What is the equation for boiling point elevation to concentration of solution?

A liquid boils at the temperature at which its vapor pressure equals atmospheric pressure.

The presence of a solute lowers the vapor pressure of the solution at each temperature, making it necessary to heat the solution to a higher temperature to boil the solution.

In dilute solutions with a nonvolatile solute, the boiling point elevation is proportional to the molality of the solute particles:
ΔTb = Kbm
ΔTb = the amount by which the boiling point is raised
m = molality (moles solute particles per kg of solution)
Kb = molal boiling-point elevation constant (solvent dependent)

Boiling Point of solution = normal boiling point of solvent + ΔTb

A solute lowers the freezing point of a solvent.

In dilute solutions, the freezing point depression is proportional to the molality of the solute particles:
ΔTf = -Kfm
ΔTf = the amount by which the freezing point is lowered
m = molality (moles solute particles per kg of solution)
Kf = molal freezing-point depression constant (solvent dependent)

Freezing Point of solution = normal freezing point of solvent + ΔTf

The colligative properties of a solution depend on the relative numbers (concentration) of solute and solvent particles, they do not depend on the nature of the particles. Colligative properties change in proportion to the concentration of the solute particles. We distinguish between four colligative properties: vapor pressure lowering, freezing point depression, boiling point elevation, and osmotic pressure. All four colligative properties fit the relationship

property = solute concentration x constant

Property	Symbol	Solute Concentration	Proportionality Constant
Vapor pressure	\(\Delta P\)	mole fraction	Po (vapor pressure of pure solvent)
Boiling Point	\(\Delta{T_b}\)	molal	Kb (boiling point constant)
Freezing Point	\(\Delta{T_f}\)	molal	Kf (freezing point constant)
Osmotic Pressure	\(P\)	molar	RT

The determination of colligative properties allows us to determine the concentration of a solution and calculate molar masses of solutes

The boiling points of solutions are all higher than that of the pure solvent. Difference between the boiling points of the pure solvent and the solution is proportional to the concentration of the solute particles:

\[\Delta{T_b} = T_b (solution) - T_b (solvent) = K_b \times m\]

where \(\Delta{T_b}\) is the boiling point elevation, \(K_b\) is the boiling point elevation constant, and m is the molality (mol/kg solvent) of the solute.

Exercise

A solution is prepared when 1.20 g of a compound is dissolved in 20.0 g of benzene. The boiling point of the solution is 80.94 oC.

What is the boiling point of pure benzene?
What is the molality of the solution?
What is the molar mass of the compound?

Answer

Questions

Explain how a non-volatile solute lowers the vapor pressure, raises the boiling point and lowers the freezing point of a solvent.
Describe the process of osmosis and reverse osmosis
Explain why ocean water is not fit for consumption by humans

Answer the following in one or two sentences.

Write the equation relating boiling point elevation to the concentration of the solution.

The boiling point elevation is directly proportional to the molality of the solution. Thus,

Δ Tb ∝ m

∴ Δ Tb ∝ Kb m

where, m is the molality of solution. The proportionality constant Kb is called boiling point elevation constant or molal elevation constant or ebullioscopic constant.

Concept: Relative Molecular Mass of Non-volatile Substances - Boiling Point Elevation

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