In the following experiment, a coffee-cup calorimeter containing 100mL of H2 is used. The initial temperature of the calorimeter is 23.0 C . If 3.40g CaCl2 of is added to the calorimeter, what will be the final temperature of the solution in the calorimeter? The heat of solution of CaCl2 is -82.8 kJ/mol.
q = -82.8 kJ/mol x (3.40/molar mass CaCl2) = about -2.5 kJ = about -2500 J.
Then -2500 = mass H2O x specific heat H2O x (T2-T1) and solve for T2. I get approximately 28 or so.
28.9 degrees C
To find the final temperature of the solution in the calorimeter, we need to use the principle of conservation of energy. First, we need to find the amount of heat released by the dissolution of CaCl2.
Step 1: Calculate the moles of CaCl2 added to the calorimeter.
The molar mass of CaCl2 is calculated as follows:
Ca: 1 atomic mass unit (amu)
Cl: 2 x 35.5 amu (as there are two chlorine atoms in CaCl2)
Total molar mass of CaCl2: 1 + 2 x 35.5 = 111.0 g/mol
Now, we can calculate the number of moles of CaCl2:
moles of CaCl2 = mass of CaCl2 / molar mass of CaCl2
moles of CaCl2 = 3.40g / 111.0 g/mol
Step 2: Calculate the heat released by the dissolution of CaCl2.
The heat of solution of CaCl2 is given as -82.8 kJ/mol.
The heat released by the dissolution of CaCl2 can be calculated using the following equation:
heat released = moles of CaCl2 x heat of solution of CaCl2
Step 3: Calculate the heat absorbed by the calorimeter.
This can be calculated using the equation:
heat absorbed = mass of water x specific heat capacity of water x change in temperature
The specific heat capacity of water is 4.18 J/g·°C.
Step 4: Set up an energy balance equation.
The heat released by the dissolution of CaCl2 is equal to the heat absorbed by the calorimeter:
heat released = heat absorbed
Finally, we can rearrange the equation and solve for the final temperature of the solution:
final temperature = (heat released / (mass of water x specific heat capacity of water)) + initial temperature
Now, we can plug in the values and solve for the final temperature.