Problem 22 - Chemistry: An Atoms-Focused Approach

Question

The following pairs of aqueous solutions are separated by a semipermeable membrane. In which direction will the solvent flow? a. \(A=0.48 M N_{a} C l ; B=55.85 \mathrm{g}\) of \(N a C 1\) dissolved in \(1.00 \mathrm{L}\) of solution b. \(A=100 \mathrm{mL}\) of \(0.982 M \mathrm{CaCl}_{2} ; \mathrm{B}=16 \mathrm{g}\) of \(\mathrm{NaCl}\) in \(100 \mathrm{mL}\) of solution c. \(A=100 \mathrm{mL}\) of \(6.56 \mathrm{mM} \mathrm{MgSO}_{4} ; \mathrm{B}=5.24 \mathrm{g}\) of \(\mathrm{MgCl}_{2}\) in \(250 \mathrm{mL}\) of solution

Step-by-Step Solution

Answer

Question: In each case, determine the direction of solvent flow through a semipermeable membrane separating aqueous solutions A and B. a. Solution A: 0.48 M NaCl; Solution B: 55.85 g NaCl in 1.00 L of solution b. Solution A: 0.982 M CaCl2 in 100 mL; Solution B: 16 g NaCl in 100 mL c. Solution A: 6.56 mM MgSO4 in 100 mL; Solution B: 5.24 g MgCl2 in 250 mL Answer: a. The solvent will flow from Solution A to Solution B. b. The solvent will flow from Solution A to Solution B. c. The solvent will flow from Solution A to Solution B.

Step 1: Find molarity for the given solutions

First, we need to calculate the molarity (\(M\)) of each solution. For that, we can use the formula: \(M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\) For solution A and B in all the cases, get the molar concentration using the given data.

Step 2: Calculate the osmotic pressure

Next, we will calculate the osmotic pressure using the formula mentioned above. For both the solutions A and B, plug the molarity and van't Hoff factors into the osmotic pressure formula.

Step 3: Compare osmotic pressure and determine the solvent flow direction

Finally, compare the osmotic pressures of each pair of solutions. The direction of solvent flow will be from the solution with lower osmotic pressure to the one with higher osmotic pressure. Now let's apply these steps to each case (a, b, and c). a. Solution A: \(0.48 M NaCl\) Solution B: \(55.85 g\) of \(NaCl\) in \(1.00 L\) of solution Calculate molarity for Solution B: Molarity = \(\frac{55.85 \, g}{(58.44\, g/mol) \times 1.00\, L} = 0.957\, M\) Now, compare the osmotic pressures of Solution A and Solution B, considering \(\text{i}=2\) for \(NaCl\) as it forms 2 ions in solution. Since the molarity of Solution B is greater than the molarity of Solution A, the solvent will flow from Solution A to Solution B. b. Solution A: \(0.982 M\, CaCl_2\) in \(100\, mL\) Solution B: \(16 g\, NaCl\) in \(100\, mL\) Calculate molarity for Solution B: Molarity = \(\frac{16 \, g}{(58.44\, g/mol) \times 0.1\, L} = 2.74\, M\) Now, compare the osmotic pressures of Solution A and Solution B, considering \(\text{i}=2\) for \(NaCl\) and \(\text{i}=3\) for \(CaCl_2\), as \(NaCl\) forms 2 ions in solution and \(CaCl_2\) forms 3 ions in solution. According to these osmotic pressures, the solvent will flow from Solution A to Solution B. c. Solution A: \(6.56\, mM\, MgSO_4\) in \(100\, mL\) Solution B: \(5.24\, g\, MgCl_2\) in \(250\, mL\) Convert \(MgSO_4\) concentration to molarity: \(M = 6.56 \times 10^{-3}\, M\) Calculate molarity for Solution B: Molarity = \(\frac{5.24 \, g}{(95.21\, g/mol) \times 0.250\, L} = 0.276\, M\) Now, compare the osmotic pressures of Solution A and Solution B, considering \(\text{i}=2\) for \(MgSO_4\) and \(\text{i}=3\) for \(MgCl_2\). In this case, the solvent will flow from Solution A to Solution B based on the determined osmotic pressures.

Key Concepts

Semipermeable membrane

In the world of chemistry, the concept of a semipermeable membrane plays a crucial role, especially in processes like osmosis. A semipermeable membrane is a thin barrier that allows certain molecules or ions to pass through it while blocking others. This selective permeability is essential in many natural and industrial processes. For example, in biological systems, semipermeable membranes regulate the passage of substances in and out of cells, maintaining the necessary balance of solutes and solvents.

The selective nature of these membranes often lets through small solvent molecules, such as water, while larger or polar solute molecules are restricted. When two solutions with different concentrations are separated by a semipermeable membrane, osmosis occurs. This is the natural movement of solvent from a region of low solute concentration (or higher solvent concentration) to a region of high solute concentration, aiming to equalize solute concentrations on each side of the membrane.

Molarity calculation

Molarity is a fundamental concept when dealing with solutions, defined as the number of moles of solute per liter of solution. It provides a way to describe the concentration of a solute in a given volume of solution and is essential for calculating the amounts of substances in chemical reactions.

To find the molarity, you can use the formula:

• \( M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \)

Carefully calculating the molarity is crucial for determining osmotic pressure in an osmosis scenario. For instance, if you are given the mass of a solute and its molar mass, you can first find the moles of that solute, then use the solution volume to find its molarity.
This calculation helps determine how much "push" one solution may have on another across a semipermeable membrane, which is essential for predicting the direction of solvent flow.

Osmotic pressure

Osmotic pressure is a concept that relates to the force required to prevent the natural process of osmosis. It is the pressure needed to stop the flow of solvent across a semipermeable membrane separating two solutions of different concentrations. This pressure can be calculated using the formula:

• \( \Pi = iMRT \)

where \( \Pi \) is the osmotic pressure, \( i \) is the Van't Hoff factor, \( M \) is molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

The osmotic pressure is directly proportional to the concentration of solutes in the solution. Therefore, by calculating the osmotic pressures of two given solutions, you can deduce the direction in which the solvent will move. Solvent will typically flow to the solution with a higher osmotic pressure, as it has a greater potential tendency to draw in solvent molecules.

Van't Hoff factor

In osmosis and osmotic pressure calculations, the Van't Hoff factor \( i \) is a crucial quantity. It is the number of particles the solute splits into or forms in a solution, impacting the colligative properties like osmotic pressure. For non-electrolytes such as sugar, \( i \) is 1 because they do not dissociate into ions. However, for electrolytes like NaCl and CaCl₂, \( i \) can be more than 1 because these substances dissociate into multiple ions.

For instance:

• NaCl dissociates into Na⁺ and Cl^-, so \( i = 2 \).
• CaCl₂ dissociates into one Ca²⁺ and two Cl^-, making \( i = 3 \).

The Van't Hoff factor helps in accurately accounting for the effect of solute particles in solutions, particularly for calculating osmotic pressure. Understanding and applying the correct Van't Hoff factor ensures more precise predictions of solvent flow direction through a semipermeable membrane.