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 of the bomb and water goes from \(23.11^{\circ} \mathrm{C}\) to \(28.91^{\circ} \mathrm{C}\). The calorimeter and water absorb \(21.9 \mathrm{~kJ}\) of heat. How much heat is given off when one mole of salicylic acid burns?

Short answer

Answer: The heat given off when one mole of salicylic acid burns is -3026.8 kJ/mol.

Step-by-step solution

Calculate the molar mass of salicylic acid

To find the molar mass of salicylic acid (C7H6O3), we add up the atomic masses of all the atoms present in the molecule. In terms of atomic mass, Carbon (C) has 12.01 g/mol, Hydrogen (H) has 1.01 g/mol, and Oxygen (O) has 16.00 g/mol. Molar mass of salicylic acid = (7 × 12.01 g/mol) + (6 × 1.01 g/mol) + (3 × 16.00 g/mol) = 138.12 g/mol

Calculate the moles of salicylic acid

We have 1.00 g of salicylic acid, and we already found its molar mass to be 138.12 g/mol. To find the moles of salicylic acid, we can use the formula: Moles = (mass)/(molar mass) Moles of salicylic acid = (1.00 g)/(138.12 g/mol) = 0.00724 mol

Calculate the heat given off by salicylic acid

We are given that the calorimeter and water absorb 21.9 kJ of heat. Since the heat absorbed by the calorimeter and water is equal to the heat given off by the salicylic acid, we can write: Heat given off by salicylic acid = -21.9 kJ

Calculate the heat given off per mole of salicylic acid

We can now find the heat given off per mole of salicylic acid by dividing the total heat given off by the moles of salicylic acid: Heat given off per mole = (Total heat given off)/(Moles of salicylic acid) Heat given off per mole = (-21.9 kJ)/(0.00724 mol) = -3026.8 kJ/mol The heat given off when one mole of salicylic acid burns is -3026.8 kJ/mol.