Question

the diagram below shows a solution with one solute. the solution fills a closed container that is divided by a membrane. the membrane is permeable to the solute particles. the volume on the left is two times as large as the volume on the right. which of the following statements describes how the solution will change over time? for the solute particles to reach equilibrium, more particles will move across the membrane from the right to the left. for the solute particles to reach equilibrium, more particles will move across the membrane from the left to the right. because the solute particles have reached equilibrium, the same number of particles will move across the membrane in each direction.

Explanation:

Step1: Calculate the concentration of solute particles in each side

The left - hand side has a volume \(V_{left}=2\space mL\) and \(n_{left} = 7\) particles. The concentration \(C_{left}=\frac{n_{left}}{V_{left}}=\frac{7}{2}=3.5\space particles/mL\). The right - hand side has a volume \(V_{right} = 1\space mL\) and \(n_{right}=2\) particles. The concentration \(C_{right}=\frac{n_{right}}{V_{right}}=\frac{2}{1}=2\space particles/mL\).

Step2: Determine the direction of particle movement

Particles move from an area of higher concentration to an area of lower concentration. Since \(C_{left}>C_{right}\), more particles will move from the left (higher concentration) to the right (lower concentration) until equilibrium is reached. At equilibrium, the concentration of solute particles on both sides will be equal. Let the number of particles on the left be \(x\) and on the right be \(y\) with \(x + y=7 + 2=9\) and \(\frac{x}{2}=\frac{y}{1}\) (because \(V_{left} = 2\space mL\) and \(V_{right}=1\space mL\)). Solving \(x = 2y\) and \(x + y=9\) gives \(y = 3\) and \(x = 6\). The net movement is from left to right.

Answer:

For the solute particles to reach equilibrium, more particles will move across the membrane from the left to the right.