Question

1a) 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. What is the heat of this reaction per mole of sucrose?

1b) One tablespoon of peanut butter has a mass of 17.0 g. It is combusted in a calorimeter whose heat capacity is 110 kJ/°C. The temperature of the calorimeter rises from 21.6 ∘C to 25.8 ∘C . What is the caloric content of peanut butter in Cal/g?

1c)When a 3.50 g sample of liquid octane (C8H18) is burned in a bomb calorimeter, the temperature of the calorimeter rises by 26.7 ∘C. The heat capacity of the calorimeter, measured in a separate experiment, is 6.10 kJ/∘C . The calorimeter also contains 3.00 kg of water, specific heat capacity of 4.18 J/g°C. Determine ΔErxn for the combustion of octane in units of kJ/mol octane.

Answer 1

a) Heat capacity = c = 7.50 kJ/^oC

Change in temperature = $\Delta$t = 22.0 ^oC

Heat generated = c$\Delta$t = 7.50*22.0 = 165 kJ

Mass of sucrose = 10.0 g

Molar mass of sucrose = 342 g/mol

number of moles of sucrose = mass/molar mass = 10.0/342 = 0.029 mol

Heat generated per mole = heat generated/number of moles = 165/0.029 = 5690 kJ/mol

Heat of the reaction per mole of sucrose = 5690 kJ/mol

b) Heat capacity = c = 110 kJ/^oC

Change in temperature = $\Delta$t = 25.8-21.6 ^oC = 4.2 ^oC

Heat generated = c$\Delta$t = 110*4.2 = 462 kJ

Convert kJ into cal

1 kcal = 4.2 kJ

So, 462 kJ = (462/4.2) kcal = 110.42 kcal

Mass of butter = 17.0 g

caloric content of peanut butter = heat generated/mass = 110.42/17.0 = 6.470 kcal/g = 6495 cal/g

caloric content of peanut butter = 6495 cal/g

c) Heat capacity = c = 6.10 kJ/^oC

Change in temperature = $\Delta$t = 26.7 ^oC

Heat generated = c$\Delta$t = 6.10*26.7 = 162.87 kJ

Mass of octane = 3.50 g

Molar mass of octane = 114 g/mol

number of moles of octane = mass/molar mass = 3.50/114 = 0.0307 mol

Heat generated per mole = heat generated/number of moles = 162.87/0.031 = 5304.9 kJ/mol

Heat of the reaction per mole of octane = 5304.9 kJ/mol