A sample of naphthalene (C10H8) that has a mass of 0.7200 g is burned in a bomb calorimeter. The mass of the calorimeter is 1.580 kg, and its specific heat is 2.55 J/(g °C). As a result of the reaction, the temperature of the calorimeter increases from 22.00°C to 29.3°C. If 1 mol of naphthalene has a mass of 128.0 g, what is the molar heat of combustion of naphthalene?
–11,300 kJ/mol
–5,230 kJ/mol
–3,760 kJ/mol
–29.4 kJ/mol
11300
To determine the molar heat of combustion of naphthalene, we need to calculate the heat transferred to the calorimeter.
First, let's calculate the heat transferred to the calorimeter using the formula:
Q = mcΔT
Where:
Q is the heat transferred (in Joules)
m is the mass of the calorimeter (in grams)
c is the specific heat capacity of the calorimeter (in J/(g °C))
ΔT is the change in temperature (final temperature - initial temperature)
Substituting the given values:
m = 1.580 kg = 1580 g
c = 2.55 J/(g °C)
ΔT = 29.3°C - 22.00°C = 7.3°C
Q = (1580 g) * (2.55 J/(g °C)) * (7.3°C)
Q = 29546.7 J
Next, we need to convert the mass of naphthalene burned to moles:
molar mass of naphthalene (C10H8) = (10 * atomic mass of carbon) + (8 * atomic mass of hydrogen)
= (10 * 12.01 g/mol) + (8 * 1.008 g/mol)
= 128.18 g/mol
moles of naphthalene = mass of naphthalene burned / molar mass of naphthalene
= 0.7200 g / 128.18 g/mol
= 0.005623 mol
Now, let's calculate the molar heat of combustion using the formula:
molar heat of combustion = heat transferred (in Joules) / moles of naphthalene
molar heat of combustion = 29546.7 J / 0.005623 mol
molar heat of combustion ≈ -5240.77 J/mol
Finally, let's convert the molar heat of combustion from Joules to kilojoules:
molar heat of combustion ≈ -5240.77 J/mol / 1000
molar heat of combustion ≈ -5.2 kJ/mol
Therefore, the molar heat of combustion of naphthalene is approximately -5.2 kJ/mol.