Problem 57 - Chemistry The Central Science

Question

A 2.200 -g sample of quinone \(\left(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}\right)\) is burned in a bomb calorimeter whose total heat capacity is 7.854 \(\mathrm{kJ} / \mathrm{c}\) . The temperature of the calorimeter increases from 23.44 to \(30.57^{\circ} \mathrm{C}\) . What is the heat of combustion per gram of quinone? Per mole of quinone?

Step-by-Step Solution

Answer

The heat released by the combustion of quinone is calculated as follows: \(q = 7.854 \, \text{kJ/c} \times (30.57°C - 23.44°C) = 55.745 \, \text{kJ}\). The heat of combustion per gram of quinone is: \(\frac{55.745 \, \text{kJ}}{2.2 \, \text{g}} = 25.34 \, \frac{\text{kJ}}{\text{g}}\). The molar mass of quinone is: \((6 \times 12.01 \, \text{g/mol}) + (4 \times 1.01 \, \text{g/mol}) + (2 \times 16.00 \, \text{g/mol}) = 108.10 \, \text{g/mol}\). Finally, the heat of combustion per mole of quinone is: \(\frac{25.34 \, \frac{\text{kJ}}{\text{g}} \times 2.2 \, \text{g}}{108.10 \, \text{g/mol}} = 0.513 \, \frac{\text{kJ}}{\text{mol}}\).

Step 1: Calculate the heat released by the combustion of quinone

We can use the formula for heat (q) to find the heat released by the combustion of the quinone sample: q = C × ΔT Here, C is the heat capacity of the bomb calorimeter and ΔT is the change in temperature. We are given both C and ΔT as 7.854 kJ/c and (30.57 - 23.44)°C, respectively. Let's calculate q: q = 7.854 kJ/c × (30.57°C - 23.44°C)

Step 2: Calculate the heat of combustion per gram of quinone

Now we'll find the heat of combustion per gram of quinone. To do this, we'll divide q by the mass of quinone: Heat of combustion per gram = q / mass of quinone Using the q value calculated in Step 1 and the given mass (2.2 g): Heat of combustion per gram = q / 2.2 g

Step 3: Calculate the molar mass of quinone

To find the heat of combustion per mole of quinone, we first need the molar mass of quinone. Quinone's molecular formula is C₆H₄O₂, so its molar mass is: Molar mass = (6 × atomic mass of C) + (4 × atomic mass of H) + (2 × atomic mass of O) Using the atomic masses for C, H, and O as 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively: Molar mass = (6 × 12.01 g/mol) + (4 × 1.01 g/mol) + (2 × 16.00 g/mol)

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

Now, we can find the heat of combustion per mole of quinone by dividing the heat of combustion per gram (calculated in Step 2) by the molar mass (calculated in Step 3): Heat of combustion per mole = (Heat of combustion per gram × mass of quinone) / Molar mass Plugging in the values obtained in Steps 2 and 3, we can find the heat of combustion per mole of quinone.

Key Concepts

Bomb Calorimeter

Understanding how the heat of combustion is determined requires a basic grasp of what a bomb calorimeter is and how it operates. A bomb calorimeter is a robust, sealed chamber used to measure the heat of combustion of a sample. It is designed to withstand the high pressures that result from combustion within the chamber. The calorimeter has a known heat capacity, which is the amount of heat required to raise its temperature by one degree Celsius.

During an experiment, the sample is placed in the calorimeter and ignited. The heat released causes an increase in the temperature of the calorimeter's contents, which includes a known volume of water. By recording the temperature change and knowing the calorimeter's heat capacity, we can calculate the total amount of heat released, usually in kilojoules, by using the formula: \[ q = C \times \Delta T \], where \( q \) represents the heat released, \( C \) is the heat capacity of the calorimeter, and \( \Delta T \) is the change in temperature.

Enthalpy Change Calculation

The enthalpy change of a reaction, often represented as \( \Delta H \), signifies the total heat change at constant pressure and is an essential component of thermodynamics and calorimetry. When determining the enthalpy change for combustion in a bomb calorimeter, we use the heat released from the reaction, as this is a constant-volume process. The formula to calculate the enthalpy change per unit mass of a substance combusted in such a calorimeter is given by: \[ \Delta h = \frac{q}{m} \], where \( \Delta h \) is the specific enthalpy change, \( q \) is the heat released during combustion, and \( m \) is the mass of the substance. We can also ascertain the enthalpy change per mole by factoring in the molar mass of the substance, providing a more standardized measure of the chemical's combustive characteristics.

Molar Mass Determination

The molar mass of a compound is the mass of one mole of that substance, and is a crucial variable for scientists and chemists. It is expressed in grams per mole (g/mol). Determining the molar mass of a compound involves summing the masses of all the atoms in one molecule of the substance. We can look up each element's atomic mass in the periodic table and perform a simple multiplication and addition to find the compound's molar mass. For example, quinone (\(C_6H_4O_2\)) has a molar mass calculated as follows:\[ Molar\ mass = (6 \times atomic\ mass\ of\ C) + (4 \times atomic\ mass\ of\ H) + (2 \times atomic\ mass\ of\ O) \]Where the atomic masses (in g/mol) are approximately 12.01 for carbon, 1.01 for hydrogen, and 16.00 for oxygen. Knowing the molar mass allows chemists to relate masses of a substance to the amount in moles, enabling the calculation of the heat of combustion per mole, which is a standardized measure used to compare different substances.