Consider the dissolution of CaCl2.

CaCl2(s) Ca2+(aq) + 2 Cl-(aq) ÄH = -81.5 kJ
A 10.4-g sample of CaCl2 is dissolved in 102 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.

Well, it looks like we have CaCl2, the infamous calcium chloride, deciding to dissolve and cause some trouble. But don't you worry, I'm here to help!

To tackle this problem, we can use the law of conservation of energy. Since we're assuming no heat is lost to the surroundings, the heat released during dissolution will be absorbed by the water, causing its temperature to increase.

First, let's calculate the heat released during the dissolution using the given enthalpy change (ÄH) and the amount of CaCl2:

Heat released = mass of CaCl2 * enthalpy change
Heat released = 10.4 g * (-81.5 kJ/mol) / molar mass of CaCl2

Now, let's determine the molar mass of CaCl2:
Ca = 40.08 g/mol
Cl2 = 2 x (35.45 g/mol)
Molar mass of CaCl2 = Ca + Cl2

Now we can calculate the heat released:
Heat released = 10.4 g * (-81.5 kJ/mol) / (40.08 g/mol + 2 x 35.45 g/mol)

Alright, now that we know the amount of heat released, we can calculate the temperature change using the equation:

Heat released = mass of water * specific heat capacity * temperature change

Plugging in the known values, we can solve for the temperature change and then find the final temperature:

Temperature change = Heat released / (mass of water * specific heat capacity)
Final temperature = Initial temperature + Temperature change

So, put your clown nose on because we're about to start calculating!

To calculate the final temperature of the solution, we can use the equation:

q(solution) + q(water) = 0

where q(solution) is the heat gained by the solution and q(water) is the heat lost by the water.

First, let's calculate the heat gained by the solution:

q(solution) = mass(solution) * specific heat capacity(solution) * ΔT(solution)

mass(solution) = mass(CaCl2) + mass(water)
mass(CaCl2) = 10.4 g
mass(water) = 102 g

mass(solution) = 10.4 g + 102 g = 112.4 g

ΔT(solution) = final temperature(solution) - initial temperature(solution)
Since both substances are at 25.0°C, ΔT(solution) = Tf - 25.0°C

Now, let's calculate the heat lost by the water:

q(water) = mass(water) * specific heat capacity(water) * ΔT(water)

mass(water) = 102 g
specific heat capacity(water) = 4.18 J/°C · g
ΔT(water) = 25.0°C - Tf

Since there is no heat lost to the surroundings, q(solution) + q(water) = 0:

mass(solution) * specific heat capacity(solution) * ΔT(solution) + mass(water) * specific heat capacity(water) * ΔT(water) = 0

Substituting the known values into the equation:

112.4 g * 4.18 J/°C · g * (final temperature(solution) - 25.0°C) + 102 g * 4.18 J/°C · g * (25.0°C - final temperature(solution)) = 0

Now, let's solve the equation for the final temperature of the solution.

To calculate the final temperature of the solution, we can use the principle of conservation of energy. We know that the dissolution of CaCl2 is an exothermic process, as indicated by the negative enthalpy change (ΔH) of -81.5 kJ. This means that energy is released during the dissolution process, resulting in an increase in temperature.

First, let's calculate the amount of heat released during the dissolution of CaCl2. We can use the equation:

q = m × ΔH

where q is the amount of heat released, m is the mass of CaCl2, and ΔH is the enthalpy change.

Given:
Mass of CaCl2 (m) = 10.4 g
Enthalpy change (ΔH) = -81.5 kJ

Convert the mass of CaCl2 to kilograms:

m = 10.4 g / 1000 = 0.0104 kg

Convert the enthalpy change to joules:

ΔH = -81.5 kJ × 1000 = -81500 J

Substitute the values into the equation:

q = (0.0104 kg) × (-81500 J) = -846 J

The negative sign indicates that energy is released.

Next, we can use the principle of conservation of energy to calculate the final temperature of the solution. The equation for heat transfer is:

q = m × c × ΔT

where q is the amount of heat transferred, m is the mass of the solution, c is the specific heat capacity of the solution, and ΔT is the change in temperature.

Given:
Mass of solution (m) = 102 g
Specific heat capacity of water (c) = 4.18 J/°C · g

Convert the mass of the solution to kilograms:

m = 102 g / 1000 = 0.102 kg

Substitute the values into the equation:

-846 J = (0.102 kg) × (4.18 J/°C · g) × ΔT

Solve for ΔT:

ΔT = -846 J / (0.102 kg × 4.18 J/°C · g)

ΔT = -196.79 °C

The negative sign indicates that the temperature of the solution decreases by 196.79 °C.

To find the final temperature of the solution, we can subtract the change in temperature from the initial temperature of 25.0°C:

Final temperature = 25.0°C - 196.79°C = -171.79°C

Therefore, the final temperature of the solution, assuming no heat lost to the surroundings, is approximately -171.79°C.

delta H for 10.4 g CaCl2 =

81.5 kJ/mol x (10.4/110.98) = about 8 kJ but you need to do it more accurtely.
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
8000J = 102g x 4.18 x (Tfinal-25). Solve for Tfinal.