Problem 58 - Chemistry The Central Science

Question

A 1.800 -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 11.66 \(\mathrm{kJ} /^{\circ} \mathrm{C}\) The temperature of the calorimeter plus contents increased from 21.36 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: \[C_6H_5OH + \frac{9}{2}O_2 \rightarrow 6CO_2 + 3H_2O\]. The heat of combustion per gram of phenol is 32.43 kJ/g, and the heat of combustion per mole of phenol is 3055.17 kJ/mol.

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

The combustion of phenol (C6H5OH) involves reacting with oxygen (O2) to produce carbon dioxide (CO2) and water (H2O). The balanced chemical equation for this combustion is: \[C_6H_5OH + \frac{9}{2}O_2 \rightarrow 6CO_2 + 3H_2O\]

Step 2: Calculate the heat released.

The total heat capacity of the calorimeter is given as 11.66 kJ/°C. The temperature of the calorimeter plus its contents increased from 21.36°C to 26.37°C. So, the temperature change is: ΔT = 26.37°C - 21.36°C = 5.01°C The heat released (q) by the combustion can be calculated using the formula: q = heat capacity × temperature change q = 11.66 kJ/°C × 5.01°C q = 58.37 kJ

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

The mass of the phenol sample is given as 1.800 g. The heat of combustion per gram can be calculated as: Heat of combustion per gram = (Heat released) / (Mass of sample) = 58.37 kJ / 1.800 g = 32.43 kJ/g

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

To find the heat of combustion per mole, we first calculate the molar mass of phenol. The molar mass of phenol (C6H5OH) is: (6 × 12.01 g/mol) + (5 × 1.01 g/mol) + 16.00 g/mol + 1.01 g/mol = 94.11 g/mol Now, we can calculate the number of moles of phenol in the sample: number of moles = (mass of sample) / (molar mass) = 1.800 g / 94.11 g/mol = 0.01911 mol Finally, we can calculate the heat of combustion per mole as: Heat of combustion per mole = (Heat released) / (number of moles) = 58.37 kJ / 0.01911 mol = 3055.17 kJ/mol So, the heat of combustion of phenol is 32.43 kJ/g and 3055.17 kJ/mol.

Key Concepts

Heat of Combustion

In calorimetry, the heat of combustion is a crucial concept. It refers to the total energy released as heat when a substance undergoes complete combustion with oxygen under standard conditions. For substances like phenol, this involves breaking down the chemical bonds and forming new ones in carbon dioxide and water.
The experiment described measures the heat of combustion through a bomb calorimeter, which restricts gas expansion for accurate measurements.

• The concept is usually expressed in units of energy per amount of substance, like \(\text{kJ/g}\) or \(\text{kJ/mol}\).
• This allows scientists and engineers to compare how much energy different fuels release upon combustion.

Understanding the heat of combustion helps in evaluating and minimizing energy costs and optimizing fuel efficiency. Such calculations then guide decisions across various industries, from automotive to power generation.

Chemical Equations

Chemical equations represent the transformation that substances undergo during a reaction. For combustion reactions, hydrocarbons or organic compounds react with oxygen to produce carbon dioxide and water, releasing energy in the process.

The calorimetry problem includes the balanced chemical equation:

• Phenol: \( \text{C}_6\text{H}_5\text{OH} + \frac{9}{2} \text{O}_2 \rightarrow 6 \text{CO}_2 + 3 \text{H}_2\text{O} \)
• Balancing these equations ensures conservation of mass and atoms from reactants to products.

Balancing the equation requires ensuring the same number of each atom appears on both sides of the equation. It reflects the stoichiometry of the reaction, which helps predict the amount of reactants needed and products formed. This groundwork is essential for determining the energy changes during combustion reactions.

Molar Mass

Molar mass is the mass of one mole of a substance, typically measured in grams per mole (g/mol). It connects mass and amount of a substance, essential for converting between these in chemical calculations. In the context of the phenol combustion problem:

• Molar mass provides the bridge to convert between grams of phenol to moles.
• The calculated molar mass of phenol is 94.11 g/mol, by summing the atomic masses of constituents in \( \text{C}_6\text{H}_5\text{OH} \).

Knowing the molar mass is necessary to determine the heat of combustion in terms of moles, not just grams. Accurate molar mass calculations help define the stoichiometric coefficients in balanced equations, crucial for completing stoichiometric calculations in thermochemistry.

Phenol Combustion

Phenol combustion is an example of a combustion reaction where the phenol (\( \text{C}_6\text{H}_5\text{OH} \)) reacts with oxygen to form carbon dioxide and water.

• This reaction happens in a calorimeter to understand the energy changes involved.
• It helps to determine the calorific value, which implies how much energy phenol can release.

Phenol is a common organic compound in chemical industries used to synthesize plastics and resins. Evaluating its combustion is important to ensure safe handling and effective energy harnessing. Understanding how these reactions occur, being able to predict the amounts of products, and measuring absorption or release of heat is fundamental in chemistry and energy sectors.