Question

the enthalpy of combustion of benzoic acid (c6h5cooh) is commonly used as the standard for calibrating constant - volume bomb calorimeters; its value has been accurately determined to be - 3226.7 kj/mol. when 3.3427 g of benzoic acid are burned in a calorimeter, the temperature rises from 22.84°c to 24.67°c. what is the heat capacity of the bomb? (assume that the quantity of water surrounding the bomb is exactly 2250 g.) round your answer to 3 significant digits.
note: reference the phase change properties of pure substances table for additional information.

Explanation:

Step1: Calculate moles of benzoic acid

Molar mass of $\text{C}_6\text{H}_5\text{COOH}$: $6(12.01)+6(1.008)+2(16.00)=122.124\ \text{g/mol}$.
Moles: $n=\frac{3.3427\ \text{g}}{122.124\ \text{g/mol}}≈0.02737\ \text{mol}$.

Step2: Find heat released

Heat released: $q = n×\Delta H_{\text{comb}} = 0.02737\ \text{mol}×(-3226.7\ \text{kJ/mol})≈-88.32\ \text{kJ}$.
Heat absorbed by calorimeter: $q_{\text{cal}}=-q=88.32\ \text{kJ}$.

Step3: Calculate temperature change

$\Delta T=24.67^\circ\text{C}-22.84^\circ\text{C}=1.83^\circ\text{C}$.

Step4: Compute heat capacity

$C=\frac{q_{\text{cal}}}{\Delta T}=\frac{88.32\ \text{kJ}}{1.83^\circ\text{C}}≈48.3\ \text{kJ/}^\circ\text{C}$.

Answer:

48.3