Question

Calculate the heat of crystallization, in kilojoules per mole, when 50.0 grams of sodium hydroxide (NaOH) is dissolved in 500.0 grams of water at 25⁰C and then cooled to 5⁰C, assuming that all the heat evolved during the process is transferred to the solution. The heat capacity of water is 4.18 J/gK, and the enthalpy of formation of NaOH is -425 kJ/mol.

Answer 1

To calculate the heat of crystallization, we first need to find the heat evolved during the process of dissolving NaOH in water and cooling the solution.1. Calculate the moles of NaOH:NaOH has a molar mass of 22.99 g/mol  Na  + 15.999 g/mol  O  + 1.007 g/mol  H  = 39.996 g/molmoles of NaOH =  50.0 g  /  39.996 g/mol  = 1.250 mol2. Calculate the heat evolved during the dissolution of NaOH:The enthalpy of formation of NaOH is -425 kJ/mol, which means that 425 kJ of heat is released per mole of NaOH when it is formed.Heat evolved during dissolution =  1.250 mol  *  -425 kJ/mol  = -531.25 kJ3. Calculate the heat absorbed by the water during cooling:The temperature change of the water is from 25C to 5C, which is a decrease of 20C.The total mass of the solution is 50.0 g  NaOH  + 500.0 g  water  = 550.0 gHeat absorbed by the water =  mass of solution  *  heat capacity of water  *  change in temperature Heat absorbed by the water =  550.0 g  *  4.18 J/gK  *  20 K  = 45980 J = 45.98 kJ4. Calculate the heat of crystallization:Since all the heat evolved during the process is transferred to the solution, the heat of crystallization can be calculated as the difference between the heat evolved during dissolution and the heat absorbed by the water.Heat of crystallization = Heat evolved during dissolution - Heat absorbed by the waterHeat of crystallization =  -531.25 kJ  -  45.98 kJ  = -577.23 kJ5. Calculate the heat of crystallization per mole of NaOH:Heat of crystallization per mole =  Heat of crystallization  /  moles of NaOH Heat of crystallization per mole =  -577.23 kJ  /  1.250 mol  = -461.78 kJ/molThe heat of crystallization of NaOH is -461.78 kJ/mol.