Question

Suppose you had a balloon made of some highly flexible semipermeable membrane. The balloon is filled completely with a \(0.2 \mathrm{M}\) solution of some solute and is submerged in a \(0.1 \mathrm{M}\) solution of the same solute:

Short answer

Since the balloon filled with \(0.2 \mathrm{M}\) solution of a solute is submerged in a \(0.1 \mathrm{M}\) solution of the same solute, water will move from the region of lower solute concentration (outside the balloon) to the region of higher solute concentration (inside the balloon) due to osmosis. As a result, the balloon will expand as the volume of the solution inside the balloon increases. This process will continue until an equilibrium is reached, and the solute concentrations inside and outside the balloon become equal.

Step-by-step solution

Understand the concept of osmosis

Osmosis is the movement of water molecules through a semipermeable membrane from a region of lower solute concentration (high water concentration) to a region of higher solute concentration (low water concentration). This movement of water molecules continues until an equilibrium is reached, and the same concentration of solute molecules is on both sides of the membrane.

Determine the initial concentrations of the solute in and outside the balloon

Initially, the inside of the balloon has a concentration of \(0.2 \mathrm{M}\) while the outside is at \(0.1 \mathrm{M}\) of the same solute.

Identify the direction of water movement

Since there is a higher solute concentration (\(0.2 \mathrm{M}\)) inside the balloon and a lower concentration (\(0.1 \mathrm{M}\)) outside the balloon, water will tend to move from the area of lower solute concentration to the area of higher solute concentration. In this case, the water will move into the balloon to reach equilibrium.

Analyze the behavior of the balloon

Due to the incoming water molecules, the volume of the solution inside the balloon will increase, thus the balloon will expand. However, as the balloon's membrane is highly flexible, it will accommodate this expansion. Continual water movement into the balloon will continue until the concentration of solute inside and outside the balloon is equal.

Key concepts

Semipermeable Membrane

Imagine a gatekeeper that allows some people to pass through while stopping others; this is similar to how a semipermeable membrane operates. It is a selective barrier that permits certain substances, like water molecules, to pass through while blocking others, such as solute particles. The semipermeable membrane is pivotal in osmosis, guiding water from an area where there are fewer obstacles (low solute concentration) to an area packed with more obstacles (high solute concentration).

The properties of this semipermeable membrane are crucial in biological systems, as it counters random solute movement, making cells function properly. It's also used purposely in dialysis machines to cleanse the blood. The capacity of the membrane to be selective depends on the size, charge, and solubility of the molecules it encounters.

Solute Concentration

In the realm of solutions, the solute concentration refers to the amount of solute present in a given volume of solvent. It's a pivotal piece of the osmosis puzzle. In the textbook exercise, a balloon with a higher concentration of solute (\(0.2 \text{M}\)) attempts to balance itself with a surrounding solution of lower solute concentration (\(0.1 \text{M}\)).

Solute concentration is not just important in an academic setting—our bodies are constantly regulating it. For instance, our kidneys work tirelessly to maintain the proper solute concentration in our blood to keep us hydrated and healthy. Students often struggle with visualizing concentration gradients, but thinking of it as the 'density' of particles in a solution might help: more particles mean higher 'density' or concentration.

Equilibrium in Osmosis

Equilibrium is the ultimate goal in the game of osmosis. It's the point where the solute concentration on both sides of the semipermeable membrane is equal, and there is no net movement of water. In the classroom, the concept of equilibrium can be difficult to grasp since it's a dynamic balance—not a static one. Even when equilibrium is achieved, water molecules continue to hustle across the membrane; it's just that equal numbers are going in both directions.

In our exercise example, equilibrium is reached not when movement stops, but when the balloon no longer swells. This is because the water’s fickle dance across the membrane has balanced out. Understanding this concept is key for students, as it helps explain how cells maintain homeostasis, i.e., a stable internal environment despite external changes.