A 1.000 gram sample of the rocket fuel hydrazine (N2H4) is burned in a bomb calorimeter. The temperature rises from 24.62°C to 28.16°C. The heat capacity of the calorimeter (including the water) is 5860 J/°C. Calculate the molar heat of combustion of hydrazine, in kJ/mole.
molar mass of N2H4 = 28+4 = 32 grams/mol
so one gram is (1/32) mol
let joules/mol = x
then
(1/32) mol * x Joules/mol = 5680 Joules/deg * (28.16 - 24.62) deg
so
x = 32 *5680 * (28.16-24.62) Joules/mol
divide by 1000 to get Kilojoules/mol
Well, it seems like hydrazine is really heating things up! Let's calculate the molar heat of combustion, shall we?
First, we need to find the heat absorbed by the calorimeter. We can use the formula:
q = mcΔT
Where:
q = heat absorbed by the calorimeter
m = mass of the calorimeter (in this case, let's assume it's the water)
c = specific heat capacity of the calorimeter
ΔT = change in temperature
Plugging in the values, we have:
q = (5860 J/°C)(3.54°C)
q = 20728.4 J
Next, we need to convert the heat absorbed by the calorimeter to moles of hydrazine combusted. Since we know the mass of the hydrazine sample (1.000 gram) and its molar mass (let's assume it's 32 g/mol), we can calculate the moles of hydrazine:
moles = mass / molar mass
moles = 1.000 g / 32 g/mol
moles = 0.03125 mol
Now, we can calculate the molar heat of combustion. Since the heat from the combustion is transferred to 0.03125 mol of hydrazine, we divide the heat absorbed by the calorimeter:
molar heat of combustion = q / moles
molar heat of combustion = 20728.4 J / 0.03125 mol
molar heat of combustion = 663515.2 J/mol
And to convert that to kJ/mol, we divide by 1000:
molar heat of combustion = 663.5152 kJ/mol
So, the molar heat of combustion of hydrazine is approximately 663.5152 kJ/mol. That's one hot fuel!
To calculate the molar heat of combustion of hydrazine (N2H4), we need to use the equation:
q = m × C × ΔT
Where:
q is the heat absorbed or released
m is the mass of the substance (in this case, the sample of N2H4)
C is the heat capacity of the calorimeter (including the water)
ΔT is the change in temperature
First, let's convert the temperature change from Celsius to Kelvin:
ΔT = (28.16°C - 24.62°C) + 273.15K = 303.69K - 297.77K = 5.92K
Next, let's substitute the given values into the equation:
q = (1.000g) × (5860J/°C) × (5.92K)
Now we can calculate q:
q = 34775.2 J
To calculate the molar heat of combustion of hydrazine, we need to convert the heat (q) to kJ and divide it by the number of moles of N2H4. The molar mass of N2H4 is:
Molar mass of N2H4 = (2 × 14.01g/mol) + (4 × 1.01g/mol) = 32.05g/mol
Now, let's calculate the number of moles:
moles of N2H4 = (1.000g) / (32.05g/mol)
moles of N2H4 ≈ 0.0312 mol
Finally, we can calculate the molar heat of combustion:
Molar heat of combustion = (34775.2 J) / (0.0312 mol) = 1,114,040 J/mol
To convert this result to kilojoules per mole, we divide by 1000:
Molar heat of combustion ≈ 1114.04 kJ/mol
Therefore, the molar heat of combustion of hydrazine (N2H4) is approximately 1114.04 kJ/mol.
To calculate the molar heat of combustion of hydrazine, we need to use the formula q = mcΔT.
In this case, q represents the heat absorbed (or released) during the combustion of hydrazine, m is the mass of the hydrazine sample (1.000 gram), c is the heat capacity of the calorimeter (5860 J/°C), and ΔT is the change in temperature (28.16°C - 24.62°C = 3.54°C).
First, let's calculate the heat absorbed by the calorimeter and water:
q_calorimeter = c * ΔT
= 5860 J/°C * 3.54°C
= 20708.4 J
Next, we'll calculate the heat absorbed by the hydrazine:
q_hydrazine = q - q_calorimeter
Now, the molar heat of combustion of hydrazine can be calculated. One mole of hydrazine has a molar mass of 32.04 g.
Molar heat of combustion = q_hydrazine / (mass of hydrazine / molar mass of hydrazine)
mass of hydrazine = 1.000 g
molar mass of hydrazine = 32.04 g/mol
Molar heat of combustion = q_hydrazine / (1.000 g / 32.04 g/mol)
Finally, we just need to convert the result from joules to kilojoules:
Molar heat of combustion = (q_hydrazine / (1.000 g / 32.04 g/mol)) / 1000
Now, let's plug in the values to find the molar heat of combustion of hydrazine in kilojoules per mole.