Final answer:
To determine the final temperature of the solution, calculate the number of moles of solute, use the heat of solution to find the total heat change, and then calculate the change in temperature for the water. Using this change in temperature, add it to the initial temperature of the water to find the final temperature in degrees Celsius.
Step-by-step explanation:
To calculate the final temperature of the solution after the soluble solid is added to water, we must first determine the number of moles present and then the heat absorbed or released during the dissolution process.
The molar mass of the soluble solid is 55.90 g/mol, and the mass given is 122.8 g. Hence, the number of moles is calculated as:
Number of moles = mass / molar mass = 122.8 g / 55.90 g/mol = 2.197 moles.
The enthalpy change of solution, Hsol, is -51.50 kJ/mol. The total heat (q) involved can be calculated using the equation:
q = moles × Hsol = 2.197 moles x -51.50 kJ/mol = -113.1465 kJ.
To find the final temperature change (ΔT), we calculate the heat gained by the water using its mass (density × volume), the specific heat capacity (C), and the temperature change, as shown in the formula:
q = mass × specific heat capacity × ΔT.
Given the density of water is 1.000 g/mL, the mass of water is:
Mass of water = density × volume = 1.000 g/mL × 634.0 mL = 634.0 g.
The heat absorbed by the water is equal to the heat released by the solid, but with the opposite sign:
ΔT = -q / (mass × specific heat capacity) = 113146.5 J / (634.0 g × 4.184 J/g°C).
Calculating this gives us the temperature change. Adding it to the initial temperature will provide us with the final temperature:
Final temperature = initial temperature + ΔT.
After completing all calculations with the correct significant figures and unit conversion, the final temperature can be obtained in degrees Celsius.