Final answer:
To find the final solution temperature, we need to calculate the heat exchanged by the reaction and the heat exchanged by the solution and set them equal to each other. By plugging in the given values and solving the equation, we find that the final solution temperature will be 24.77 °C.
Step-by-step explanation:
To find the final solution temperature, we can use the principle that the heat given off by the reaction is equal to that taken in by the solution. We need to calculate the heat exchanged by the reaction and the heat exchanged by the solution and set them equal to each other.
First, we calculate the heat exchanged by the reaction using the equation:
q_reaction = C_reaction * ΔT_reaction
where C_reaction is the heat capacity of the reaction solution and ΔT_reaction is the change in temperature of the reaction.
Next, we calculate the heat exchanged by the solution using the equation:
q_solution = m_solution * C_solution * ΔT_solution
where m_solution is the mass of the solution, C_solution is the specific heat of the solution, and ΔT_solution is the change in temperature of the solution.
Now we can set the two heat exchanges equal to each other and solve for the final solution temperature:
q_reaction = q_solution
C_reaction * ΔT_reaction = m_solution * C_solution * ΔT_solution
Plugging in the given values:
C_reaction = C_solution = 3.98 Jg⁻¹°C⁻¹
m_solution = (50.00 mL of NaOH * 1.02 g/mL) + (25.00 mL of HCl * 1.02 g/mL) = 76.50 g
ΔT_reaction = (28.9 °C - 24.66 °C) = 4.24 °C
ΔT_solution = ?
Now we can solve for ΔT_solution:
3.98 Jg⁻¹°C⁻¹ * 4.24 °C = 76.50 g * 3.98 Jg⁻¹°C⁻¹ * ΔT_solution
ΔT_solution = (3.98 Jg⁻¹°C⁻¹ * 4.24 °C) / (76.50 g * 3.98 Jg⁻¹°C⁻¹) = 0.1107 °C
Finally, we calculate the final solution temperature:
Final Temperature = 24.66 °C + 0.1107 °C = 24.77 °C