To find the work done in this combustion process, we need to consider the bomb calorimeter as a closed system. In this case, the work done is zero because there is no volume change. Therefore, the formula becomes:
ΔE = q + 0
qv = ΔE
Now let's calculate the heat flow at constant volume:
(a) The heat flow at constant volume, qv, can be calculated using the formula:
qv = ΔE
To find ΔE, we need to consider the heat absorbed by the water and the heat absorbed by the nickel bomb calorimeter. The heat absorbed by the water can be calculated using the formula:
qwater = mcΔT
where:
m = mass of water = 975 mL = 975 g (since the density of water is 1 g/mL)
c = specific heat capacity of water = 4.184 J/g°C (approximate value)
ΔT = change in temperature = final temperature - initial temperature = 29.55°C - 23.50°C = 6.05°C
Substituting the values into the equation:
qwater = (975 g) (4.184 J/g°C) (6.05°C)
Next, we need to calculate the heat absorbed by the nickel bomb calorimeter. The heat absorbed by the nickel bomb calorimeter can be calculated using the formula:
qcalorimeter = mcΔT
where:
m = mass of nickel = 285.0 g
c = specific heat capacity of nickel = 0.826 J/g°C (given)
ΔT = change in temperature = final temperature - initial temperature = 29.55°C - 23.50°C = 6.05°C
Substituting the values into the equation:
qcalorimeter = (285.0 g) (0.826 J/g°C) (6.05°C)
Finally, we can find the total heat flow at constant volume:
qv = qwater + qcalorimeter
Substitute the calculated values and calculate qv.
(b) The energy released per mole of acetone, in kJ/mol, can be found by dividing the heat flow at constant volume by the number of moles of acetone burned.
To calculate the number of moles of acetone burned, we need to use the molar mass of acetone, which is 58.08 g/mol.
Number of moles = mass of acetone (g) / molar mass of acetone (g/mol)
Substitute the given mass of the hydrocarbon acetone and the molar mass into the formula, and calculate the number of moles.
Now, divide the heat flow at constant volume (qv) by the number of moles of acetone to get the energy released per mole of acetone.
(c) To calculate the heat of combustion per mole, ΔH_comb/mole, we need to balance the equation for the combustion of acetone.
The balanced equation for the complete combustion of acetone is:
2CH3COCH3 + 9O2 → 6CO2 + 8H2O
The ΔH_comb/mole can be calculated using the formula:
ΔH_comb/mole = qv / number of moles of acetone burned
Substitute the calculated qv and the number of moles of acetone burned into the formula, and calculate ΔH_comb/mole.