Assume that 0.311 g of diborane is combusted in a calorimeter whose heat capacity (Ccalorimeter) is 7.854 kJ/°C at 17.64°C. What is the final temperature of the calorimeter?
what is the heat of combustion for diborane?
To determine the final temperature of the calorimeter, we can use the principle of conservation of energy. The heat released by the combustion of diborane is equal to the heat absorbed by the calorimeter.
First, we need to calculate the heat released by the combustion of diborane. The chemical equation for the combustion of diborane (B2H6) is:
2 B2H6(g) + 6 O2(g) -> 4 B2O3(s) + 6 H2O(g)
The balanced equation shows that 2 moles of diborane release heat, which we can calculate using the molar mass of diborane (B2H6):
Molar mass of B2H6 = (2 x Atomic mass of B) + (6 x Atomic mass of H)
= (2 x 10.81 g/mol) + (6 x 1.01 g/mol)
= 27.98 g/mol
Now, we can calculate the heat released by the combustion of 0.311 g of diborane:
Heat released = (0.311 g / 27.98 g/mol) x Heat of combustion of diborane
The heat of combustion of diborane is typically given as -1962 kJ/mol. However, we need to divide this value by 2 because the balanced equation shows that 2 moles of diborane release heat:
Heat of combustion of 1 mole of B2H6 = -1962 kJ/mol / 2
= -981 kJ/mol
Substituting the values into the equation, we get:
Heat released = (0.311 g / 27.98 g/mol) x -981 kJ/mol
Next, we can calculate the heat absorbed by the calorimeter using the equation:
Heat absorbed = Ccalorimeter x ΔT
Rearranging the equation to solve for ΔT:
ΔT = Heat absorbed / Ccalorimeter
Substituting the values, we get:
ΔT = (Heat released) / Ccalorimeter
Now, we can calculate the change in temperature (ΔT) by dividing the heat released by the heat capacity of the calorimeter:
ΔT = [(0.311 g / 27.98 g/mol) x -981 kJ/mol] / 7.854 kJ/°C
Simplifying the equation:
ΔT = (-10.984 kJ) / 7.854 kJ/°C
Finally, we can calculate the final temperature by adding the change in temperature (ΔT) to the initial temperature of the calorimeter:
Final temperature = Initial temperature + ΔT
Note: The initial temperature of the calorimeter is 17.64°C.
Final temperature = 17.64°C + ΔT
To find the final temperature of the calorimeter, we need to calculate the heat released by the combustion of diborane and then use that to determine the final temperature based on the calorimeter's heat capacity.
1. Calculate the heat released by the combustion of diborane:
Diborane (B2H6) reacts with oxygen (O2) to produce boron oxide (B2O3) and water (H2O), and releases heat in the process. The balanced equation for the combustion reaction is:
2B2H6(g) + 6O2(g) -> 2B2O3(s) + 6H2O(g)
The molar mass of diborane (B2H6) is 27.67 g/mol.
We are given that 0.311 g of diborane is combusted.
So, the number of moles of diborane combusted can be calculated by dividing the mass of diborane by its molar mass:
moles of diborane = 0.311 g / 27.67 g/mol
From the balanced equation, we see that 2 moles of diborane release heat. Therefore, the moles of diborane combusted will release half the amount of heat.
Moles of diborane releasing heat = (moles of diborane) / 2
2. Calculate the heat released by the combustion reaction:
The heat released by the combustion reaction can be calculated using the heat of combustion of diborane, which is a known value. Let's assume the heat of combustion of diborane is -1826 kJ/mol.
Heat released = (moles of diborane releasing heat) * (heat of combustion of diborane)
3. Use the heat released to determine the final temperature of the calorimeter:
The formula to calculate the final temperature of the calorimeter is:
q = Ccalorimeter * (Tfinal - Tinitial)
where q is the heat transferred, Ccalorimeter is the heat capacity of the calorimeter, Tfinal is the final temperature, and Tinitial is the initial temperature.
Rearranging the formula, we get:
Tfinal = (q / Ccalorimeter) + Tinitial
We are given that the heat capacity of the calorimeter is 7.854 kJ/°C and the initial temperature is 17.64°C.
Plugging in the values, we can calculate the final temperature.
By following these steps, you should be able to find the final temperature of the calorimeter.