Problem 58 - Chemistry The Central Science In Si Units

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 \(27.50^{\circ} \mathrm{C}\). (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

(a) The balanced equation is \(\mathrm{C}_6\mathrm{H}_5\mathrm{OH} + 7\mathrm{O}_2 \rightarrow 6\mathrm{CO}_2 + 3\mathrm{H}_2\mathrm{O} \). (b) The heat of combustion is 32.45 kJ/g and 3053 kJ/mol.

Step 1: Write the Chemical Equation

First, we need to write the balanced chemical equation for the combustion of phenol. Phenol (\(\mathrm{C}_6\mathrm{H}_5\mathrm{OH}\)) burns in oxygen to produce carbon dioxide and water: \[ \mathrm{C}_6\mathrm{H}_5\mathrm{OH} + 7\mathrm{O}_2 \rightarrow 6\mathrm{CO}_2 + 3\mathrm{H}_2\mathrm{O} \].

Step 2: Calculate the Temperature Change

Determine the change in temperature of the calorimeter. The temperature increases from 21.50°C to 27.50°C. The temperature change is: \[ \Delta T = 27.50 - 21.50 = 6.00^{\circ} \mathrm{C} \].

Step 3: Calculate the Heat Released

Use the calorimeter's heat capacity to determine the heat released. Heat released, \(q\), is given by the formula: \[ q = C \times \Delta T \], where \(C\) is the calorimeter heat capacity and \(\Delta T\) is the temperature change. \[ q = 11.90 \ \mathrm{kJ/^{\circ}C} \times 6.00 \ ^{\circ}C = 71.40 \ \mathrm{kJ} \].

Step 4: Find Heat of Combustion Per Gram

Calculate the heat of combustion per gram of phenol. Since 2.20 g of phenol was burned, the heat of combustion per gram is: \[ \text{Heat per gram} = \frac{71.40 \ \mathrm{kJ}}{2.20 \ \mathrm{g}} = 32.45 \ \mathrm{kJ/g} \].

Step 5: Determine Molar Mass of Phenol

Calculate the molar mass of phenol (\(\mathrm{C}_6\mathrm{H}_5\mathrm{OH}\)). The molar mass is \(6(12.01) + 5(1.01) + 16.00 + 1.01 = 94.11 \ \mathrm{g/mol}\).

Step 6: Calculate Heat of Combustion Per Mole

Using the heat of combustion per gram and the molar mass, find the heat of combustion per mole of phenol: \[ \text{Heat per mole} = 32.45 \ \mathrm{kJ/g} \times 94.11 \ \mathrm{g/mol} = 3053 \ \mathrm{kJ/mol} \].

Key Concepts

Phenol Combustion

The combustion of phenol involves a chemical reaction where phenol (\(\mathrm{C}_6\mathrm{H}_5\mathrm{OH}\)) interacts with oxygen (\(\mathrm{O}_2\)) to yield carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)). This process exemplifies a type of chemical reaction known as a combustion reaction.Combustion reactions typically involve an organic compound reacting with oxygen to release energy in the form of heat and light. Phenol is a type of hydrocarbon known for its aromatic ring and hydroxyl group, which means it requires a lot of oxygen for complete combustion.

• The balanced chemical equation for phenol combustion is: \[ \mathrm{C}_6\mathrm{H}_5\mathrm{OH} + 7\mathrm{O}_2 \rightarrow 6\mathrm{CO}_2 + 3\mathrm{H}_2\mathrm{O} \]
• Balancing this equation ensures that the same number of each atom is present on both sides, preserving mass and charge according to the law of conservation of mass.

Calorimeter Heat Capacity

The calorimeter heat capacity is a crucial factor in calorimetry experiments. It refers to the amount of heat required to change the temperature of the calorimeter, including its contents, by one degree Celsius. A calorimeter acts like a thermal container, capturing the heat from a chemical reaction to measure the energy changes, without allowing external influences to interfere. The heat capacity of the calorimeter is an inherent property, and in this exercise, it is given as \(11.90 \, \mathrm{kJ/^{\circ}C}\).Key aspects to consider include:

• The heat released during combustion can be determined using the formula \(q = C \times \Delta T\), where \(q\) is the heat gained by the calorimeter, \(C\) is the heat capacity, and \(\Delta T\) is the change in temperature as the reaction proceeds.
• The greater the calorimeter's heat capacity, the more heat is required to change its temperature, making it essential for precise measurement.

Balanced Chemical Equation

A balanced chemical equation is vital in chemistry as it represents a chemistry rule – the conservation of mass. This involves adjusting the coefficients of reactants and products so that the number of atoms for each element is the same on both sides of the equation, which is necessary for correctly predicting the reaction yield and energy changes. Beyond simply fulfilling an academic exercise, balanced equations:

• Provide insight into the stochiometric ratios, which are the quantitative relationships between reactants and products in a chemical reaction.
• Help in calculating the heat of combustion, which requires knowing the exact amount of reactants and products involved.

Heat of Combustion

The heat of combustion is a measure of the energy released when a substance completely combusts with oxygen. This energy, typically expressed in kilojoules per mole (kJ/mol), is an important aspect of thermochemistry, offering insights into the energy efficiency of fuels and chemical processes.For phenol, the heat of combustion can be calculated per gram or per mole:

• To find it per gram, divide the total heat released by the mass of phenol: \(\text{Heat per gram} = \frac{\text{Total Heat}}{\text{mass of phenol}}\).
• For heat per mole, this value is adjusted by the molar mass of phenol, emphasizing the importance of even a basic understanding of molar relationships in chemistry.
• This measure helps indicate the potential energy output available when using phenol as a fuel source.

Understanding these concepts aids in comprehending how energy is transferred and transformed in chemical reactions, an essential aspect of both academic and practical chemistry.