Consider the reaction C12H22O11 (s) + 12O2 (g) →12CO2 (g) + 11H2O (l) in which 10.0 g of sucrose, C12H22O11, was burned in a bomb calorimeter with a heat capacity of 7.50 kJ/∘C. The temperature increase inside the calorimeter was found to be 22.0 ∘C. Calculate the change in internal energy, ΔE, for this reaction per mole of sucrose.

the change in internal energy per mole of sucrose is 5989 KJ/mol

Explanation:

Since the calorimeter is a bomb calorimeter, where the volume remains constant

ΔE = Qrx

And assuming no heat losses to the surroundings

Qv + Qrx = 0

Cc*ΔT - Qrx = 0,

Qrx = Cc * ΔT = 7.50 KJ/°C * 22 °C = 165 KJ

the change in internal energy is calculated dividing by the number of sucrose moles involved n. the molecular weight of sucrose is

Mw = 12 * 12g/mol + 22 * 1g/mol + 11 * 16 g/mol = 342 g/mol

n = m / Mw = 10 g / 342 g/mol = 0.029 mol

the change in internal energy per mole of sucrose is

Δe = ΔE/n = 165 KJ/0.029 mol = 5989 KJ/mol