more thermodynamics:?

Question

The heats of solution of sodium nitrate and anhydrous copper sulfate are 21 and -66.5 kJ/mol respectively. Assuming no interaction, what mass of sodium nitrate must be dissolved with 10g of copper sulfate in order to ensure no temperature change?

Any help would be great! Thanks heaps

I'm really lost on this one, not sure where to start. The answer is meant to be 16.9g if that helps?

Answer 1

First find the number of moles of Copper Sulfate present in the sample by dividing its mass by the molar mass of Copper Sulfate.
Moles of Cu(SO4) = 10 grams / 159.62 g/mol
Moles of Cu(SO4) = .0626 moles

Now find the heat released when this number of moles is dissolved in solution by multiplying the number of moles by the molar heat of solution.
ΔH = moles of Cu(SO4) * Molar heat of solution
ΔH = .0626 moles * -66.5 kJmol
ΔH = -4.17 kJ

In order to keep the solution’s temperature constant the heat released in the dissolving process by the Copper Sulfate must be equal to the heat absorbed by the dissolving process of the Sodium Nitrate. Setting these two quantities equal and opposite allows us to solve for the number of moles of Sodium Nitrate needed to dissolve.

ΔH = +4.17 kJ = moles of NaNO3 * +21 kJ/mol
Moles of NaNO3 = +4.17 kJ / 21 kJ/mol
Moles of NaNO3 = .20 moles

Now that we know the number of moles of NaNO3 needed, all we need do now is multiply by the molar mass of Sodium Nitrate to find the number of grams of NaNO3.

Mass of NaNO3 needed = .20 moles of NaNO3 * 85 g/mol
Mass of NaNO3 = 17 grams.