In the following experiment, a coffee-cup calorimeter containing 100 \rm mL of \rm H_2O is used. The initial temperature of the calorimeter is 23.0 \rm ^{\circ}C. If 9.80 g of \rm CaCl_2 is added to the calorimeter, what will be the final temperature of the solution in the calorimeter? The heat of solution \Delta H_{\rm soln} of \rm CaCl_2 is \rm -82.8~kJ/mol.
The heat added to the calorimeter was 82,800 J x (9.80/110.98) = ?
? = mass H2O x specific heat H2O x (Tfinal-Tinitial) = 0
Substitute and solve for Tf.
Err.. Dr Bob do we add the mass of CaCl2 with H2O? when we want to find m
To find the final temperature of the solution in the calorimeter, we can use the principle of conservation of energy. The heat gained by the solution equals the heat lost by the water and calorimeter.
Here are the steps to calculate the final temperature of the solution:
Step 1: Calculate the heat gained by the solution.
The heat gained by the solution can be calculated using the formula:
q_solution = m_solution * C_solution * ΔT_solution
Where:
q_solution is the heat gained by the solution
m_solution is the mass of the solution (in grams)
C_solution is the specific heat capacity of the solution (assumed to be the same as water, which is 4.18 J/g·°C)
ΔT_solution is the change in temperature of the solution (final temperature - initial temperature)
In this case, the mass of the solution (water) is 100 mL which is equal to 100 g since the density of water is 1 g/mL. The change in temperature (ΔT_solution) is simply the final temperature minus the initial temperature.
Step 2: Calculate the heat lost by the water and calorimeter.
The heat lost by the water and calorimeter can be calculated using the same equation as above:
q_water_calorimeter = m_water_calorimeter * C_water_calorimeter * ΔT_water_calorimeter
Where:
q_water_calorimeter is the heat lost by the water and calorimeter
m_water_calorimeter is the mass of the water and calorimeter (in this case, the mass of water is 100 g plus the mass of the calorimeter, which can be assumed to be negligible)
C_water_calorimeter is the specific heat capacity of water (4.18 J/g·°C)
ΔT_water_calorimeter is the change in temperature of the water and calorimeter (final temperature - initial temperature)
Step 3: Apply the principle of conservation of energy.
According to the principle of conservation of energy, the heat gained by the solution is equal to the heat lost by the water and calorimeter:
q_solution = -q_water_calorimeter
Since the heat of solution (ΔH_soln) is given in kJ/mol, we need to convert it to J/g. Since the molar mass of CaCl2 is 110.98 g/mol, we can use the equation:
ΔH_soln = q_solution/mol_CaCl2
q_solution = ΔH_soln * mol_CaCl2
Where:
ΔH_soln is the heat of solution (-82.8 kJ/mol)
mol_CaCl2 is the number of moles of CaCl2
Step 4: Calculate the number of moles of CaCl2.
To calculate the number of moles of CaCl2, we can use its molar mass and the given mass:
mol_CaCl2 = mass_CaCl2 / molar_mass_CaCl2
Where:
mass_CaCl2 is the given mass of CaCl2 (9.80 g)
molar_mass_CaCl2 is the molar mass of CaCl2 (110.98 g/mol)
Step 5: Substitute the values into the equation.
Now that we have all the necessary values, we can substitute them into the equation:
q_solution = ΔH_soln * mol_CaCl2
Step 6: Calculate the final temperature of the solution.
Now that we know the heat gained by the solution, we can rearrange the equation from Step 1 to solve for the final temperature:
ΔT_solution = q_solution / (m_solution * C_solution)
Finally, add the ΔT_solution to the initial temperature to obtain the final temperature of the solution.