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 1L 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)

The correct answer is Option (3) → (B)<(A)<(D)<(C).

To determine the increasing order of osmotic pressure generated by the solutions in the given scenarios, we need to apply the formula for osmotic pressure (\( \pi \)):

\(\pi = i C  R  T\)

Where:

\( \pi \) = osmotic pressure

\( i \) = van't Hoff factor (which is 1 for non-electrolytes since they do not dissociate)

\( C \) = molarity of the solute (moles of solute per liter of solution)

\( R \) = universal gas constant (constant)

\( T \) = temperature in Kelvin (constant at 298 K)

Since all cases involve immersion in pure water, the volume of water is the critical factor for determining the molarity.

(A) 0.5 moles of solute in 1 L of water:

\(C_A = \frac{0.5 \text{ moles}}{1 \text{ L}} = 0.5 \text{ M}\)

(B) 0.25 moles of solute in 1 L of water:

\(C_B = \frac{0.25 \text{ moles}}{1 \text{ L}} = 0.25 \text{ M}\)

(C) 0.1 moles of solute in 0.01 L of water:

\(C_C = \frac{0.1 \text{ moles}}{0.01 \text{ L}} = 10 \text{ M}\)

(D) 0.2 moles of solute in 0.05 L of water:

\(C_D = \frac{0.2 \text{ moles}}{0.05 \text{ L}} = 4 \text{ M}\)

Order of Osmotic Pressure

Now, we can rank the osmotic pressures based on their molarity:

\( C_A = 0.5 \) M

\( C_B = 0.25 \) M

\( C_C = 10 \) M

\( C_D = 4 \) M

Increasing Order of Osmotic Pressure: \( C_B < C_A < C_D < C_C \)

In terms of cases, this translates to: (B) < (A) < (D) < (C)

Conclusion

The correct order of increasing osmotic pressure generation at 298 K is: (B) < (A) < (D) < (C).