Question

You have two aqueous solutions separated by a semipermeable membrane. One contains \(5.85 \mathrm{g}\) of NaCl dissolved in \(100 .\) mL of solution, and the other contains 8.88 g of \(\mathrm{KNO}_{3}\) dissolved in \(100 .\) mL of solution. In which direction will solvent flow: from the NaCl solution to the KNO \(_{3}\) solution, or from \(\mathrm{KNO}_{3}\) to \(\mathrm{NaCl}\) ? Explain briefly.

Short answer

Solvent flows from KNO3 to NaCl, as NaCl is more concentrated.

Step-by-step solution

Calculate the molarity of NaCl solution

First, calculate the number of moles of NaCl. The molar mass of NaCl is 58.44 g/mol. Since there are 5.85 g of NaCl:\[ \text{moles of NaCl} = \frac{5.85}{58.44} \approx 0.100 \text{ mol} \]The volume of the solution is 0.1 L (100 mL), so the molarity \( M \) is:\[ M(NaCl) = \frac{0.100}{0.1} = 1.00 \text{ M} \]

Calculate the molarity of KNO3 solution

Next, calculate the number of moles of KNO3. The molar mass of KNO3 is 101.10 g/mol. Since there are 8.88 g of KNO3:\[ \text{moles of KNO3} = \frac{8.88}{101.10} \approx 0.088 \text{ mol} \]The volume of the solution is 0.1 L (100 mL), so the molarity \( M \) is:\[ M(KNO3) = \frac{0.088}{0.1} = 0.88 \text{ M} \]

Determine the direction of solvent flow

The solvent will move from the solution with lower concentration (lower molarity) to the solution with higher concentration through osmosis. From Step 1, \( M(NaCl) = 1.00 \text{ M} \) and from Step 2, \( M(KNO3) = 0.88 \text{ M} \). Since the NaCl solution is more concentrated than the KNO3 solution, the solvent flows from the KNO3 solution to the NaCl solution.

Key concepts

Molarity

Molarity is a way to express the concentration of a solution. It is defined as the number of moles of solute present in one liter of solution. To find molarity, you need two things: the amount of the solute in moles, and the total volume of the solution in liters.

In the exercise you provided, we calculated the molarity for two solutions. First, for sodium chloride (NaCl), we determined the number of moles by dividing the mass of NaCl (5.85 g) by its molar mass (58.44 g/mol), giving us approximately 0.100 moles. Then, since the volume of the solution is 0.1 liters (100 mL), we find the molarity as 1.00 M.

• Formula: Molarity (M) = moles of solute / liters of solution
• Unit: mol/L

Understanding molarity helps in comparing the concentrations of different solutions, which is crucial for predicting the movement of solvents across membranes.

Semipermeable membrane

A semipermeable membrane is like a selective barrier that allows some particles to pass while blocking others. It's essential in processes like osmosis. Specifically, in this exercise, it allows water molecules to move but not larger molecules like NaCl or KNO3. This characteristic is pivotal in many biological and chemical processes. In our exercise, because the membrane is semipermeable, it enables the solvent (usually water) to move between the two solutions based on their concentrations.

• Only solvent molecules (e.g., water) can cross the membrane.
• The solute particles (e.g., NaCl, KNO3) remain on their respective sides.

This selective movement ensures the correct flow of solvent required by osmotic conditions, where it moves from the region of lower solute concentration to the region of higher solute concentration.

Solution concentration

When we talk about solution concentration, we're discussing how much solute is present within a specific volume of solution. Concentration can be represented in different ways, such as percentage concentration, mass per volume, and most relevantly here, molarity.

Solution concentration impacts various properties of solutions, such as boiling point, freezing point, and especially, osmotic pressure. The exercise uses molarity to express concentration, which helps predict solvent movement through osmosis. With sodium chloride's molarity at 1.00 M and potassium nitrate's at 0.88 M, we know the direction of solvent flow—moving from the less concentrated KNO3 solution to the more concentrated NaCl solution.

• Higher concentration means more solute particles in the solution.
• In osmosis, the solvent moves towards the solution with a higher concentration.

Accurately identifying solution concentration is vital in understanding and predicting the flow of molecules in chemical reactions and biological systems.