The heat capacity of a bomb calorimeter is 87.5 kJ/K (this value is for the total heat capacity including that of the water jacket around the reaction chamber). If 67.2g of CH4 (g), is combusted under such reaction conditions, what will be the increase in temperature of the calorimeter? Delta Ecombustion for CH4 (g) is -885.4 kJ/mol.
Calculate the heat energy release:
The number of moles of CH4 you are burning is 67.2/16 = 4.20 mol
Multiply that by 885.4 kJ/mol for the heat release. Then divide that by 87.5 kJ/K for the temperature rise.
Or, you could do it all at once
Delta T = (67.2g*885.4kJ/mol)/(16 g/mol*87.5 kJ/K) = ? K
To calculate the increase in temperature of the calorimeter, we can use the heat capacity formula:
q = CΔT
where q is the heat transferred, C is the heat capacity of the calorimeter, and ΔT is the change in temperature.
First, we need to calculate the heat transferred (q) during the combustion of CH4. We can use the following steps:
1. Calculate the moles of CH4:
- Convert the given mass of CH4 (67.2g) to moles using the molar mass of CH4 (16.04 g/mol).
- Divide the mass by the molar mass: 67.2g / 16.04 g/mol = 4.19 mol CH4.
2. Calculate the heat released (ΔEcombustion) for the combustion of 1 mole of CH4:
- Use the given value of ΔEcombustion for CH4: -885.4 kJ/mol.
3. Calculate the heat released for the combustion of 4.19 moles of CH4:
- Multiply the ΔEcombustion value by the number of moles: -885.4 kJ/mol * 4.19 mol = -3699.526 kJ.
Now that we have the heat transferred during combustion (q), we can calculate the change in temperature (ΔT) of the calorimeter using the heat capacity (C):
q = CΔT
-3699.526 kJ = 87.5 kJ/K * ΔT
Divide both sides by 87.5 kJ/K:
ΔT = (-3699.526 kJ) / (87.5 kJ/K) ≈ -42.28 K
Since temperature change cannot be negative, the change in temperature of the calorimeter is approximately 42.28 K.