A 2.461-g sample of glutamic acid, C5H9NO4 (147.13 g/mol) was burned in a bomb calorimeter with
excess oxygen. The temperature of the calorimeter and the water before combustion was 23.76 °C; after
combustion the calorimeter and the water had a temperature of 29.46 °C. The calorimeter had a heat capacity of
660 J/K, and contained 1.405 kg of water. Use these data to calculate the molar heat of combustion (in kJ) of
glutamic acid
dH(comb) = [dH(cal)*(Tfinal-Tinitial)] + [dH(H2O)*(Tf-Ti)
dH(comb) = [660 J/K*(29.46-23.76)] + [1,405 g*4,184*(29.46-23.78)]
dH(comb) will be in J for a 2.461 g sample of glutamic acid. Convert to kJ/mol. Check my thinking.
To calculate the molar heat of combustion of glutamic acid, we need to use the following equation:
q = mcΔT
where q is the heat energy absorbed by the water, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
Firstly, let's calculate the heat energy absorbed by the water during the combustion of the glutamic acid.
We have the following information:
- Mass of glutamic acid (molecule) = 2.461 g
- Molar mass of glutamic acid (C5H9NO4) = 147.13 g/mol
- Initial temperature of water = 23.76 °C
- Final temperature of water = 29.46 °C
- Specific heat capacity of water = 4.184 J/g°C
- Mass of water = 1.405 kg (or 1405 g)
Step 1: Calculate the heat energy absorbed by water:
q = mcΔT
q = (1405 g) x (4.184 J/g°C) x (29.46 °C - 23.76 °C)
q = 1405 g x 4.184 J/g°C x 5.7 °C
q = 40,814.68 J
Step 2: Convert joules to kilojoules:
q = 40,814.68 J ÷ 1000
q = 40.81468 kJ
Step 3: Convert the heat energy to molar heat of combustion using the molar mass of glutamic acid:
Molar heat of combustion = q ÷ (mass of glutamic acid/molar mass of glutamic acid)
Note: Make sure the mass of the glutamic acid is in grams and the molar mass is in grams/mol.
Molar heat of combustion = 40.81468 kJ ÷ (2.461 g/147.13 g/mol)
Molar heat of combustion = 40.81468 kJ ÷ 2.461 g x 147.13 g/mol
Molar heat of combustion = 40.81468 kJ ÷ 360.96093 g/mol
Molar heat of combustion ≈ 0.113 kJ/mol
Therefore, the molar heat of combustion of glutamic acid is approximately 0.113 kJ/mol.