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A solution of a non-volatile solute in water freezes at - 0.30° C. The vapour pressure o f pure w ater at 298 K is 23.51 torr. For water, Kf = 1.86 K mol-1 kg. Thus, vapour pressure of the solution (in torr)
  • a)
    23.44
  • b)
    23.00
  • c)
    20.41
  • d)
    22.47
Correct answer is option 'A'. Can you explain this answer?
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A solution of a non-volatile solute in water freezes at - 0.30° C...
(a) For    mole of non-volatile solute in w2 g solvent, depression in freezing point is
By Raoult’s law,
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Most Upvoted Answer
A solution of a non-volatile solute in water freezes at - 0.30° C...
Given data:
Freezing point depression, ∆Tf = Tfpure solvent - Tfsolution = 0 - (-0.30) = 0.30°C
Kf = 1.86 K mol-1 kg
Vapour pressure of pure water at 298 K, P° = 23.51 torr

To find: Vapour pressure of the solution (Psolution)

Solution:
We can use the formula for the depression in vapour pressure to calculate the vapour pressure of the solution.

∆P = Psolution - P° = Kf × molality

where molality = moles of solute / mass of solvent in kg

We can assume that the mass of the solvent is equal to the mass of the solution since the solute is non-volatile and does not contribute significantly to the mass.

Let's assume that we have 1 kg of the solution.
Then, the molality of the solution, b = moles of solute / mass of solvent in kg = moles of solute / 1 kg
Since we are not given the moles of solute, we cannot calculate the molality directly.
However, we can use the freezing point depression to calculate the moles of solute.

∆Tf = Kf × b × i
where i is the van't Hoff factor, which is equal to 1 for non-electrolytes.

Substituting the given values, we get:

0.30 = 1.86 × b × 1
b = 0.30 / 1.86 = 0.1613 mol/kg

Now, we can calculate the vapour pressure of the solution:

∆P = Kf × b
Psolution - P° = 1.86 × 0.1613
Psolution = 23.44 torr

Therefore, the vapour pressure of the solution is 23.44 torr, which is closest to option A (23.44).
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Direction: Read the passage given below and answer the following questions:Boiling point or freezing point of liquid solution would be affected by the dissolved solids in the liquid phase. A soluble solid in solution has the effect of raising its boiling point and depressing its freezing point. The addition of non-volatile substances to a solvent decreases the vapour pressure and the added solute particles affect the formation of pure solvent crystals.According to many researches the decrease in freezing point directly correlated to the concentration of solutes dissolved in the solvent. This phenomenon is expressed as freezing point depression and it is useful for several applications such as freeze concentration of liquid food and to find the molar mass of an unknown solute in the solution. Freeze concentration is a high quality liquid food concentration method where water is removed by forming ice crystals. This is done by cooling the liquid food below the freezing point of the solution. The freezing point depression is referred as a colligative property and it is proportional to the molar concentration of the solution (m), along with vapour pressure lowering, boiling point elevation, and osmotic pressure. These are physical characteristics of solutions that depend only on the identity of the solvent and the concentration of the solute. The characters are not depending on the solute’s identity.Q.Colligative properties are

A solution of a non-volatile solute in water freezes at - 0.30° C. The vapour pressure o f pure w ater at 298 K is 23.51 torr. For water, Kf = 1.86 K mol-1 kg. Thus, vapour pressure of the solution (in torr)a)23.44b)23.00c)20.41d)22.47Correct answer is option 'A'. Can you explain this answer?
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