A sample of 1.150 g of sucrose (342.3 g mol-1) undergoes combustion in a bomb calorimeter. If the temperature rises by 4.22 °C and the heat capacity of the calorimeter assembly (including the water) is 4.90 kJ °C-1, what is the heat of combustion of sucrose, in kJ mol-1?
q = Ccal x dT = 4.90 kJ/C x 4.22 = ? kJ
? kJ x (342.3/1.150) = ?kJ/mol sucrose
To find the heat of combustion of sucrose (C12H22O11), we need to use the equation q = mCΔT, where:
- q is the heat (in kJ)
- m is the mass of the substance being burned (in g)
- C is the heat capacity of the calorimeter assembly (in kJ/°C)
- ΔT is the change in temperature (in °C)
First, we need to find the heat released by the combustion of sucrose. The heat released can be calculated using the equation:
q = mCΔT
Given:
- m = 1.150 g (mass of sucrose)
- C = 4.90 kJ/°C (heat capacity of calorimeter assembly)
- ΔT = 4.22 °C (change in temperature)
Plugging in the values, we have:
q = (1.150 g)(4.90 kJ/°C)(4.22 °C)
q = 24.944 kJ
Next, we need to convert the heat released to the heat of combustion per mole of sucrose. The molar mass of sucrose (C12H22O11) is 342.3 g/mol.
To find the heat of combustion per mole, we divide the heat released by the number of moles:
Heat of combustion of sucrose = (24.944 kJ) / (1.150 g / 342.3 g/mol)
Heat of combustion of sucrose = (24.944 kJ) / (0.00336206 mol)
Heat of combustion of sucrose = 7420.194 kJ/mol (rounded to 4 significant figures)
Therefore, the heat of combustion of sucrose is approximately 7420.194 kJ/mol.
To find the heat of combustion of sucrose in kJ/mol, we need to use the formula:
q = mcΔT
Where:
- q is the heat transfer,
- m is the mass of the substance,
- c is the specific heat capacity of the substance,
- ΔT is the change in temperature.
In this case, the substance is water, and we have the heat capacity of the calorimeter assembly. So, we can use the formula:
q = CΔT
Where:
- C is the heat capacity,
- ΔT is the change in temperature.
We are given:
- ΔT = 4.22 °C
- C = 4.90 kJ/°C
Substituting these values into the formula, we have:
q = (4.90 kJ/°C) * (4.22 °C)
q = 20.678 kJ
This is the amount of heat released in the combustion of the entire calorimeter assembly (including the water).
Now, we need to find the heat of combustion per mole of sucrose. We can calculate this by dividing the heat released by the molar mass of sucrose.
The molar mass of sucrose (C12H22O11) is 342.3 g/mol.
To find the heat of combustion per mole of sucrose, we calculate:
Heat of combustion per mole = (20.678 kJ) / (1.150 g / 342.3 g/mol)
Heat of combustion per mole = 20.678 kJ / 3.365 mol
Therefore, the heat of combustion of sucrose is approximately 6.14 kJ/mol.