A semi-permeable membrane separates a solution that is \(0.012 \mathrm{M}\) in glucose from one that is \(0.250 \mathrm{M}\) in glucose. \(\mathrm{On}\) which of these solutions must pressure be applied to prevent a net flow of water through the membrane? (a) On the \(0.012 \mathrm{M}\) solution (b) On the \(0.250 \mathrm{M}\) solution (c) Equal pressure on both the solutions (d) The pressure on \(0.012 \mathrm{M}\) solution should be double the pressure on \(0.250 \mathrm{M}\) solution.

The semi-permeable membrane is a critical feature in the process of osmosis. It is a type of biological or synthetic barrier that allows certain particles to pass through while restricting others. In the context of osmosis, these membranes will enable the passage of solvent molecules, such as water, but not the solute molecules or ions present in the solution.

Semi-permeable membranes are selective in their permeability. The pores in these membranes are of such a size that only smaller molecules like water can traverse the membrane unhindered, whereas larger molecules like glucose cannot. This selectivity is crucial for maintaining cellular function in living organisms and for various industrial processes such as water purification and dialysis.

In our textbook problem, the membrane separates solutions of different glucose concentrations, allowing only water to move between them while keeping glucose molecules effectively contained within their respective sides of the membrane. The fundamental role of the semi-permeable membrane here is to facilitate the osmosis process by providing the condition for water to move from the area of lower solute concentration to the area of higher solute concentration. This movement is pivotal to the concept of osmotic pressure that is established across the membrane.

Solute concentration, often expressed in molarity (M) which is moles of solute per liter of solution, is essential in predicting the direction of water movement during osmosis. The concentration gradient between two solutions dictates the osmotic flow; water tends to move from a region of lower solute concentration to that of a higher one.

The concept of solute concentration is fundamental to understanding how osmosis can cause various biological and chemical effects. For instance, cells in our bodies are constantly regulating solute concentrations within their cytoplasm to maintain proper pressure and function. Disruptions in these concentrations can lead to cellular and systemic complications.

In the context of our textbook example, there are two solutions with different glucose concentrations, one at 0.012 M and the other at 0.250 M. Water will naturally move from the lower concentration solution to the higher one, leading to a potential imbalance. Therefore, understanding solute concentrations helps us predict osmosis behavior and allows us to take corrective actions, such as applying pressure to counteract osmotic flow.

Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of water across a semi-permeable membrane. It is a measure of the tendency of a solution to take in water by osmosis, driven by a difference in solute concentrations.

The higher the difference in solute concentrations, the greater the osmotic pressure. Osmotic pressure is a colligative property; that is, it depends on the number of solute particles in a solution and not the identity of the particles.

In our exercise, to prevent water from moving into the higher concentration glucose solution (0.250 M), you must apply pressure to it. The necessary pressure must be equal to or exceed the osmotic pressure created by the concentration gradient to stop the net flow of water. This concept can have applications in medical treatments, like preventing the swelling of tissues during intravenous therapy, and industrial processes, like reverse osmosis water purification systems.