Question

\(0.1 \mathrm{M} \mathrm{NaCl}\) and \(0.05 \mathrm{M} \mathrm{BaCl}_{2}\) solutions are separated by a semi-permeable membrane in a container. For this system, choose the correct answer: (a) There is no movement of any solution across the membrane (b) Water flows from \(\mathrm{BaCl}_{2}\) solution towards \(\mathrm{NaCl}\) solution (c) Water flows from \(\mathrm{NaCl}\) solution towards \(\mathrm{BaCl}_{2}\) solution (d) Osmotic pressure of \(0.1 \mathrm{M} \mathrm{NaCl}\) is lower than the osmotic pressure of \(\mathrm{BaCl}_{2}\) (assume complete dissociation)

Short answer

Water flows from the BaCl2 solution towards the NaCl solution (answer b), and the osmotic pressure of 0.1M NaCl is higher than the osmotic pressure of 0.05M BaCl2 (answer d is incorrect).

Step-by-step solution

Understand Osmosis

Osmosis is the movement of solvent (usually water) across a semi-permeable membrane from a lower concentration solution to a higher concentration solution. The purpose of this movement is to equalize the solute concentrations on the two sides of the membrane.

Identify the Solutions and Their Concentrations

The exercise presents two solutions: 0.1M NaCl and 0.05M BaCl2. These concentrations are given in molarity (M), which is moles of solute per liter of solution.

Determine the Dissociation in Solution

NaCl dissociates into Na+ and Cl- ions, yielding two particles per molecule when it fully dissociates. BaCl2 dissociates into Ba2+ and two Cl- ions, yielding three particles per molecule when it fully dissociates.

Calculate Particles Contributed by Each Solute

Since NaCl yields two particles per molecule, the 0.1M solution effectively has 0.2M particles. BaCl2 yields three particles per molecule, so the 0.05M solution effectively has 0.15M particles.

Comparing Osmotic Pressures

Osmotic pressure is directly related to the concentration of particles in solution. The solution with the higher effective concentration of particles will exert a higher osmotic pressure.

Choose the Correct Option

Considering the effective concentration of particles, the 0.1M NaCl has a higher effective concentration (0.2M) compared to the 0.05M BaCl2 solution (0.15M). Therefore, water will move towards the NaCl solution, and the osmotic pressure of the NaCl solution will be higher than that of the BaCl2 solution.

Key concepts

Semipermeable Membrane

In the context of osmosis, a semipermeable membrane is a critical component. It’s a thin barrier that allows certain molecules, typically solvent molecules like water, to pass through while blocking others, usually solute molecules or ions. These membranes are selective in nature, meaning they have pores or openings of a specific size that only permit molecules of a certain size and shape to diffuse across them.

Picture this as a sieve that can allow small grains of sand to pass, but not larger pebbles. In our exercise concerning the movement of water between NaCl and BaCl₂ solutions, it’s the semipermeable membrane that determines the direction of water flow based on differences in concentration on either side. If, for instance, you wonder why the salts don't pass through the membrane, it's because the molecules or ions are too large compared to the small water molecules that easily go through.

Osmotic Pressure

Moving on to osmotic pressure, imagine it as a force exerted by the solute particles in solution. When water moves from a lower to a higher concentration of solute via a semipermeable membrane, it’s because of the osmotic pressure difference. It’s essentially the 'pulling' pressure that draws water towards a higher concentration of solute to attempt to equalize concentrations across the membrane.

In the exercise, the osmotic pressure is significant because it dictates the flow of water. To quantify this, scientists use the formula \(\Pi = iCRT\), where \(\Pi\) is the osmotic pressure, \(i\) represents the number of particles the solute dissociates into, \(C\) is the molar concentration, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin. The higher the solute concentration (or more specifically, the particle concentration after dissociation), the greater the osmotic pressure.

Electrolyte Dissociation

Lastly, let’s dive into electrolyte dissociation. Electrolytes are substances that produce ions when dissolved in water. This process, known as dissociation, turns a compound like NaCl into charged particles (ions), specifically Na⁺ and Cl^–.

The degree to which these compounds dissociate is crucial for understanding osmotic pressure. For example, NaCl dissociates completely in water to form two separate ions. In contrast, something like BaCl₂ dissociates to produce one Ba²⁺ and two Cl^– ions, resulting in three particles from just one molecule of the solute. This is a key point in our exercise, as it explains how 0.05M of BaCl₂, which seems like a lower concentration than 0.1M NaCl, actually produces more particles upon dissociation. Thus, the effective particle concentration after dissociation must be considered when calculating osmotic pressures and predicting the direction of water movement in osmotic processes.