Consider the dissolution of CaCl2.
CaCl2(s) Ca2+(aq) + 2 Cl-(aq) ÄH = -81.5 kJ
A 12.4 g sample of CaCl2 is dissolved in 100. g of water, with both substances at 25.0°C. Calculate the final temperature of the solution assuming no heat lost to the surroundings and assuming the solution has a specific heat capacity of 4.18 J/°C·g.
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To solve this problem, we can use the principle of conservation of energy. The heat gained by the water when dissolving the CaCl2 is equal to the heat lost by the CaCl2.
First, we need to determine the amount of heat gained by the water. We can use the following equation to calculate the heat gained (q1):
q1 = m1 * C1 * ΔT1
Where:
- q1 is the heat gained by the water
- m1 is the mass of water (100.0 g)
- C1 is the specific heat capacity of water (4.18 J/°C·g)
- ΔT1 is the change in temperature of the water
Next, we need to determine the amount of heat lost by the CaCl2. The heat lost by the CaCl2 can be calculated using the heat of dissolution (∆H) and the amount of CaCl2 dissolved:
q2 = ∆H * n
Where:
- q2 is the heat lost by the CaCl2
- ∆H is the heat of dissolution (-81.5 kJ/mol)
- n is the number of moles of CaCl2 dissolved
To find the number of moles of CaCl2 dissolved, we can use the molar mass of CaCl2 (110.98 g/mol):
n = m2 / M2
Where:
- m2 is the mass of CaCl2 (12.4 g)
- M2 is the molar mass of CaCl2 (110.98 g/mol)
Now, since the heat gained by the water is equal to the heat lost by the CaCl2 (assuming no heat lost to the surroundings), we can set q1 equal to q2 and solve for the change in temperature of the water (ΔT1):
q1 = q2
m1 * C1 * ΔT1 = ∆H * n
Rearranging the equation, we get:
ΔT1 = (∆H * n) / (m1 * C1)
Plugging in the values, we can calculate the change in temperature of the water:
ΔT1 = (-81.5 kJ/mol * (12.4 g / 110.98 g/mol)) / (100.0 g * 4.18 J/°C·g)
Finally, the final temperature of the solution can be found by subtracting the change in temperature from the initial temperature of the water (25.0°C):
Final temperature = 25.0°C - ΔT1
Calculating this value will give us the final temperature of the solution.