When 2.85 g of HC7H5O2 (molar mass = 122.12 g/mol) was burned in a bomb calorimeter, the temperature of the calorimeter changed from 24.05 ºC to 29.19 ºC. What is the heat capacity of the calorimeter in units of kJ/ºC?
To find the heat capacity of the calorimeter, we can use the formula:
Heat Capacity = q / ΔT
where q is the heat released or absorbed by the reaction and ΔT is the change in temperature.
First, we need to calculate the heat released by the reaction using the equation:
q = m × ΔT × C
where m is the mass of the substance burned and C is the specific heat capacity of the substance.
Given:
m = 2.85 g
ΔT = (29.19 ºC - 24.05 ºC) = 5.14 ºC
C = ???
To find the heat released by the reaction (q), we can use the equation:
q = m × ΔT × C
Re-arranging the equation to solve for C, we have:
C = q / (m × ΔT)
We already know the mass (m) and ΔT, so we need to determine q. We can calculate q using the equation:
q = heat released = moles of substance × ΔH
To find the moles of the substance burned, we can use the equation:
moles = mass / molar mass
Given:
Mass (m) = 2.85 g
Molar mass = 122.12 g/mol
ΔH = ???
First, we calculate the moles of HC7H5O2 burned:
moles = Mass / Molar mass
moles = 2.85 g / 122.12 g/mol
moles ≈ 0.0234 mol (rounded to four decimal places)
Now, we need to determine the heat of the reaction (ΔH). Since the substance is burned, we can assume that the reaction is combustion. The heat of combustion of HC7H5O2 is typically -3850 kJ/mol. Therefore, ΔH = -3850 kJ/mol.
Now, we can calculate the heat released by the reaction (q):
q = moles × ΔH
q = 0.0234 mol × -3850 kJ/mol
q ≈ -89.79 kJ (rounded to two decimal places)
Finally, we can calculate the heat capacity of the calorimeter (C):
C = q / (m × ΔT)
C = -89.79 kJ / (2.85 g × 5.14 ºC)
C ≈ -6.58 kJ/ºC (rounded to two decimal places)
Therefore, the heat capacity of the calorimeter is approximately -6.58 kJ/ºC. Note that the negative sign indicates that the calorimeter is losing heat to the surroundings.
To find the heat capacity of the calorimeter, we can use the formula:
q = mcΔT
where q is the heat transferred, m is the mass of the substance being burned, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
In this case, the mass of HC7H5O2 burned is given as 2.85 g, the change in temperature (ΔT) is (29.19 ºC - 24.05 ºC) = 5.14 ºC, and the specific heat capacity (c) is what we're trying to find.
Since the heat transferred (q) is absorbed by the calorimeter, we can rearrange the formula to solve for c:
c = q / (m * ΔT)
So, we need to calculate q first.
The heat transferred (q) can be calculated using the equation:
q = nΔH
where n is the number of moles and ΔH is the enthalpy change for the reaction.
To calculate n, we can use the equation:
n = m / M
where M is the molar mass of HC7H5O2.
Substituting the given values:
n = 2.85 g / 122.12 g/mol
n ≈ 0.0234 mol
Now, let's calculate q using the enthalpy change.
Since the substance is burned, we assume it is a combustion reaction. The balanced chemical equation for the combustion of HC7H5O2 is:
2 HC7H5O2 + 17 O2 -> 14 CO2 + 8 H2O
To calculate ΔH for the reaction, we need to know the standard enthalpy of formation (ΔHf) for each component.
Looking up the values, we find:
ΔHf(HC7H5O2) = -424.7 kJ/mol
ΔHf(CO2) = -393.5 kJ/mol
ΔHf(H2O) = -285.8 kJ/mol
Applying the equation:
ΔH = (14 mol CO2 * ΔHf(CO2)) + (8 mol H2O * ΔHf(H2O)) - (2 mol HC7H5O2 * ΔHf(HC7H5O2))
ΔH = (14 mol * (-393.5 kJ/mol)) + (8 mol * (-285.8 kJ/mol)) - (2 mol * (-424.7 kJ/mol))
ΔH ≈ -5320.6 kJ
Finally, we can calculate q using the equation:
q = n * ΔH
q = 0.0234 mol * (-5320.6 kJ/mol)
q ≈ -124.6 kJ
Now, we can substitute the values into the formula to find c:
c = q / (m * ΔT)
c = (-124.6 kJ) / (2.85 g * 5.14 ºC)
c ≈ -8.39 kJ/ºC
Therefore, the heat capacity of the calorimeter is approximately -8.39 kJ/ºC. The negative sign indicates that the calorimeter releases heat.
q = mass x Ccal x (Tf-Ti)
q = 2.85 x Ccal x (29.19-24.05)
Solve for Ccal. You will need to look up the value of q which is the heat of combustion for benzoic acid and substitute that for q. Note that heat of combustion is - but this heat is being added to the calorimeter so change the sign to + for the q value.