In the following experiment, a coffee-cup calorimeter containing 100. mL of H2O is used. The initial temperature of the calorimeter is 23.0 degrees C. If 3.80 g of CaCl2 is added to the calorimeter, what will be the final temperature of the solution in the calorimeter? The heat of solution, Delta H, of CaCl_2 is -82.8 kJ/mol.
I found the answer -14.6 degrees C and it was not correct. I am not quite sure where my math went wrong.
It would have helped if you had posted your work. That way I could find the error. As it is I'm slogging around in the dark. If CaCl2 is exothermic you know the temperature should go up and ot down.
3.80g/molar mass CaCl2 = mols.
mols CaCl2 x 82800 = ? Joules.
?J = mass H2O x specific heat H2O x (Tfinal-23.0) = 0 and solve for Tfinal.
Thank you Dr Bob, I actually realized right after I posted the question I was not including the 100 g of H2O in my math.
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.