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?

To find the molar heat of combustion of naphthalene, we need to calculate the heat energy released during the combustion reaction.

First, let's calculate the heat absorbed by the calorimeter.

The heat absorbed by the calorimeter can be calculated using the formula:

Q = m * c * ΔT

Where:
Q = heat energy absorbed by the calorimeter
m = mass of the calorimeter (1.580 kg)
c = specific heat of the calorimeter (2.55 J/(g°C))
ΔT = change in temperature (final temperature - initial temperature)

ΔT = 29.3°C - 22.00°C = 7.3°C

Now, let's convert the mass of the calorimeter to grams.

m = 1.580 kg * 1000 g/kg
m = 1580 g

Substituting the values into the formula:

Q = (1580 g) * (2.55 J/(g°C)) * (7.3°C)
Q = 29573.5 J

Next, let's calculate the moles of naphthalene burned.

1 mole of naphthalene = 128.0 g

Given that the mass of the naphthalene sample is 0.7200 g:

moles = mass / molar mass
moles = 0.7200 g / 128.0 g/mol
moles ≈ 0.005625 mol

To find the molar heat of combustion, we need to divide the heat energy released by the moles of naphthalene burned.

Molar heat of combustion = Q / moles

Molar heat of combustion = 29573.5 J / 0.005625 mol

Molar heat of combustion ≈ 5,250,133 J/mol

To find the molar heat of combustion of naphthalene (C10H8), we need to calculate the heat released during the combustion reaction.

Step 1: Calculate the heat absorbed by the calorimeter.
The formula to calculate the heat absorbed or released is given by:

q = mcΔT

where q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.

Using the given values:

m = 1.580 kg + 0.7200 g = 1.58072 kg
c = 2.55 J/(g°C)
ΔT = 29.3°C - 22.00°C = 7.3°C

q = (1.58072 kg)(2.55 J/(g°C))(7.3°C)
q ≈ 29.033 J

Step 2: Calculate the number of moles of naphthalene.
1 mol of naphthalene has a mass of 128.0 g, and the mass of the sample used is 0.7200 g. So, we can calculate the moles of naphthalene as:

moles = mass / molar mass
moles = 0.7200 g / 128.0 g/mol
moles ≈ 0.005625 mol

Step 3: Calculate the molar heat of combustion.
The molar heat of combustion is the amount of heat released when 1 mole of a substance is burned. So, we can calculate it using the formula:

molar heat of combustion = q / moles

molar heat of combustion ≈ 29.033 J / 0.005625 mol
molar heat of combustion ≈ 5152.8 J/mol

Therefore, the molar heat of combustion of naphthalene is approximately 5152.8 J/mol.