Final answer:
The final temperature of the aqueous solution is approximately 33.53°C.
Step-by-step explanation:
To calculate the final temperature of the aqueous solution, we can use the equation for heat transfer, q = m * c * ΔT, where q is the heat transferred, m is the mass of the solution, c is the specific heat capacity of the solution, and ΔT is the change in temperature.
First, we need to calculate the mass of the solution. The density of water is given as 1.00 g/mL, so the total volume of the solution is 400.0 mL. Using the density, we can calculate the mass of the solution as 400.0 g.
Next, we need to calculate the change in temperature, ΔT. The initial temperature of the mixture is given as 22.5°C. Since the reaction is exothermic, the change in temperature is negative, so ΔT = final temperature - initial temperature = -T.
Substituting the values into the equation, we have q = (400.0 g) * (4.184 J/gK) * (-T). The heat transfer, q, is equal to the change in enthalpy, ΔH, of the reaction, which is given as -56.07 kJ. We can convert this to joules by multiplying by 1000, so ΔH = -56.07 kJ * 1000 = -56070 J.
Setting q = ΔH, we can solve for T. Rearranging the equation, we have T = (56070 J) / (400.0 g * 4.184 J/gK). Calculating this, we find that T ≈ -33.53 K. Since temperature cannot be negative, the final temperature of the aqueous solution is approximately 33.53°C.