Naphthalene combustion can be used to calibrate the heat capacity of a bomb calorimeter. The heat of combustion of naphthalene is -40.1 kJ/g. When 0.8210 g of naphthalene was burned in a calorimeter containing 1,000. g of water, a temperature rise of 4.21°C was observed. What is the heat capacity of the bomb calorimeter excluding the water?
40,100 J/g x 0.8210 g = q
q = [mass H2O x specific heat H2O x delta T] + Ccal x delta T.
Solve for Ccal.
To find the heat capacity of the bomb calorimeter excluding the water, we can use the formula:
Q = m × C × ΔT
Where:
Q = heat transferred or absorbed
m = mass
C = specific heat capacity
ΔT = change in temperature
First, we need to find the heat transferred to the water.
Q_water = m_water × C_water × ΔT
Given:
m_water = 1000 g (mass of water)
C_water = 4.18 J/g°C (specific heat capacity of water)
ΔT = 4.21 °C
Convert units:
m_water = 1000 g = 1000 g ÷ 1000 = 1 kg
Now, substitute the values into the equation:
Q_water = 1 kg × 4.18 J/g°C × 4.21 °C
Q_water = 17.6282 kJ
Next, we need to calculate the moles of naphthalene burned.
moles_naphthalene = mass_naphthalene ÷ molar_mass_naphthalene
Given:
mass_naphthalene = 0.8210 g
molar_mass_naphthalene = 128.17 g/mol
moles_naphthalene = 0.8210 g ÷ 128.17 g/mol
moles_naphthalene = 0.00640 mol
Now, we can determine the heat transferred from the naphthalene to the bomb calorimeter:
Q_calorimeter = moles_naphthalene × heat_of_combustion_naphthalene
Given:
heat_of_combustion_naphthalene = -40.1 kJ/g
Q_calorimeter = 0.00640 mol × -40.1 kJ/g
Q_calorimeter = -0.2566 kJ
Since the heat transferred to the bomb calorimeter is equal to the sum of the heat transferred to the water and the heat transferred from the naphthalene, we can write:
Q_calorimeter = Q_water + Q_naphthalene
-0.2566 kJ = 17.6282 kJ + Q_naphthalene
Now, rearrange the equation to solve for Q_naphthalene:
Q_naphthalene = -0.2566 kJ - 17.6282 kJ
Q_naphthalene = -17.8848 kJ
Finally, we can calculate the heat capacity of the bomb calorimeter excluding the water:
C_calorimeter = Q_naphthalene ÷ ΔT
C_calorimeter = -17.8848 kJ ÷ 4.21 °C
C_calorimeter = -4.25 kJ/°C
Therefore, the heat capacity of the bomb calorimeter excluding the water is -4.25 kJ/°C.
To find the heat capacity of the bomb calorimeter excluding the water, we need to use the equation:
q = m × C × ΔT
Where:
q is the heat transferred
m is the mass of the substance (in this case, naphthalene)
C is the specific heat capacity of the substance
ΔT is the change in temperature
First, let's calculate the heat transferred (q) in this combustion reaction. The combustion of naphthalene releases heat, which is transferred to the water in the calorimeter.
q = m × ΔH
Where:
q is the heat transferred
m is the mass of the substance (in this case, naphthalene)
ΔH is the heat of combustion of the substance
Given that the mass of naphthalene burned is 0.8210 g and the heat of combustion of naphthalene is -40.1 kJ/g, we can calculate q:
q = (0.8210 g) × (-40.1 kJ/g)
q = -32.841 kJ
Next, we use the q value to find the heat capacity of the calorimeter (C) excluding the water.
q = C × ΔT
Rearranging the equation, we get:
C = q / ΔT
Given that the temperature rise (ΔT) is 4.21°C, we can calculate the heat capacity (C):
C = (-32.841 kJ) / (4.21°C)
C ≈ -7.79 kJ/°C
Therefore, the heat capacity of the bomb calorimeter excluding the water is approximately -7.79 kJ/°C. Since heat capacity is usually defined as a positive value, we can take the absolute value to express it as 7.79 kJ/°C.