To calculate the amount of heat released during the dissolution of calcium chloride (CaCl₂) in water, we can use the formula:

$q = m \cdot c \cdot \Delta T$

where:

• $q$ is the heat released (in joules),
• $m$ is the mass of the solution (in grams),
• $c$ is the specific heat of the solution (in J/(g°C)),
• $\Delta T$ is the change in temperature (in °C).

Step 1: Determine the mass of the solution

The mass of the solution is the sum of the mass of CaCl₂ and the mass of water:

$m_{\text{solution}} = m_{\text{CaCl2}} + m_{\text{water}} = 6.52 \, \text{g} + 67.5 \, \text{g} = 74.02 \, \text{g}$

Step 2: Determine the temperature change ($\Delta T$)

The temperature change is the final temperature minus the initial temperature:

$\Delta T = T_{\text{final}} - T_{\text{initial}} = 48.8 \, \text{°C} - 20.0 \, \text{°C} = 28.8 \, \text{°C}$

Step 3: Use the formula to calculate the heat released

Now, we can plug all the known values into the heat equation:

$q = (74.02 \, \text{g}) \cdot (4.184 \, \text{J/g°C}) \cdot (28.8 \, \text{°C})$

$q = 8749.57 \, \text{J}$

Step 4: Convert joules to kilojoules

Since the question asks for the answer in kJ, we convert from joules to kilojoules:

$q = \frac{8749.57 \, \text{J}}{1000} = 8.75 \, \text{kJ}$

Final Answer:

The amount of heat released is 8.75 kJ.

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Would you like further details or have any questions? Here are some related questions:

1. How would the heat released change if the specific heat of the solution was different?
2. How can the enthalpy change of dissolution be calculated from this heat value?
3. What assumptions are made in calculating the heat released in this problem?
4. How would the heat released change if the mass of the water were increased?
5. How do you convert heat from joules to calories or other energy units?

Tip: Always remember to use the total mass of the solution, not just the solvent, when calculating heat changes.