Question

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

Short answer

Solvent flows from the KNO₃ solution to the NaCl solution.

Step-by-step solution

Calculate Molarity of NaCl Solution

First, determine the molarity of the NaCl solution. Calculate the number of moles of NaCl using the formula \( n = \frac{\text{mass}}{\text{molar mass}} \). The molar mass of NaCl is \(58.44 \text{ g/mol}\). So, \( n_{\text{NaCl}} = \frac{5.85 \text{ g}}{58.44 \text{ g/mol}} = 0.1 \text{ mol} \). The volume of the solution is \(0.1 \text{ L}\). Hence, the molarity of the NaCl solution is \(0.1 \text{ mol/L}\).

Calculate Molarity of KNO₃ Solution

Next, calculate the molarity of the KNO₃ solution. The molar mass of KNO₃ is \(101.1 \text{ g/mol}\). Calculate the moles of KNO₃: \( n_{\text{KNO}_3} = \frac{8.88 \text{ g}}{101.1 \text{ g/mol}} \approx 0.0878 \text{ mol} \). The volume of the solution is \(0.1 \text{ L}\). So, the molarity of the KNO₃ solution is \(0.0878 \text{ mol/L}\).

Compare Solute Concentrations for Osmosis

Osmosis causes the solvent to move from the lower concentration solution to the higher concentration solution. Compare the molarity values: NaCl solution has a molarity of \(0.1 \text{ mol/L}\) and KNO₃ has \(0.0878 \text{ mol/L}\).

Determine the Direction of Solvent Flow

Since the NaCl solution has a higher concentration (\(0.1 \text{ mol/L}\)) compared to the KNO₃ solution (\(0.0878 \text{ mol/L}\)), the solvent will flow from the KNO₃ solution to the NaCl solution, moving towards the higher solute concentration.

Key concepts

Molarity

Molarity is a crucial concept in chemistry that describes the concentration of a solute in a solution. It is expressed as moles of solute per liter of solution, with the unit \(\text{mol/L}\). This measure allows us to understand how much of a particular substance is present in a given volume of liquid, which can be very helpful in predicting reactions and properties of solutions.
To calculate molarity, you first need to determine the moles of the solute. Moles can be calculated using the formula: \( n = \frac{\text{mass}}{\text{molar mass}} \). Once you have the moles, divide it by the volume of the solution in liters to get the molarity: \( M = \frac{n}{V} \,\) where \( V \) is the volume in liters.

In the exercise at hand, you determine the molarity of each solution by plugging in the appropriate numbers. For the NaCl solution, this involves dividing 0.1 moles of \(\text{NaCl}\) by 0.1 liters, resulting in a molarity of 0.1 \(\text{mol/L}\). The same process for the KNO₃ solution gives a slightly lower molarity of 0.0878 \(\text{mol/L}\).

• High molarity indicates a more concentrated solution.
• Understanding molarity helps in predicting the movement of solvents in reactions like osmosis.
• Molarity directly influences the direction in which solutes dissolve and react.

Semipermeable Membrane

A semipermeable membrane is a barrier that allows the passage of certain molecules while blocking others. This selective permeability is key to processes like osmosis. Such membranes let through solvent molecules (like water) but restrict larger solute molecules.

These membranes are critical in biological systems and various industrial applications. They help maintain balance by allowing only specific substances to enter or leave a confined space. In our exercise, the semipermeable membrane separates the NaCl and KNO₃ solutions and controls solvent movement based on the concentration of solutes on either side.

• Permits only solvent and some small molecules to pass through.
• Essential for transporting substances in living cells.
• Facilitates balancing solute concentrations in solutions.

Understanding how semipermeable membranes function helps explain the movement of water or other solvents in everyday processes, including the swelling of plant cells or the purification of water.

Concentration Gradient

The concentration gradient is a term that represents the difference in solute concentration between two areas. It is the driver behind the movement of substances like solvents across a semipermeable membrane. When there's a concentration gradient, molecules tend to move from an area of higher concentration to one of lower concentration until equilibrium is achieved.

In osmosis, the solvent (often water) moves from the side with lower solute concentration to the side with higher solute concentration through the semipermeable membrane. This movement aims to equalize the concentration on both sides of the membrane. In our exercise, the solvent moves from the KNO₃ solution (0.0878 \(\text{mol/L}\)) to the NaCl solution (0.1 \(\text{mol/L}\)) due to the concentration gradient.

• Drives the natural movement of molecules.
• Critical in processes like osmosis and diffusion.
• Affects how quickly substances are transferred or spread in solutions.

By understanding concentration gradients, we can predict and explain various physical and chemical processes, including how nutrients are absorbed in the body or how gases are exchanged in the lungs.