Question

Solution a is a 1.0 m solution with a nonionic solute and water as the solvent. solution b is a 1.0 m solution with the same nonionic solute and ethanol as the solvent. which solution has the greatest increase in its boiling point (relative to the pure solvent)?

Answer 1

Answer: solution b

Explanation: Formula used for Elevation in boiling point for non ionic solutes,

$\Delta T_b=k_b\times m$

where,

$T_b$ = change in boiling point

$k_b$ = boiling point constant

m = molality

As the molality is same for solution a and b, the change in boiling point depends on the value of boiling point constants of water and ethanol.

$k_b{water}=0.512^0Ckg/mol$ and $k_b{ethanol}=1.22^0Ckg/mol$

Thus solution b with higher value of $k_b$ as solvent has the greatest increase in its boiling point (relative to the pure solvent)

Answer 2

The solution of ethanol will have the greatest increase in boiling point.
   The formula for boiling point elevation is:
 Î”Tb = Kb · bB
 where
 Î”Tb = boiling point elevation
 Kb = ebullioscopic constant for the solvent
 bB = molarity of the solution
   Since in the solute is nonionic, we don't have to worry about the molecules of the solute breaking up into multiple ions, thereby increasing the effective molarity of the solution. So which ever solvent has the highest ebullioscopic constant, will have the greatest increase in boiling point. This constant can be calculated by the equation:
 Kb = RTb^2M/ΔHv
 where
 R = Ideal gas constant
 Tb = boiling point of pure solvent
 M = Molar mass of solvent
 Î”Hv = heat of vaporization per mole of solvent
   For our purposes, we can ignore the idea gas constant, and instead look at only the boiling point, molar mass, and heat of vaporization. Then calculate Tb^2M/ΔHv So let's do so:
 (Note: Not bothering to be precise in molar mass. If the end result is close, then I'll bother. Otherwise, just using nice round numbers).
   Water
 Boiling point: 373.15 K
 Molar mass: 18 g/mol
 heat of vaporization: 40660 J/mol
 Tb^2M/ΔHv: 61.64
   Ethanol
 Boiling point: 351.52 K
 Molar mass: 46 g/mol
 heat of vaporization: 38600 J/mol
 Tb^2M/ΔHv: 147.26
   The value of Tb^2M/ΔHv is significantly greater for ethanol than it is for water (by more than 2 to 1), so it will have the greatest increase in boiling point.