A sample of benzoic acid weighting 1.567 g was burned in a calorimeter. If the initial temperature was 22 degrees Celsius,the final temperature was 31.1 degrees celsius, and the heat capacity of the calorimeter was 4.88 kJ/ degrees Celsius, what is the heat of combustion of benzoic acid?
q = heat released by the combustion = Qcal x delta T.
q/mass sample = heat/gram. If you want it in moles convert heat/gram to heat/mol. The usual way of report is kJ/mol.
To find the heat of combustion of benzoic acid, we need to calculate the amount of heat absorbed by the calorimeter and the water.
First, let's determine the amount of heat absorbed by the calorimeter using the formula:
q_calorimeter = heat capacity of calorimeter * change in temperature
Given:
Heat capacity of calorimeter = 4.88 kJ/°C
Change in temperature = 31.1°C - 22°C = 9.1°C
q_calorimeter = 4.88 kJ/°C * 9.1°C
q_calorimeter = 44.408 kJ
Next, let's calculate the amount of heat absorbed by the water using the formula:
q_water = mass of water * specific heat capacity of water * change in temperature
The specific heat capacity of water is approximately 4.18 J/g°C. However, we need to convert the mass of water to grams as the specific heat capacity is given in J/g°C.
Given that the mass of water is not provided, we can assume that the mass of water is equal to the mass of benzoic acid since it is stated that the benzoic acid was burned in the calorimeter. Therefore, the mass of water is 1.567 g.
q_water = 1.567 g * (4.18 J/g°C) * (31.1°C - 22°C)
q_water = 68.3888 J ≈ 0.0684 kJ
Now, let's calculate the total amount of heat absorbed by the system (calorimeter and water):
q_total = q_calorimeter + q_water
q_total = 44.408 kJ + 0.0684 kJ
q_total = 44.4764 kJ
The heat of combustion of benzoic acid can be obtained by dividing the total heat absorbed by the number of moles of benzoic acid burned.
To determine the number of moles of benzoic acid, we need its molar mass. The molar mass of benzoic acid (C7H6O2) can be calculated as follows:
molar mass = (7 * atomic mass of carbon) + (6 * atomic mass of hydrogen) + (2 * atomic mass of oxygen)
Using the periodic table, the atomic masses are approximately:
Carbon (C) = 12.01 g/mol
Hydrogen (H) = 1.01 g/mol
Oxygen (O) = 16.00 g/mol
molar mass = (7 * 12.01 g/mol) + (6 * 1.01 g/mol) + (2 * 16.00 g/mol)
molar mass = 122.12 g/mol
Finally, to calculate the heat of combustion (ΔH) per mole of benzoic acid:
ΔH = q_total / number of moles of benzoic acid
number of moles of benzoic acid = mass of benzoic acid / molar mass of benzoic acid
Given that the mass of benzoic acid is 1.567 g:
number of moles of benzoic acid = 1.567 g / 122.12 g/mol
number of moles of benzoic acid ≈ 0.012825 mol
ΔH = 44.4764 kJ / 0.012825 mol
ΔH ≈ 3475.47 kJ/mol
Therefore, the heat of combustion of benzoic acid is approximately 3475.47 kJ/mol.