When a 0.245-g sample of benzoic acid is combusted in a bomb calorimeter, the temperature rises 1.643 ∘c . when a 0.260-g sample of caffeine, c8h10o2n4, is burned, the temperature rises 1.436 ∘c . using the value 26.38 kj/g for the heat of combustion of benzoic acid, calculate the heat of combustion per mole of caffeine at constant volume.

The heat of combustion per moles of caffeine is 4220 kJ/mol

Explanation:

Step 1: Data given

⇒ When  benzoic acid sample of 0.245 grams is burned the temperature rise is 1.643 °C

⇒ When 0.260 gram of caffeine is burned, the temperature rise is 1.436 °C

⇒ Heat of combustion of benzoic acid = 26.38 kJ/g

Step 2: Calculate the heat released: for combustion of benzoic acid

0.245 g benzoic acid *  26.38 kJ/g = 6.4631 kJ

Step 3: Calculate the heat capacity of the calorimeter:

c = Q/ΔT

Q = 6.4631 kJ   / 1.643°C = 3.934 kJ/ °C

Step 4: Calculate moles of a 0.260 g sample of caffeine:

Moles caffeine = Mass caffeine / Molar mass caffeine

0.260 grams/ 194.19 g/mol  = 0.0013389 moles

Step 5: Calculate heat released: for combustion of caffeine

Q = c * ΔT

Q = 3.934 kJ/°C * 1.436 °C = 5.65 kJ

Step 6: Calculate the heat of combustion per mole of caffeine  

5.65 kJ  /  0.0013389 moles = 4219.9 kJ/mol  ≈ 4220 kJ/mol

The heat of combustion per moles of caffeine is 4220 kJ/mol