In the following experiment, a coffee-cup calorimeter containing 100 mL of H20 is used. The initial temperature of the calorimeter is 23.0 C . If 3.60 g of CaCl2is added to the calorimeter, what will be the final temperature of the solution in the calorimeter? The heat of the change in enthalpy (H)soln solution of CaCl2 is -82.8kJ/mol.
The specific heat of H2O is 4.18 kJ/g or 75.24 kJ/mol
Change 3.60 g CaCl2 to moles; moles = grams/molar mass
(-82,800 J/mol x moles CaCl2) + [moles H2O x specific heat water(J/mol) x (Tfinal-Tinitial)] = 0
Check my thinking.
it isn't necessary to change the mass in grams to moles. the equation reads out q=s*m*(final temp - initial temp) where q is the change in enthalpy, s is specific heat, and m is mass.
To find the final temperature of the solution, we can use the equation:
q = m * c * ΔT
Where:
q = heat absorbed or released by the system (final temperature - initial temperature)
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
1. Calculate the heat absorbed or released by the system (q):
q = -Hsoln (because the change in enthalpy is negative)
q = -(-82.8 kJ/mol) = 82.8 kJ
2. Calculate the mass of CaCl2 in the solution:
Given: Mass of CaCl2 = 3.60 g
3. Convert the mass of CaCl2 to moles:
Moles of CaCl2 = Mass of CaCl2 / Molar mass of CaCl2
The molar mass of CaCl2 = 40.08 g/mol (from the periodic table)
Moles of CaCl2 = 3.60 g / 40.08 g/mol = 0.090 mol
4. Calculate the heat capacity (C) of the solution:
Given: Specific heat of H2O = 75.24 kJ/mol
Heat capacity of the solution = Specific heat of H2O / Molar mass of H2O
Heat capacity of the solution = 75.24 kJ/mol / 18.02 g/mol = 4.173 kJ/g
Note: We rounded the specific heat capacity to 4.173 kJ/g for calculation purposes.
5. Calculate the heat absorbed or released by the water in the calorimeter:
Heat absorbed or released by water (qwater) = mass of H2O * specific heat of H2O * ΔT
Given: Initial temperature of the calorimeter (Tinitial) = 23.0°C
Final temperature of the solution (Tfinal) = ?
qwater = (100 g + 3.60 g) * 4.173 kJ/g * (Tfinal - 23.0°C)
qwater = 103.6 kJ * (Tfinal - 23.0°C)
6. Set up an equation to solve for ΔT:
q + qwater = 0
82.8 kJ + 103.6 kJ * (Tfinal - 23.0°C) = 0
7. Solve the equation for Tfinal:
82.8 kJ + 103.6 kJ * (Tfinal - 23.0°C) = 0
103.6 kJ * (Tfinal - 23.0°C) = -82.8 kJ
(Tfinal - 23.0°C) = -82.8 kJ / 103.6 kJ
(Tfinal - 23.0°C) = -0.798
Tfinal = -0.798 + 23.0°C
Tfinal = 22.2°C
Therefore, the final temperature of the solution in the calorimeter is approximately 22.2°C.
To find the final temperature of the solution in the calorimeter, we need to apply the principle of conservation of energy.
First, calculate the heat released or absorbed by the dissolution of CaCl2 using the given change in enthalpy of solution and the amount of CaCl2 added.
1. Calculate the moles of CaCl2 added:
- The molar mass of CaCl2 is 110.98 g/mol.
- Use the given mass of CaCl2 (3.60 g) and the molar mass to calculate the moles of CaCl2:
Moles of CaCl2 = mass of CaCl2 / molar mass of CaCl2
2. Calculate the heat released or absorbed by the dissolution of CaCl2:
- The given change in enthalpy of solution (ΔHsoln) is -82.8 kJ/mol.
- Multiply the moles of CaCl2 by the change in enthalpy of solution to find the heat released or absorbed:
Heat released or absorbed = moles of CaCl2 * ΔHsoln
Next, we can use the principle of conservation of energy to determine the final temperature of the solution:
3. Calculate the heat exchanged between the solution and the calorimeter:
- The heat exchanged between the solution and the calorimeter is equal to the heat released or absorbed by the dissolution of CaCl2. Therefore:
Heat exchanged = Heat released or absorbed
4. Calculate the heat exchanged in joules:
- Since the specific heat of water is given in kJ/g, we need to convert the mass of water to grams and the specific heat to joules/g.
- The specific heat of water is 4.18 kJ/g or 75.24 kJ/mol.
- Multiply the mass of water by the specific heat to find the heat exchanged in joules:
Heat exchanged in joules = mass of water * specific heat
5. Apply the principle of conservation of energy:
- The heat exchanged between the solution and the calorimeter is equal to the heat exchanged in joules.
- Therefore:
Heat exchanged = Heat exchanged in joules
6. Use the equation Q = m * c * ΔT to find the final temperature:
- Rearrange the equation to solve for ΔT:
ΔT = Q / (m * c)
- Substitute the known values:
ΔT = Heat exchanged / (mass of water * specific heat)
Finally, add ΔT to the initial temperature to find the final temperature:
Final temperature = Initial temperature + ΔT