Sure! Let's walk through the problem step by step to find the heat change for the solution.
### Given Data:
1. Mass of the solution (m): \( 41.3 \, \text{g} \)
2. Specific heat capacity (c): \( 4.04 \, \text{J/g}^\circ\text{C} \)
3. Initial Temperature (T_initial): \( 21.2^\circ\text{C} \)
4. Final Temperature (T_final): \( 76.6^\circ\text{C} \)
### Formula for Heat Change:
The heat change for the solution can be calculated using the formula:
[tex]\[ q_{\text{soln}} = m \times c \times (T_f - T_i) \][/tex]
### Step-by-Step Solution:
1. Determine the temperature change (ΔT):
[tex]\[ ΔT = T_{\text{final}} - T_{\text{initial}} \][/tex]
[tex]\[ ΔT = 76.6^\circ\text{C} - 21.2^\circ\text{C} \][/tex]
[tex]\[ ΔT = 55.4^\circ\text{C} \][/tex]
2. Substitute the values into the formula:
[tex]\[ q_{\text{soln}} = 41.3 \, \text{g} \times 4.04 \, \text{J/g}^\circ\text{C} \times 55.4^\circ\text{C} \][/tex]
3. Calculate the heat change (q_soln):
[tex]\[ q_{\text{soln}} = 41.3 \times 4.04 \times 55.4 \][/tex]
4. The multiplication yields:
[tex]\[ q_{\text{soln}} = 9243.600799999998 \, \text{J} \][/tex]
### Final Result:
The heat change for the solution is [tex]\( 9243.600799999998 \, \text{J} \)[/tex].
