A 1.20g sample of benzoic acid is burned in excess of )2 in a bomb calorimeter immersed in 1300 g of water. The temperature of the water rises from 25 to 30.2 degrees C. The heat of combustion of benzoic acid is -26.4 kJ/g. The heat capacity of water is 4.18. What is the heat capacity of the bomb calorimeter (in J/C)?
q = [mass H2O x specific heat H2O x (Tfinal-Tinitial)] + [Ccal x (Tfinal-Tinitial)]
q = 26,400 J/g x 1.20 g = ?
Substitute " for q in the first equation along with the other data and solve for Ccal. q is + for the first equation.
To find the heat capacity of the bomb calorimeter, we need to use the formula:
Q = m × c × ΔT
Where:
Q is the heat transferred
m is the mass of the substance (in this case, water)
c is the specific heat capacity of the substance (in this case, water)
ΔT is the change in temperature
First, we need to calculate the heat transferred by the water:
Q_water = m_water × c_water × ΔT_water
Given:
m_water = 1300 g (mass of water)
c_water = 4.18 J/g°C (specific heat capacity of water)
ΔT_water = 30.2°C - 25°C = 5.2°C (change in temperature)
Now, substitute the given values into the formula:
Q_water = 1300 g × 4.18 J/g°C × 5.2°C
Next, calculate the heat transferred by the combustion of benzoic acid:
Q_combustion = m_benzoic_acid × ΔH_combustion
Given:
m_benzoic_acid = 1.20 g (mass of benzoic acid)
ΔH_combustion = -26.4 kJ/g (heat of combustion of benzoic acid)
Convert ΔH_combustion to J/g:
ΔH_combustion = -26.4 kJ/g × 1000 J/kJ = -26,400 J/g
Now, substitute the given values into the formula:
Q_combustion = 1.20 g × -26,400 J/g
Finally, since the bomb calorimeter is immersed in water, the heat transferred by the combustion of benzoic acid is equal to the heat transferred by the water:
Q_water = Q_combustion
Therefore, we can equate the two equations:
1300 g × 4.18 J/g°C × 5.2°C = 1.20 g × -26,400 J/g
From here, solve for the unknown variable (heat capacity of the bomb calorimeter) by rearranging the equation:
Bomb calorimeter's heat capacity = (1300 g × 4.18 J/g°C × 5.2°C) / (1.20 g × -26,400 J/g)
Calculate the expression to find the heat capacity of the bomb calorimeter.