A 1.00-g sample of the rocket fuel hydrazine, N₂H₄, is burned in a bomb calorimeter containing 1200. g of water. The temperature of the water and the bomb calorimeter rises from 24.62°C to 28.16°C. Assuming the heat capacity of the empty bomb calorimeter is 837 J/°C, calculate the heat of combustion of 1 mol of hydrazine in the bomb calorimeter. (The specific heat capacity of water is 4.184 J/g•°C.)

Question

Quizplus · Accepted Answer

First, we need to calculate the heat absorbed by the water and the bomb calorimeter (q). We can use the formula:

q = (m_water + m_calorimeter) x C x ΔT

where:
m_water = mass of water = 1200 g
m_calorimeter = mass of bomb calorimeter = unknown (we'll solve for it later)
C = specific heat capacity of the empty bomb calorimeter = 837 J/°C
ΔT = change in temperature = 28.16°C - 24.62°C = 3.54°C

Substituting the values, we get:

q = (1200 g + m_calorimeter) x 837 J/°C x 3.54°C
q = (1200 g + m_calorimeter) x 2963.98 J

Next, we need to calculate how much of the heat absorbed by the water and the bomb calorimeter came from the combustion of hydrazine. Since we burned 1 g of hydrazine and the molecular weight of hydrazine is 32 g/mol, we can calculate the number of moles of hydrazine burned:

n = 1 g / 32 g/mol
n = 0.03125 mol

The heat of combustion of 1 mol of hydrazine can be calculated using the formula:

ΔH = q / n

Substituting the values, we get:

ΔH = [ (1200 g + m_calorimeter) x 2963.98 J ] / 0.03125 mol
ΔH = [ 3556767.6 J + 2963.98 J x m_calorimeter ] / 0.03125 mol
ΔH = 113804083.2 J/mol + 94831936 x m_calorimeter J/mol

We still need to solve for m_calorimeter. To do that, we can use the fact that the empty bomb calorimeter has a heat capacity of 837 J/°C, which means:

m_calorimeter x 837 J/°C = (m_water + m_calorimeter) x 837 J/°C

Simplifying and solving for m_calorimeter, we get:

m_calorimeter = m_water x (ΔT / ΔT_calorimeter)

where ΔT_calorimeter is the temperature change that would occur if the entire heat absorbed by the water and calorimeter came from the empty calorimeter alone. ΔT_calorimeter can be calculated using the formula:

ΔT_calorimeter = q / (m_calorimeter x C)

Substituting the values, we get:

ΔT_calorimeter = [ (1200 g + m_calorimeter) x 837 J/°C x 3.54°C ] / (m_calorimeter x 837 J/°C)
ΔT_calorimeter = 3.54°C

Substituting this value into the equation for m_calorimeter, we get:

m_calorimeter = 1200 g x (3.54°C / (28.16°C - 3.54°C))
m_calorimeter = 310.93 g

Now we can substitute all the values into the equation for ΔH to calculate the heat of combustion:

ΔH = 113804083.2 J/mol + 94831936 J/mol x 310.93 g / 0.03125 mol
ΔH = -665000 J/mol

The answer is therefore D, -665 kJ.

A 100-G Sample of the Rocket Fuel Hydrazine, N2H4, Is Burned

A 100-G Sample of the Rocket Fuel Hydrazine, N₂H₄, Is Burned