Final answer:
To find the final temperature when 15.0 g of CaCl₂ is dissolved in 175.0 g of water, calculate the moles of CaCl₂, use the enthalpy change to determine the heat released, and apply the specific heat capacity formula to find the temperature change.
Step-by-step explanation:
To determine the final temperature of the solution when 15.0 g of CaCl₂ is dissolved, we’ll need to use the energy released from the dissolution process and the concept of specific heat capacity. The dissolution of calcium chloride is exothermic, releasing heat to the surroundings, in this case, the water in which it is being dissolved.
First, we need to calculate the moles of CaCl₂ in 15.0 g using the molar mass of CaCl₂ (110.98 g/mol):
Moles of CaCl₂ = 15.0 g / 110.98 g/mol
Next, we can determine the amount of heat (q) released using the enthalpy change (ΔH) for the reaction and the number of moles calculated:
q = moles of CaCl₂ × ΔH
Since the specific heat capacity of the solution (Cs) is 4.184 J/g°C, and we know the mass of the solution (which is the mass of the water plus the mass of CaCl₂), we can use the formula:
q = m×Cs×ΔT
Where m is the total mass of the solution and ΔT is the change in temperature. We can use this formula to find ΔT.
By substituting the calculated heat (q) into the formula and rearranging for ΔT, we can find the change in temperature:
ΔT = q / (m×Cs)
Finally, add ΔT to the initial temperature to find the final temperature:
Final temperature = Initial temperature + ΔT