Final answer:
The final temperature of the solution after dissolving 11.0 g of CaCl2 in 118 g of water is approximately 40.38°C. This is calculated by considering the heat released from the dissolution process and applying the formula to find the change in temperature.
Step-by-step explanation:
To calculate the final temperature of the solution after dissolving 11.0 g of CaCl2 in 118 g of water, assuming that the dissolution is an exothermic process with ΔH = -81.5 kJ per mole and that no heat is lost to the surroundings, we need to use the formula q = mcΔT, where q is the heat absorbed or released, m is the mass of the solution, c is the specific heat capacity, and ΔT is the change in temperature.
First, find the number of moles of CaCl2 dissolved using its molar mass (approximately 111 g/mol). The mass of 11.0 g corresponds to roughly 0.099 moles. The total heat released when this amount dissolves is 0.099 moles × 81.5 kJ/mol = 8.069 kJ or 8069 J.
Then, using the specific heat capacity of the solution (4.18 J/°C · g), we can find the change in temperature with the formula q = mcΔT rearranged to ΔT = q / (mc). Assume the total mass of the solution is the mass of the water plus the mass of CaCl2, which is 129 g. Plugging in the values, ΔT = 8069 J / (129 g × 4.18 J/°C · g) which equals approximately 15.38°C. This rise is added to the initial temperature of 25.0°C to get the final temperature, which is approximately 40.38°C.