Problem 11 - Chemistry The Central Science In Si Units

Question

Suppose you had a balloon made of some highly flexible semipermeable membrane. The balloon is filled completely with a \(0.2 M\) solution of some solute and is submerged in a \(0.1 \mathrm{M}\) solution of the same solute: Initially, the volume of solution in the balloon is \(0.25 \mathrm{~L}\). Assuming the volume outside the semipermeable membrane is large, as the illustration shows, what would you expect for the solution volume inside the balloon once the system has come to equilibrium through osmosis?

Step-by-Step Solution

Answer

The volume inside the balloon will be 0.5 L at equilibrium.

Step 1: Understand Osmosis

Osmosis is the movement of water across a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. This process continues until equilibrium is reached.

Step 2: Identify Initial Conditions

The initial concentration of the solute inside the balloon is higher ( 0.2 M ) than outside ( 0.1 M ). The initial volume of the solution inside the balloon is 0.25 L .

Step 3: Predict Water Movement

Since osmosis will cause water to move from the lower concentration outside ( 0.1 M ) to the higher concentration inside ( 0.2 M ), the volume inside the balloon will increase.

Step 4: Calculate Equilibrium

The goal is to equalize the concentrations to achieve equilibrium. Let the final volume inside the balloon be V_f. Initially, there are 0.2 imes 0.25 = 0.05 ext{ moles} of solute inside. At equilibrium, concentration inside should equal outside:\[ \frac{0.05}{V_f} = 0.1 \]Solve for V_f:\[ V_f = \frac{0.05}{0.1} = 0.5 ext{ L} \]

Step 5: Conclude the Result

After osmosis reaches equilibrium, the volume inside the balloon will increase to 0.5 L as water moves into the balloon to equalize solute concentrations.

Key Concepts

Semipermeable Membrane

A semipermeable membrane is a crucial component in the process of osmosis. It's a type of barrier that selectively allows certain molecules, like water, to pass through while blocking others, such as solute particles. Imagine it as a fine sieve that permits only the tiniest molecules to go from one side to another. This selective permeability is key to maintaining balance between different solutions.

In the example of a balloon, the walls of the balloon itself act as the semipermeable membrane. Water can traverse this membrane, moving from a region where it is in higher concentration to where it is lower. Such movement helps in achieving equilibrium, a state where the concentrations on either side of the membrane become balanced. The membrane does not permit larger solute molecules to pass, thus driving the movement of water specifically, rather than the solute. This unique property is what allows cells in our bodies, as well as other biological systems, to regulate their internal environments effectively.

Equilibrium in Solutions

Equilibrium in solutions is achieved when the concentrations of solute are equal on both sides of a semipermeable membrane. This state signifies balance, where there is no net movement of water across the membrane. In our balloon scenario, water originally moves from outside the balloon (where the solute concentration is lower) to inside (where the solute concentration is higher).

As water moves inward, it increases the volume inside the balloon, eventually diluting the solute concentration until it equals the concentration outside the balloon. Once these concentrations are equal, water will continue to move back and forth, but there will be no net change in volume. Achieving equilibrium is crucial for maintaining the proper function of many biological and chemical systems, as it ensures that the concentration of substances is kept constant over time. This equilibrium is a dynamic process, meaning that even though the equal state is reached, molecules continue to move back and forth maintaining balance.

Concentration Gradient

A concentration gradient refers to the difference in the concentration of a solute across a semi-permeable membrane. It represents the driving force for osmosis and other diffusion processes. In our example, before osmosis commences, there is a concentration gradient between the inside of the balloon ( 0.2 M ) and the outside solution ( 0.1 M ).

This gradient causes water molecules to move from the area of lower solute concentration (outside) to the area of higher solute concentration (inside). Think of the concentration gradient as a hill that causes molecules to flow naturally from the higher part to the lower part.

The movement continues until the gradient is diminished, achieving equilibrium where no further net water movement occurs. This gradient is a key concept not just in chemistry and biology, but also in fields such as environmental science, where it influences the movement of nutrients and pollutants in ecosystems.

Solution Volume Calculation

Solution volume calculation in osmosis requires understanding both the initial conditions and the changes that occur as equilibrium is reached. Initially, the balloon holds 0.25 L of a 0.2 M solution, which means there are 0.05 moles of solute inside it. As the system strives for equilibrium, more water enters the balloon from the surrounding 0.1 M solution to equalize the solute concentrations.

To calculate the final volume (V_f) when equilibrium is achieved, we use the formula for concentration: \( \frac{0.05}{V_f} = 0.1 \) . By rearranging the equation and solving for V_f, we find that the final volume is 0.5 L.

This doubling of the initial volume demonstrates the inflow of water needed to align the concentrations inside and outside the balloon. Such calculations help in quantitatively understanding the impact of diffusion and osmosis in various contexts, making it an invaluable skill in chemistry and biology. The result highlights the necessity of water movement in achieving solute balance, which is pivotal in many natural processes and technological applications.