When 0.373 g of compound X is burned completely in a bomb calorimeter containing 3000
g of water, a temperature rise of 0.341 C is observed. What is ∆Urxn for the combustion
of compound X? The hardware component of the calorimeter has a heat capacity of 3.19
kJ/ ◦C. The specific heat of water is 4.184 J/g · ◦ C, and the MW of X is 56.0 g/mol.
Answer in units of kJ/mol
q = (mass H2O x specific heat water x delta T) + (Ccal x delta T)
q/0.373 = J/g and that x 56 = J/mol. Convert to kJ/mol
To calculate ∆Urxn for the combustion of compound X, we need to consider the heat transfer that occurs during the reaction. The calculation can be done using the heat capacity of the calorimeter and the heat absorbed by the water.
Here are the steps to calculate ∆Urxn:
1. First, determine the heat absorbed by the water. To do this, we need to use the equation:
q = m * c * ∆T
Where:
q = heat absorbed by the water (in Joules)
m = mass of water (in grams)
c = specific heat of water (in J/g·°C)
∆T = temperature change of the water (in °C)
Given data:
m = 3000 g (mass of water)
c = 4.184 J/g·°C (specific heat of water)
∆T = 0.341 °C (temperature rise)
Substituting the values into the equation:
q = 3000 g * 4.184 J/g·°C * 0.341 °C
Calculating the value of q will give you the heat absorbed by the water, expressed in Joules.
2. Next, convert the heat absorbed by the water from Joules to kilojoules by dividing the value by 1000:
q = q / 1000
3. Now, calculate the heat released (or absorbed) by the hardware component of the calorimeter. The heat capacity of the calorimeter (C) is given as 3.19 kJ/°C. Multiply the heat capacity by the temperature change (∆T) to find the heat released or absorbed:
q_calorimeter = C * ∆T
Substituting the values:
q_calorimeter = 3.19 kJ/°C * 0.341 °C
4. Calculate the total heat involved in the reaction by summing up the heat absorbed by the water (q) and the heat released or absorbed by the calorimeter (q_calorimeter):
q_total = q + q_calorimeter
5. Convert the mass of compound X to moles using the molar mass (MW) of X:
moles_X = mass_X / MW
Given data:
mass_X = 0.373 g
MW = 56.0 g/mol
moles_X = 0.373 g / 56.0 g/mol
6. Calculate the enthalpy change (∆U) using the equation:
∆Urxn = q_total / moles_X
Substitute the values:
∆Urxn = q_total / (0.373 g / 56.0 g/mol)
The result of this calculation will give you ∆Urxn in units of kJ/mol.
By following these steps and doing the calculations, you will be able to find the value of ∆Urxn for the combustion of compound X.