What is the formula for molar heat of solution?

There is no formula for the molar heat of solution.

You have to do an experiment to determine the heat of solution of a substance.

Experimentally, you dissolve a known amount of the substance in a given mass of the solvent and measure the temperature change.

Then you use the of the solution and the number of moles of the solute to calculate the molar heat of solution.

Example

What is the molar heat of ammonium nitrate if 8.00 g of NH₄NO₃ dissolved in 50.0 g of water in a coffee cup calorimeter causes the temperature to drop by 10.1 °C? Assume that the specific heat capacity of the solution is 4.18 J·°C⁻¹g⁻¹.

Solution

There are two heats involved.

heat of solution of NH₄NO₃ + heat from water = 0

##q_1+ q_2 = 0##

##n = "moles of NH"_4"NO"_3 = "8.00 g NH"_4"NO"_3 × ("1 mol NH"_4"NO"_3)/("80.0 g NH"_4"NO"_3) = "0.100 mol NH"_4"NO"_3##

##q_1 = nΔH_"soln" = "0.100 mol" × ΔH_"soln"##

##m = "mass of solution" = "50.0 g + 8.00 g" = "58.0 g"##

##q_2 = mcΔT = "58.0 g" × "4.184 J°C"⁻¹"g"⁻¹ × "(-10.1 °C)" = "-2450 J"##

##q_1 + q_2 = "0.100 mol" × ΔH_"soln" – "2450 J" = 0##

##ΔH_"soln" = "+2450 J"/"0.100 mol" = "+24 500 J/mol" = "+24.5 kJ/mol"##