To determine the final temperature of the solution in the calorimeter, you need to use the principle of energy conservation.
First, let's calculate the heat released by the dissolution of CaCl2:
1. Start by finding the moles of CaCl2 added to the calorimeter.
- You know the mass of CaCl2 is 3.80 g.
- To find the moles, divide the mass by the molar mass of CaCl2.
The molar mass can be found by adding up the atomic masses of the elements: Ca = 40.08 g/mol, Cl = 35.45 g/mol.
- So, the molar mass of CaCl2 is 40.08 + (2 * 35.45) = 110.98 g/mol.
- Divide the mass (3.80 g) by the molar mass (110.98 g/mol) to get the moles of CaCl2.
2. Calculate the heat released using the heat of solution (ΔH) of CaCl2.
- The heat of solution (ΔH) is given as -82.8 kJ/mol.
- Multiply the moles of CaCl2 by the heat of solution to get the heat released.
Next, we can apply the principle of energy conservation:
3. The heat released by the dissolution of CaCl2 is equal to the heat absorbed by the water in the calorimeter, according to the law of energy conservation.
- The specific heat capacity of water, denoted as C, is 4.18 J/g°C.
- The initial and final temperatures in Celsius are given as 23.0°C and the unknown "final temperature" respectively.
- Consider the change in temperature of water as ΔT = final temperature - initial temperature.
Now, we can set up and solve the equation:
4. Equation: heat released = heat absorbed
- Convert the heat released from kilojoules to joules by multiplying by 1000.
- Use the formula: heat released = heat absorbed.
- Set up the equation as follows: (moles of CaCl2) * (heat of solution) = (mass of water) * (specific heat capacity) * (ΔT).
Once you solve the equation for the final temperature, you should get the correct result. Make sure to double-check each step to identify any errors in your calculations.