The enthalpy of solution of CaCl2 is -82.88kJ. If the specific heat of the solution is 4.184J/g*C and the calorimeter constant can be neglected, what will be the final temperature after 5.36g of CaCl2 is dissolved in 100.0g of H2O at 25.0C?

Question

The enthalpy of solution of CaCl2 is -82.88kJ. If the specific heat of the solution is 4.184J/g*C and the calorimeter constant can be neglected, what will be the final temperature after 5.36g of CaCl2 is dissolved in 100.0g of H2O at 25.0C?

I assume the enthalpy given is kj/mole.

Mutiply that enthalpy by the fraction of mole (5.36/molmassCaCl2), set it equal to mcDeltaT, and solve for deltaT. Use 100 g as the mass of the water, and c for water.

Answer 1

Please why are we using just the mass of water and not the total mass of the solution

Answer 2

Yes, the given enthalpy of solution (-82.88 kJ) is typically given in kJ/mol. To find the final temperature after dissolving 5.36g of CaCl2 in 100.0g of H2O at 25.0°C, you can use the equation:

ΔH = mcΔT

where:
ΔH is the enthalpy change (in J)
m is the mass of the solution (in g)
c is the specific heat of the solution (in J/g°C)
ΔT is the change in temperature (in °C)

To use this equation, you need to convert the given enthalpy of solution from kJ/mol to J/g. This can be done by dividing the enthalpy by the molar mass of CaCl2.

First, determine the molar mass of CaCl2. Calcium (Ca) has a molar mass of 40.08 g/mol, and chlorine (Cl) has a molar mass of 35.453 g/mol. Since there are two chlorine atoms in CaCl2, the molar mass of CaCl2 is:

40.08 g/mol + (2 × 35.453 g/mol) = 110.98 g/mol

Now that we have the molar mass, we can calculate the enthalpy change per gram of CaCl2:

Enthalpy change per gram of CaCl2 = (-82.88 kJ/mol) / (110.98 g/mol) ≈ -0.746 kJ/g

Next, substitute the known values into the ΔH = mcΔT equation:

-0.746 kJ/g = (5.36 g + 100.0 g) × (4.184 J/g°C) × ΔT

Note that the total mass of the solution is the sum of the mass of CaCl2 (5.36 g) and the mass of water (100.0 g).

Now, solve for ΔT:

ΔT = (-0.746 kJ/g) / [(5.36 g + 100.0 g) × (4.184 J/g°C)]
≈ -0.013°C (rounded to three decimal places)

Since the change in temperature (ΔT) is negative, it means that the final temperature will be slightly lower than the initial temperature of 25.0°C.

To find the final temperature, simply subtract the absolute value of ΔT from the initial temperature:

Final temperature = 25.0°C - |ΔT|
= 25.0°C - 0.013°C
≈ 24.987°C (rounded to three decimal places)

Therefore, the final temperature after dissolving 5.36g of CaCl2 in 100.0g of H2O at 25.0°C is approximately 24.987°C.