When 0.515 g of compound X is burned completely in a bomb calorimeter containing 3000 g of water, a temperature rise of 0.243◦C is observed. What is �Urxn for the combustion of compound X? The hardware component of the calorimeter has a heat capacity of 3.12kJ/◦C. The specific heat of water is 4.184J/g ·◦C, and the MW of X is 56.0 g/mol.
Answer in units of kJ/mol
q = [mass H2O x specific heat H2O x (Tfinal-Tinitial)] + [Ccal x (Tfinal-Tinitial)]
Then delta E/g = q/0.515 g
delta E/mol = delta E/g x (56.0 g/mol)
To find the �Urxn (change in internal energy) for the combustion of compound X, we need to calculate the amount of heat released during the combustion reaction.
First, we need to find the heat absorbed by the water in the calorimeter. The formula for heat absorbed by a substance is given by:
q = m * C * ΔT
where:
q is the heat absorbed (in Joules),
m is the mass of the substance (in grams),
C is the specific heat of the substance (in J/g·◦C), and
ΔT is the change in temperature (in ◦C).
In this case, we're using water, so the specific heat of water is 4.184 J/g·◦C.
Given that the mass of water is 3000 g and the change in temperature is 0.243◦C, we can calculate the heat absorbed by the water using the formula:
q_water = 3000 g * 4.184 J/g·◦C * 0.243◦C
Now, let's convert the heat absorbed by the water to kJ:
q_water = (3000 g * 4.184 J/g·◦C * 0.243◦C) / 1000
Next, we need to calculate the heat capacity of the calorimeter, given as 3.12 kJ/◦C.
The heat absorbed by the calorimeter is given by:
q_calorimeter = ΔT * C_calorimeter
where:
q_calorimeter is the heat absorbed by the calorimeter (in Joules), and
C_calorimeter is the heat capacity of the calorimeter (in kJ/◦C).
Using the given values, we can calculate the heat absorbed by the calorimeter by multiplying the heat capacity (3.12 kJ/◦C) by the change in temperature (0.243◦C).
q_calorimeter = 3.12 kJ/◦C * 0.243◦C
Now, let's add the heat absorbed by the water and the calorimeter together to find the total heat released during the combustion reaction:
q_total = q_water + q_calorimeter
Finally, we can calculate the �Urxn (change in internal energy) for the combustion of compound X by dividing the total heat released (in Joules) by the number of moles of compound X.
The number of moles of compound X can be calculated using the formula:
moles = mass / molar mass
In this case, the mass of compound X is given as 0.515 g, and the molar mass is given as 56.0 g/mol.
moles_X = 0.515 g / 56.0 g/mol
Finally, we can calculate �Urxn using the formula:
�Urxn = q_total / moles_X
Divide q_total (in Joules) by moles_X (in moles) to get the answer in units of kJ/mol.