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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 3.1007 g of benzoic acid are burned in a calorimeter, the temperature rises from 21.84°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.)

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Answer:

28.96 kJ/°C

Explanation:

We are given;

  • Enthalpy change (ΔH) = −3226.7 kJ/mol
  • The reaction is exothermic since the heat change is negative;
  • Mass of benzoic acid = 3.1007 g
  • Temperature change (21.84°C to 24.67°C) = 2.83°C

We are required to find the heat capacity of benzoic acid;

Step 1: Moles of benzoic acid

Moles = Mass ÷ molar mass

Molar mass of benzoic = 122.12 g/mol

Therefore;

Moles = 3.1007 g ÷ 122.12 g/mol

          = 0.0254 moles

Step 2: Determine the specific heat capacity

Heat change for 1 mole = 3226.7 kJ

Moles of Benzoic acid = 0.0254 moles

But;

Specific heat capacity × ΔT = Moles × Heat change

  cΔT = nΔH

Therefore;

Specific heat capacity,c = nΔH ÷ ΔT

                                     = (3226.7 kJ × 0.0254 moles) ÷ 2.83°C

                                    = 28.96 kJ/°C

Therefore, the specific heat capacity of benzoic acid is 28.96 kJ/°C

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