The molar heat of solution of a substance is found to be +35.34 kJ/mol. The addition of 0.20 moles of this substance to 1.5 L water initially at 55. °C results in a temperature decrease. Assume the specific heat of the resulting solution to be equal to that of pure water. Find the final temperature of the solution.

To find the final temperature of the solution, we can use the principle of heat transfer. The heat gained or lost by a substance can be calculated using the equation:

q = m * c * ΔT

Where:
q = heat gained or lost (in joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g·°C)
ΔT = change in temperature (in °C)

In this case, we are given the molar heat of solution (+35.34 kJ/mol), the moles of the substance added (0.20 mol), and the initial temperature of the water (55. °C). However, we need to convert the molar heat of solution to heat per gram of the substance:

ΔH = q / moles

Given:
Molar heat of solution (ΔH) = +35.34 kJ/mol
Moles of substance (moles) = 0.20 mol

We can calculate the heat gained or lost by the substance by multiplying the molar heat of solution by the number of moles:
q = ΔH * moles

Converting kJ to J:
q = (ΔH * moles) * 1000

Now, we can calculate the change in temperature using the equation:
q = m * c * ΔT

Since the specific heat capacity of pure water is considered to be equal to that of the resulting solution, we can assume c = 4.18 J/g·°C.

Rearranging the equation, we can solve for ΔT:
ΔT = q / (m * c)

Given:
q = (ΔH * moles) * 1000
m = mass of water = 1.5 L = 1500 g
c = 4.18 J/g·°C

Substituting the values into the equation, we get:
ΔT = ((ΔH * moles) * 1000) / (m * c)

Finally, we can calculate the final temperature of the solution by subtracting ΔT from the initial temperature of the water:

Final temperature = Initial temperature - ΔT

Substituting the values we have, we can find the final temperature of the solution.