Question

Which of the following statements is false?
A) Two different solutions of sucrose of the same molality prepared in different solvents will have the same depression in the freezing point.
B) The osmotic pressure of a solution is given by the equation $\text{ }\\!\\!\pi\\!\\!\text{ = CRT }$ (where C is the molarity of the solution)
C) Decreasing order of osmotic pressure for 0.01M aqueous solutions of barium chloride, potassium chloride, acetic acid and sucrose is $\text{ BaC}{{\text{l}}_{\text{2}}}\text{ }>\text{ KCl }>\text{ C}{{\text{H}}_{\text{3}}}\text{COOH }>\text{ Sucrose }$
D) According to Raoult’s law the vapour pressure exerted by a volatile component of a solution is directly proportional to its mole fraction in the solution

Answer 1

colligative properties are those which depend entirely upon the number of particles of the solute dissolved in a known volume of a given solvent. The colligative properties depend on the nature of solvent. The colligative properties can thus be rightly regarded as the properties of the solvent in a given solution. The depressing in the freezing is stated as follows,
$\text{ }\Delta {{\text{T}}_{f}}={{\text{K}}_{\text{f}}}\times \text{m }$

Complete step by step answer:
We are interested in determining the false statement.
A) Freezing point is a temperature at which the lowering of the freezing point is observed on the addition of solute. Depression in the freezing point is a colligative property. The depression in the freezing point is $\text{ }\Delta {{\text{T}}_{f}}\text{ }$ directly proportional to the molality of the solution. The depression in freezing point is mathematically stated as follows,
$\text{ }\Delta {{\text{T}}_{f}}={{\text{K}}_{\text{f}}}\times \text{m =}{{\text{K}}_{\text{f}}}\times \dfrac{{{\text{w}}_{\text{2}}}}{{{\text{M}}_{\text{2}}}{{\text{w}}_{\text{1}}}}\text{ }$
Where ${{\text{K}}_{\text{f}}}$ is a cryoscopic constant or molal freezing point depression constant, $\text{ }{{\text{w}}_{\text{2}}}\text{ }$ is a mass of solute in Kg,${{\text{M}}_{\text{2}}}$ is a molar mass of solute, and $\text{ }{{\text{w}}_{1}}\text{ }$ is the weight of solvent. Thus depression in the freezing point is related to the weight of the solvent. The cryoscopic constant depends on the solvent taken.
Thus two different solutions of the same molality in the different solvent will not have the same depression in freezing point.
B) Osmotic pressure is the difference in the pressure between the pure liquid and the solvent when there is an equilibrium between the solute and the solvent particles across the semipermeable membrane. Osmotic pressure is a colligative property.it is proportional to the concentration of solute C in the solution. It is written as follows,
$\text{ }\\!\\!\pi\\!\\!\text{ = CRT }$
Where C is the molarity of a solution, R is gas constant and T is the absolute temperature.
C) The osmotic pressure depends on the molar mass of the non-volatile solute. It is represented as follows,
$\text{ }\\!\\!\pi\\!\\!\text{ = }\dfrac{{{\text{w}}_{\text{2}}}}{{{\text{M}}_{\text{2}}}\text{V}}\text{RT }$
The decreasing order of the osmotic pressure for $\text{ 0}\text{.01 M }$ aqueous solution for barium chloride, potassium chloride, acetic acid, and sucrose would be,
$\text{ BaC}{{\text{l}}_{\text{2}}}\text{ }>\text{ KCl }>\text{ C}{{\text{H}}_{\text{3}}}\text{COOH }>\text{ Sucrose }$
This order depends on the ease of solute or ions to pass through the semipermeable membrane (SPM). Bigger solute particles are difficult to pass through the SPM but smaller may pass.
D) According to Raoult's law the partial pressure of any volatile component of a solution at any temperature is equal to the vapour pressure of the pure component multiplied by the mole fraction of that component in the solution. For an ‘n’ number of moles of a volatile liquid and p as the partial pressure, Raoult's law for a volatile liquid is written as follows,
$\text{ P = x }{{\text{p}}^{\text{0}}}\text{ }$
Where ${{\text{p}}^{\text{0}}}$ partial pressure of the liquid, x is mole fraction, and P is the pressure of the liquid.
Thus, statement (B), (C), and (D) is correct.

Hence, (A) is the correct option.

Note: Note that, colligative properties are the properties that depend on the number of solute particles present and not on nature. But colligative properties depend on the nature of the solvent. As the proportionality factor $\text{ }{{\text{K}}_{\text{f }}}$ , $\text{ }{{\text{K}}_{\text{b }}}$ are solvent dependent on constants. The movement of solute across the SPM depends on the size of the solute.