Question

Salicylic acid, \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\), is one of the starting materials in the manufacture of aspirin. When \(1.00 \mathrm{~g}\) of salicylic acid burns in a bomb calorimeter, the temperature rises from \(23.11^{\circ} \mathrm{C}\) to \(28.91^{\circ} \mathrm{C}\). The temperature in the bomb calorimeter increases by \(2.48^{\circ} \mathrm{C}\) when the calorimeter absorbs \(9.37 \mathrm{~kJ}\). How much heat is given off when one mole of salicylic acid is burned?

Short answer

Based on the step by step solution, calculate the heat given off when one mole of salicylic acid is burned.

Step-by-step solution

Find the molar mass of salicylic acid

To calculate the heat given off per mole, we first need to find the molar mass of salicylic acid, \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\): Molar mass = (7 × 12.01 (C) + 6 × 1.01 (H) + 3 × 16.00 (O)) g/mol = 138.12 g/mol

Calculate the moles of salicylic acid burned

Now that we know the molar mass, we can calculate the moles of salicylic acid burned: moles = mass / molar mass moles = 1.00 g / 138.12 g/mol = 0.00724 mol

Calculate the temperature change during combustion

Calculate the difference between the initial and final temperatures of the calorimeter: ΔT = T_final - T_initial ΔT = 28.91°C - 23.11°C = 5.80°C

Find the heat capacity of the bomb calorimeter

We know the calorimeter absorbs 9.37 kJ when its temperature increases by 2.48°C. We can find the heat capacity (C) by dividing the absorbed heat (q_cal) by the temperature change (ΔT_cal): C = q_cal / ΔT_cal C = 9.37 kJ / 2.48°C = 3.78 kJ/°C

Calculate the heat given off during the combustion

Using the temperature change (ΔT) from Step 3 and the heat capacity (C) from Step 4, we can calculate the heat given off during the combustion (q_comb): q_comb = C × ΔT q_comb = 3.78 kJ/°C × 5.80°C = 21.92 kJ

Calculate the heat given off per mole of salicylic acid

Now that we know the heat given off during combustion and the moles of salicylic acid burned, we can find the heat released per mole: Heat per mole = q_comb / moles Heat per mole = 21.92 kJ / 0.00724 mol = 3028 kJ/mol The heat given off when one mole of salicylic acid is burned is approximately 3028 kJ/mol.

Key concepts

Bomb Calorimeter

A bomb calorimeter is a specialized device used to measure the amount of heat produced during a chemical reaction, particularly combustion. In a typical setup, a small sample of the substance being tested is placed in a strong, sealed container called a bomb, which is then filled with oxygen to facilitate complete combustion of the material. The bomb is immersed in a water bath, and the entire assembly is insulated to prevent heat loss.

During the combustion of the sample, the heat released is absorbed by the water and the calorimeter itself. By measuring the temperature change of the water (ΔT), and knowing the specific heat capacity - the amount of heat required to change the temperature of a substance by one degree - we can calculate the amount of heat (q) released during the reaction. The exercise improves upon this by calculating the heat for a per mole basis, giving a clearer understanding of the combustion energy of salicylic acid.

Heat of Combustion

The heat of combustion is a critical value in thermochemistry, referring to the amount of heat released when a substance undergoes complete combustion with oxygen under standard conditions. This measurement is essential for understanding the energy content of various substances. When a compound like salicylic acid burns, it releases energy in the form of heat, which can be precisely measured using a bomb calorimeter.

To gain a comprehensive understanding of a substance's energetic properties, scientists calculate the heat of combustion per mole. This standardization allows for comparisons between different substances. In the given exercise, we calculate the heat released when one mole of salicylic acid burns, providing insight into the energy available during the formulation of aspirin.

Molar Mass Calculation

The molar mass is a fundamental concept in chemistry, representing the mass of one mole of a substance and it is expressed in grams per mole (g/mol). The molar mass is calculated by summing the atomic masses of all the atoms in a molecule of the substance. This value is crucial for converting between the mass of a substance and the amount of substance in moles, allowing chemists to use the mole concept to accurately measure substances for reactions and calculations.

In our exercise, to determine the heat given off per mole, we first calculate the molar mass of salicylic acid by adding the atomic masses of carbon (C), hydrogen (H), and oxygen (O), and then use this molar mass to find the number of moles of salicylic acid that were combusted. This step is essential because it establishes the relationship between the mass of the sample used and the amount in moles, which leads to the final calculation of the heat of combustion per mole.