mole \(\text{g/mol}\). For phenol \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH} \), follow these steps:

• Identify the molar masses: carbon (C) is \(12.01\,\text{g/mol}\), hydrogen (H) is \(1.01\,\text{g/mol}\), and oxygen (O) is \(16.00\,\text{g/mol}\).
• Calculate the total molar mass:

\[ 6 \times 12.01\, \text{g/mol} + 5 \times 1.01\, \text{g/mol} + 16.00\, \text{g/mol} + 1.01\, \text{g/mol} = 94.11\, \text{g/mol}\]Understanding molar mass is crucial because it links the mass of phenol to the number of moles, which is essential for calculating the energy of combustion per mole. In this exercise, multiplying the heat of combustion per gram by the molar mass gives the heat of combustion per mole, aiding in understanding the energy dynamics of phenol.