Understanding Osmotic Pressure and Concentration

The question asks us to arrange different scenarios based on the osmotic pressure they generate when a cell containing a solute solution is immersed in pure water. Osmotic pressure is a colligative property, meaning it depends on the number of solute particles in a given volume of solution, not the identity of the solute.

When a cell with a higher solute concentration inside is placed in pure water, water moves into the cell across the semipermeable cell wall. This influx of water creates pressure inside the cell, which is the osmotic pressure. The magnitude of this pressure is directly proportional to the difference in solute concentration between the inside and outside of the cell. Since the cell is immersed in pure water (which has zero solute concentration), the osmotic pressure generated is solely determined by the solute concentration inside the cell.

The osmotic pressure ($\Pi$) can be calculated using the formula:

\(\Pi = iMRT\)

Where:

• \(i\) is the van't Hoff factor (number of particles the solute dissociates into, assume 1 for simple solutes)
• \(M\) is the molar concentration (molarity) of the solute (moles of solute per liter of solution)
• \(R\) is the ideal gas constant
• \(T\) is the temperature in Kelvin

At a constant temperature (298 K) and assuming the same type of solute (constant \(i\)), the osmotic pressure ($\Pi$) is directly proportional to the molar concentration (\(M\)). Therefore, to arrange the scenarios by increasing osmotic pressure, we need to calculate the molarity for each case and arrange them in increasing order of molarity.

Calculating Molarity for Each Scenario

Molarity (\(M\)) is calculated as:

\(M = \frac{\text{Moles of solute}}{\text{Volume of solution (in Liters)}}\)

We are given the moles of solute and the volume of water. For dilute solutions, the volume of water is a good approximation for the volume of the solution.

1. Scenario (A):

   • Moles of solute = 0.5 moles
   • Volume of water = 1 L
   • Molarity \(M_A = \frac{0.5 \text{ moles}}{1 \text{ L}} = 0.5 \text{ M}\)

2. Scenario (B):

   • Moles of solute = 0.25 moles
   • Volume of water = 1 L
   • Molarity \(M_B = \frac{0.25 \text{ moles}}{1 \text{ L}} = 0.25 \text{ M}\)

3. Scenario (C):

   • Moles of solute = 0.1 moles
   • Volume of water = 0.01 L
   • Molarity \(M_C = \frac{0.1 \text{ moles}}{0.01 \text{ L}} = 10 \text{ M}\)

4. Scenario (D):

   • Moles of solute = 0.2 moles
   • Volume of water = 0.05 L
   • Molarity \(M_D = \frac{0.2 \text{ moles}}{0.05 \text{ L}} = \frac{0.2 \times 100}{0.05 \times 100} = \frac{20}{5} = 4 \text{ M}\)

Comparing Molarities and Osmotic Pressure

Now, let's list the calculated molarities:

Since osmotic pressure is directly proportional to molarity, we arrange the scenarios in increasing order of their molarity:

0.25 M < 0.5 M < 4 M < 10 M

This corresponds to the scenarios:

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

Therefore, the increasing order of osmotic pressure generation is (B) < (A) < (D) < (C).

Arrangement of Osmotic Pressure Generation

Based on the molarity calculations, the osmotic pressure generated by the cells in pure water at 298 K increases in the following order:

Cell (B) < Cell (A) < Cell (D) < Cell (C)

This is because Cell (B) has the lowest solute concentration, while Cell (C) has the highest solute concentration. The movement of water into the cell due to osmosis will be greatest for the cell with the highest internal solute concentration, resulting in the highest osmotic pressure.

Revision Table: Key Concepts in Osmotic Pressure

Additional Information: Factors Affecting Osmotic Pressure

Osmotic pressure is a critical concept in biology and chemistry, particularly in understanding cellular processes and solution properties. Beyond molarity, other factors influence osmotic pressure:

• Temperature (T): Osmotic pressure is directly proportional to the absolute temperature ($\Pi \propto T$). As temperature increases, the kinetic energy of molecules increases, affecting water movement.
• van't Hoff factor (i): For electrolytes that dissociate in solution (e.g., NaCl dissociates into Na⁺ and Cl⁻, so \(i=2\)), the effective number of particles is greater than the moles of solute added. This factor accounts for dissociation or association of solute particles. In this problem, we assumed \(i=1\) for simplicity, meaning the solute does not dissociate.
• Nature of the membrane: While the question specifies the cell wall's permeability, the characteristics of the membrane (like its permeability to water) affect the rate of osmosis, but the equilibrium osmotic pressure is determined by concentration and temperature.

Understanding osmotic pressure helps explain phenomena like turgor pressure in plant cells, the functioning of kidneys, and the principles behind desalination technologies.