Question

Consider the following apparatus: a test tube covered with a non permeable elastic membrane inside a container that is closed with a cork. A syringe goes through the cork. a. As you push down on the syringe, how does the membrane covering the test tube change? b. You stop pushing the syringe but continue to hold it down. In a few seconds, what happens to the membrane?

Short answer

a. As you push down on the syringe, the membrane covering the test tube moves inward due to the increased pressure inside the container. b. When you stop pushing but continue to hold the syringe down, the membrane remains in its deformed state as the pressure inside the container stays constant and equilibrium is reached.

Step-by-step solution

Scenario A: Pushing down the syringe

When you push down on the syringe, you increase the pressure inside the container, since the gas inside the container gets compressed due to less moving space for the gas molecules. As a result of the increased pressure inside the container, the elastic membrane covering the test tube will experience an additional force from the gas molecules in the container, which pushes it inward. The membrane will change its shape and move toward the inside of the test tube, balancing the increased pressure acting on the outside.

Scenario B: Holding the syringe down

Once you stop pushing the syringe but continue to hold it down, the pressure inside the container remains constant as long as the container's parameters, like temperature and size, do not change. After a few seconds, the gas particles will redistribute themselves inside the container and reach equilibrium. Since the pressure on the outside of the membrane remains the same, and the pressure on the inside of the membrane does not change (given that the membrane is non-permeable to the gas particles), the membrane will remain in its deformed state. It will not return to its initial position as long as the syringe is held down and the pressure inside the container remains constant.

Key concepts

Elastic Membrane

An elastic membrane is like a stretchy skin that can change its shape when a force is applied. In the context of a test tube covered by this membrane, it behaves just like a balloon would when you squeeze it. When the pressure inside the container where the test tube is located increases, the membrane is pushed inward. This means the membrane is flexible and can handle changes in pressure by expanding or contracting. It is crucial to note that because the membrane is non-permeable, gas cannot pass through it, keeping the inside of the test tube from being directly affected by changes in the container's gas environment. Thus, the elastic nature helps maintain the integrity of what's inside the test tube by balancing outside pressures.

Gas Molecules

Gas molecules are tiny particles that move around freely in a container. When you push the syringe down, you're making the container smaller. This means the gas molecules have less space and are forced closer together, resulting in increased pressure. This is similar to squeezing air into a smaller space; the molecules bump into each other more often and against the walls of the container more forcefully. This occurs because gases flow to fill up the available volume, and when that volume decreases, density and pressure increase. This increased pressure is what causes the elastic membrane to change shape, reflecting how active and dynamic gas molecules can be inside a closed system.

Equilibrium

Equilibrium is a state where things balance and stabilize. When you stop pushing down the syringe — but keep it in place — the gas molecules in the container eventually spread out evenly. They will rearrange themselves so that the pressure inside remains stable. Equilibrium in this case means that all forces inside the container are balanced, and the system does not change unless further alteration takes place, like changing the container's temperature or volume. The membrane stays deformed at equilibrium because the overall pressure inside the container is evenly maintained at a higher level than when the syringe wasn't pressed.

Pressure Change

Pressure change happens whenever the amount of force that gas molecules exert on the container walls is altered. This can occur in different scenarios, such as pushing or pulling the syringe, heating, or cooling the container, which changes the speed and behavior of the gas molecules. In this exercise, the act of pushing the syringe down creates a higher pressure environment around the test tube covered by the elastic membrane. As the gas becomes compressed, the membrane is affected by the new pressure conditions. This ability to understand and predict changes in pressure is key to many scientific and industrial applications, where control over pressure can be essential to desired outcomes, like preserving substances or creating specific reactions.