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Latent heat of fusion and latent heat of vaporisation of a solvent are in the ratio of 1: 6 and freezing point and boiling point (in Kelvin scale) are in the ratio of 2:3. Thus, ratio of elevation in boiling point to depression in freezing point of 1 molal solution is
  • a)
    1/2
  • b)
    1/4
  • c)
    3/4
  • d)
    3/8
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Latent heat of fusion and latent heat of vaporisation of a solvent are...
(d) Kb (molal elevation constant) is related to latent heat of vaporisation (ΔHV)and boiling point (Tb)of solvent by relation.
Similarly, Kf (molal depression constant) is related to latent heat of fusion ((ΔHf) and boiling point 7, of solvent by relation.
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Latent heat of fusion and latent heat of vaporisation of a solvent are...
Latent Heat of Fusion and Latent Heat of Vaporization:
- The latent heat of fusion is the amount of heat energy required to change a substance from solid to liquid at its melting point.
- The latent heat of vaporization is the amount of heat energy required to change a substance from liquid to gas at its boiling point.

Given: Ratio of latent heat of fusion : latent heat of vaporization = 1 : 6

Freezing Point and Boiling Point:
- The freezing point is the temperature at which a substance changes from liquid to solid.
- The boiling point is the temperature at which a substance changes from liquid to gas.

Given: Ratio of freezing point : boiling point = 2 : 3

Ratio of Elevation in Boiling Point to Depression in Freezing Point:
Let's assume that the solvent is water for simplicity.

- When a solute is added to a solvent, it raises the boiling point and lowers the freezing point of the solvent. This phenomenon is known as boiling point elevation and freezing point depression.
- The extent of boiling point elevation and freezing point depression depends on the concentration of the solute in the solution.

Let's consider a 1 molal solution, which means 1 mole of solute is dissolved in 1 kg of solvent.

- Boiling point elevation is given by the equation: ΔTb = Kb * m
- ΔTb is the elevation in boiling point
- Kb is the molal boiling point elevation constant for the solvent
- m is the molality of the solution (moles of solute per kg of solvent)
- Freezing point depression is given by the equation: ΔTf = Kf * m
- ΔTf is the depression in freezing point
- Kf is the molal freezing point depression constant for the solvent

Using the Ratios:
Given:
- Ratio of latent heat of fusion : latent heat of vaporization = 1 : 6
- Ratio of freezing point : boiling point = 2 : 3

Let's consider the latent heat of fusion as Lf and the latent heat of vaporization as Lv.

- Lf : Lv = 1 : 6
- Lf/Lv = 1/6

Now, let's consider the freezing point as Tf and the boiling point as Tb.

- Tf : Tb = 2 : 3
- Tf/Tb = 2/3

Calculating the Ratio:
We need to find the ratio of elevation in boiling point to depression in freezing point for a 1 molal solution.

- ΔTb = Kb * m
- ΔTf = Kf * m

Since the molality (m) is the same for both equations, we can compare the molal boiling point elevation constant (Kb) to the molal freezing point depression constant (Kf).

- ΔTb/ΔTf = Kb/Kf

Using the given ratios:
- ΔTb/ΔTf = (Tb - 100)/(0 - Tf) = 3/2

We can rewrite this equation as:
- (Tb - 100)/(0 - Tf) = 3/2
- (Tb - 100)/(2Tf) = 3/2
- (Tb -
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Latent heat of fusion and latent heat of vaporisation of a solvent are in the ratio of 1: 6 and freezing point and boiling point (in Kelvin scale) are in the ratio of 2:3. Thus, ratio of elevation in boiling point to depression in freezing point of 1 molal solution isa)1/2b)1/4c)3/4d)3/8Correct answer is option 'D'. Can you explain this answer?
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