what is the molality

Question

what is the molality of an aqueous solution of calcium nitrate that has a boiling point of 102.5 C

Answer 1

Boiling point elevation problems usually involve the addition of relatively nonvolatile molecular compounds to the solvent.  In this case, calcium nitrate is ionic.  This compound is expected to cause more boiling point elevation than a corresponding amount of molecular compound because each mole of the ionic compound yields three moles of ions.  In concentrated solutions of ionic compounds, many of the ions tend to associate into ion-pairs.  So in this case, the boiling point of the water would be something less than expected from the 3 to 1 ratio of ions to parent compound.  In any case one could still give a minimum value for the molality of the calcium nitrate solution:

 

The k_b for water is +0.513 degrees C / m

 

boiling point elevation = 2.5 deg C = 0.513 deg C/ m  (3 moles of ions/mole of formula unit)(m_Ca(NO3)2)

 

m_Ca(NO3)2 = 1.62 mol/kg solvent

Answer 2

The boiling point elevation of water is 0.512 °C / molal.

 

Since the boiling point of the solution has been elevated by 2.5 °C, the molality of the solution is 2.5 / 0.512 = 4.88 M