Question

If \(0.1\) molar solution of glucose is separated from \(0.1\) molar solution of cane sugar by a semipermeable membrane, then which one of the following statements is correct? (a) Water will flow from glucose solution into cane sugar solution. (b) Cane sugar will flow across the membrane into glucose solution. (c) Glucose will flow across the membrane into cane sugar solution. (d) There will be no net movement across the semipermeable membrane.

Short answer

There will be no net movement across the semipermeable membrane because both solutions have the same molar concentration. Hence, option (d) is correct.

Step-by-step solution

Understand osmosis

Osmosis is the movement of solvent molecules through a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. The movement continues until there is an equilibrium in solute concentration on both sides of the membrane.

Compare the molar concentrations

We are given a 0.1 molar solution of glucose and a 0.1 molar solution of cane sugar. Since the molar concentrations are the same, the solutions are isotonic with respect to each other. Therefore, the tendency of water to move through osmosis is the same from the glucose to the cane sugar solution as it is from the cane sugar to the glucose solution.

Determine the net movement across the membrane

Given that both solutions have equal molar concentrations, the net movement of water across the semipermeable membrane will be zero. This means that no net osmosis will occur, and the water level on both sides will remain constant assuming that the membrane is impermeable to the solutes (glucose and cane sugar).

Key concepts

Semipermeable Membrane

A semipermeable membrane is a critical component in the process of osmosis. It acts as a filter that selectively allows certain molecules or ions to pass through it, while blocking others. Typically, these membranes will enable the passage of solvent molecules, such as water, but prevent solute molecules, like sugar or salt, from moving freely.

In the context of the given exercise, the semipermeable membrane allows water molecules to move between the glucose and cane sugar solutions. It is through this membrane that the principle of osmosis is applied to determine the direction of solvent flow, based on the solute concentration of the solutions on either side.

Solute Concentration

Solute concentration refers to the amount of solute dissolved in a solvent, creating a solution. It's typically measured in units like molarity, which is moles of solute per liter of solution. In osmosis problems, understanding solute concentration is fundamental because it dictates the direction of water movement.

For the exercise in question, both solutions of glucose and cane sugar have the same molar concentration, which is 0.1 molar. This equality in concentration means that the driving force for osmosis, which is the imbalance in solute concentration, does not exist, and therefore, there is no net movement of water across the membrane due to osmosis.

Isotonic Solutions

When two solutions exert the same osmotic pressure across a semipermeable membrane, they are said to be isotonic to each other. This means that they have an equal concentration of solutes that cannot cross the membrane, leading to a balance in water movement.

In an isotonic situation, as presented in the exercise, there is no net movement of solvent across the membrane because the solute concentrations are equal. The absence of osmotic flow implies that the level of water in the two solutions will remain constant, as long as other dynamic factors do not interfere. Understanding isotonic conditions is crucial when discussing the movement of fluids in biological systems or designing experiments.

Physical Chemistry Competitive Exams

Students preparing for competitive exams in physical chemistry should be well-versed in the principles of osmosis and related processes. Topics like semipermeable membranes, solute concentration, isotonic solutions, and principles of equilibrium are fundamental and frequently tested.

Problems similar to the given osmosis exercise are common in such exams, as they test a student's ability to apply concepts in practical scenarios. To excel, it's important for students to understand the underlying principles deeply, practice similar problems, and be adept at reasoning through complex scenarios where multiple physical chemistry concepts are at play.