Question

# Potassium nitrate has a lattice energy of -163.8 kcal/mol and a heat of hydration of -155.5...

Potassium nitrate has a lattice energy of -163.8 kcal/mol and a heat of hydration of -155.5 kcal/mol. How much potassium nitrate has to dissolve in water to absorb 1.00x102 kJ of heat?

Given :

Lattice energy of Potassium nitrate is -163.8 kCal/mol

Heat of hydration = -155.5 kcal /mol

Heat absorption = 1.00 E2 kJ

Heat of solution = Lattice energy + heat of hydration.

= -163.8 kcal/mol + (-155.5 kcal/mol)

=-319.3 kcal/mol

Lets convert kcal /mol to kJ/mol

1 kcal = 4.184 kJ

Heat of solution in kJ/mol

=(-319.3 kcal /mol ) * ( 4.184 kJ/kcal )

= -1335.9

= -1336. kJ/mol

Now for to dissolve 1 mol potassium nitrate there needs 1336 kJ heat

Now heat absorbed = 1.00 E 2 KJ

Amount of potassium nitrate required to absorb 1.00 E 2 kJ heat

= 1.00 E 2 kJ * 1 mol / 1336. kJ

= 0.075 mol potassium nitrate

Lets convert moles of potassium nitrate to mass

= 0.075 mol * molar mass

Molar mass of potassium nitrate = 101.1032 g/mol

Mass of potassium nitrate in g = 0.075 mol * 101.1032 g/mol

= 7.57 X 100   g potassium nitrate.

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