Sure, let's solve this step-by-step.
We need to determine the heat of solution for the dissolving process, given the initial and final temperatures of the solution, along with the masses and specific heat capacity. We'll follow these steps:
1. Calculate the total mass of the solution:
The mass of calcium hydroxide, \( \text{Ca(OH)}_2 \), is \( 7.41 \, \text{g} \).
The mass of water is \( 50.0 \, \text{g} \).
Therefore, the total mass of the solution \( m_{\text{soln}} \) is:
[tex]\[
m_{\text{soln}} = 7.41 \, \text{g} + 50.0 \, \text{g} = 57.41 \, \text{g}
\][/tex]
2. Determine the change in temperature, \( \Delta T \):
The initial temperature \( T_i \) is \( 21.50^\circ \text{C} \).
The final temperature \( T_f \) is \( 28.25^\circ \text{C} \).
So, the change in temperature \( \Delta T \) is:
[tex]\[
\Delta T = T_f - T_i = 28.25^\circ \text{C} - 21.50^\circ \text{C} = 6.75^\circ \text{C}
\][/tex]
3. Apply the formula for heat of the solution (\( q_{\text{soln}} \)):
Use the equation:
[tex]\[
q_{\text{soln}} = m_{\text{soln}} \times c_{\text{soln}} \times \Delta T
\][/tex]
where:
- \( m_{\text{soln}} = 57.41 \, \text{g} \)
- \( c_{\text{soln}} = 4.18 \, \text{J/g}^\circ \text{C} \) (specific heat capacity of the solution)
- \( \Delta T = 6.75^\circ \text{C} \)
Therefore, the heat of the solution is:
[tex]\[
q_{\text{soln}} = 57.41 \, \text{g} \times 4.18 \, \text{J/g}^\circ \text{C} \times 6.75^\circ \text{C}
\][/tex]
4. Calculate \( q_{\text{soln}} \):
[tex]\[
q_{\text{soln}} = 57.41 \times 4.18 \times 6.75 = 1619.82315 \, \text{J}
\][/tex]
So, the heat of the solution for the dissolving process is [tex]\( 1619.82315 \, \text{J} \)[/tex].
