Question

Arrange the following in increasing order of their osmotic pressure generation at 298 K:
(The cell wall is permeable to water and not to the solute molecules)
(A) If a cell containing 0.5 moles of solute dissolved in 1 L of water is immersed in pure water.
(B) If a cell containing 0.25 moles of solute dissolved in 1 L of water is immersed in pure water.
(C) If a cell containing 0.1 moles of solute dissolved in 0.01 L of water is immersed in pure water.
(D) If a cell containing 0.2 moles of solute dissolved in 0.05 L of water is immersed in pure water.
Choose the correct answer from the options given below:

• (B) < (A) < (D) < (C)
• (D) < (A) < (B) < (C)
• (C) < (B) < (A) < (D)
• (C) < (A) < (B) < (D)

Answer 1

The Correct Option is A

The osmotic pressure (\( \pi \)) of a solution can be determined using the formula: 
\( \pi = iCRT \)
Where:

• \( i \) = van 't Hoff factor (for non-electrolyte solutions, \( i = 1 \))
• \( C \) = molarity of the solution
• \( R \) = Ideal gas constant = 0.0821 L·atm/mol·K
• \( T \) = temperature in Kelvin

Since the temperature and gas constant are the same for all cases, the osmotic pressure depends on the molarity:

• (A) Moles of solute = 0.5; Volume = 1 L;
  Molarity, \( C_A = \frac{0.5}{1} = 0.5 \, \text{M}\)
• (B) Moles of solute = 0.25; Volume = 1 L;
  Molarity, \( C_B = \frac{0.25}{1} = 0.25 \, \text{M}\)
• (C) Moles of solute = 0.1; Volume = 0.01 L;
  Molarity, \( C_C = \frac{0.1}{0.01} = 10 \, \text{M}\)
• (D) Moles of solute = 0.2; Volume = 0.05 L;
  Molarity, \( C_D = \frac{0.2}{0.05} = 4 \, \text{M}\)

Arranging these molarities in increasing order gives: \( C_B < C_A < C_D < C_C \). Therefore, the solution with the lowest molarity will generate the lowest osmotic pressure, and the highest molarity will generate the highest osmotic pressure. Thus, in increasing order of osmotic pressure: (B) < (A) < (D) < (C).

The correct arrangement is: (B) < (A) < (D) < (C).

Answer 2

To determine the osmotic pressure generated by each solution, we use the formula for osmotic pressure, π: π = iCRT, where i is the van 't Hoff factor, C is the concentration of solute in mol/L, R is the ideal gas constant (0.0821 L atm K^-1 mol^-1), and T is the temperature in Kelvin (298 K). Since the cell wall is permeable to water and not to solute molecules, i = 1.0 for all solutions as there is no dissociation. 

Let's calculate C for each case:

(A) 0.5 moles in 1 L: C = 0.5 M

(B) 0.25 moles in 1 L: C = 0.25 M

(C) 0.1 moles in 0.01 L: C = 10 M

(D) 0.2 moles in 0.05 L: C = 4 M

Substituting for each:

(A) π = 1 × 0.5 × 0.0821 × 298 = 12.239 atm

(B) π = 1 × 0.25 × 0.0821 × 298 = 6.119 atm

(C) π = 1 × 10 × 0.0821 × 298 = 244.58 atm

(D) π = 1 × 4 × 0.0821 × 298 = 97.912 atm

Now, arrange the osmotic pressures in increasing order: (B) (6.119 atm) < (A) (12.239 atm) < (D) (97.912 atm) < (C) (244.58 atm). Thus, the increasing order of osmotic pressure generation is: (B) < (A) < (D) < (C).

Hence, the correct answer is: (B) < (A) < (D) < (C)