At constant volume, the heat combustion of a particular compound is -3447.0 KJ/mol. When 1.205 g of this compound (molar mass = 119.94 g/mol) was burned in a bomb calorimeter, the temperature of the calorimeter (including its contents) rose by 5.007 degrees C. What is the heat capacity (calorimeter constant) of the calorimeter?
I need this explained to me very well! I have tried going by other explanations online, but they are not helping! I keep doing it wrong and getting the wrong answer. I have no idea how to solve it, so I need in depth help, please :).
To solve this problem, we can use the concept of heat capacity. Heat capacity is defined as the amount of heat required to raise the temperature of an object by 1 degree Celsius. In this case, we are trying to find the heat capacity of the calorimeter, which is the object that absorbs the heat produced during combustion.
The heat released during combustion is given by the equation:
q = n * ΔH
Where q is the heat released, n is the number of moles, and ΔH is the heat of combustion. We can calculate the number of moles of the compound burned by dividing its mass by its molar mass:
n = mass / molar mass
n = 1.205 g / 119.94 g/mol
n ≈ 0.01005 mol
Now, we need to convert the temperature change from Celsius to Kelvin, as the heat change should be in the same unit as the heat capacity:
ΔT = 5.007°C = 5.007 K
Next, we can calculate the heat released during the combustion:
q = n * ΔH
q = 0.01005 mol * -3447.0 kJ/mol
q ≈ -34.63 kJ
Finally, we can use the formula for heat capacity to find the calorimeter constant:
q = C * ΔT
Solving for C:
C = q / ΔT
C = -34.63 kJ / 5.007 K
C ≈ -6.920 kJ/K
Now, let's analyze the negative sign. The negative sign indicates that heat was released, which is the case during combustion. However, since heat capacity is conventionally positive, we can take the absolute value of the calculated heat capacity:
C ≈ 6.920 kJ/K
So, the heat capacity (calorimeter constant) of the calorimeter is approximately 6.920 kJ/K.
It's important to keep track of the units and use the correct formulas and coefficients to arrive at the correct answer. Make sure to double-check your calculations, particularly the conversion of units and moles.