Respuesta :
The solution of ethanol will have the greatest increase in boiling point.
The formula for boiling point elevation is:
ΔTb = Kb · bB
where
ΔTb = 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
ΔHv = 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.
The formula for boiling point elevation is:
ΔTb = Kb · bB
where
ΔTb = 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
ΔHv = 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.
Answer: solution b
Explanation: Formula used for Elevation in boiling point for non ionic solutes,
[tex]\Delta T_b=k_b\times m[/tex]
where,
[tex]T_b[/tex] = change in boiling point
[tex]k_b[/tex] = 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.
[tex]k_b{water}=0.512^0Ckg/mol[/tex] and [tex]k_b{ethanol}=1.22^0Ckg/mol[/tex]
Thus solution b with higher value of [tex]k_b[/tex] as solvent has the greatest increase in its boiling point (relative to the pure solvent)
