Chem help!

Question

Sodium hydroxide (NaOH) has a lattice energy of -887 kJ/mol and a heat of hydration of -932 kJ/mol.

 

How much solution could be heated to boiling by the heat evolved by the dissolution of 23.5 g of NaOH? (For the solution, assume a heat capacity of 4.0 J/g⋅∘C, an initial temperature of 25.0 ∘C, a boiling point of 100.0 ∘C, and a density of 1.05 g/mL.)

Answer 1

The lattice energy for NaOH is + 887 kJ/mol. The heat of solution is the difference between the lattice energy (positive) and the heat evolved from hydration (negative).  The heat of solution for NaOH is therefore:

                      887 kJ/mol - 932 kJ/mol =  - 45 kJ/mol

 

To calculate the heat evolved by dissolving 23.5 g of NaOH, you have to convert to moles and then multiply by the heat of solution.

 

               23.5 g NaOH   |   mol NaOH     |   -45 kJ           |  10³ J      =  -2.6437 x 10⁴  J

                                    | 40.00 g NaOH |    mol  NaOH    |  kJ

 

                         -Heat lost = heat gained                

 

The heat required to heat a mass of solution to boiling = mass of solution (4.184 J/g°C) (100°C - 25°C)

 

                      2.6437 x 10⁴ J  = mass (4.184 J/g°C)(75°C)

 

                         mass of solution =     2.6437 x 104 J          =   84.25 g of solution = 23.5 g NaOH in 60.75 g of 

                                                      4.184 J/g°C) (75°C)               water

 

            Converting this to volume,  84.25 g solution  |  mL        =   80.2 mL

                                                                           | 1.05 g

 

Please note that this does not include boiling the 60.75 g of water which would require an additional 40.65 kJ/mol or 

 

   40.65 kJ   | 60.75 g water  | mol H₂O            =    137 kJ   heat of vaporization

        mol     |                      |  18.015 g H₂O