Problem 80 - Chemistry: The Central Science

Question

You have an evacuated container of fixed volume and known mass and introduce a known mass of a gas sample. Measuring the pressure at constant temperature over time, you are surprised to see it slowly dropping. You measure the mass of the gas-filled container and find that the mass is what it should be-gas plus container-and the mass does not change over time, so you do not have a leak. Suggest an explanation for your observations.

Step-by-Step Solution

Answer

The observed pressure drop in the container can be explained by either a chemical reaction involving the gas molecules or adsorption of the gas molecules to the container walls. The constant mass of the gas-filled container supports the adsorption theory, as the gas molecules are still present in the container (bound to the walls) but not actively contributing to the pressure inside the container.

Step 1: Understanding the situation

First, let's analyze the given situation. We have a closed container with a certain mass of gas. The pressure is measured at a constant temperature and is decreasing over time. We know that there is no leak, and the mass of the container plus the gas is constant.

Step 2: Considering the gas laws

Let's think about how the ideal gas law could explain this behavior. The ideal gas law is given by the equation: \(PV = nRT\) Where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. Here, the volume V and the temperature T are constant. Now, since the pressure is decreasing and we know that the mass of the container plus the gas is constant, it suggests that the number of moles of gas, n, inside the container is decreasing.

Step 3: Considering possible explanations

The fact that the number of moles of the gas inside the container is decreasing, despite the container not having a leak, could be explained by a chemical reaction happening inside the container. This reaction could involve the gas molecules reacting with the container's walls or, if there is more than one gas in the container, the gas molecules could be reacting with each other. Another explanation could be that the gas molecules are adsorbing to the container's walls. Adsorption is a surface phenomenon, where gas molecules attach to the surface of a solid (in this case, the container walls). As more and more molecules are adsorbed, the number of gas molecules in the container effectively decreases, and hence the pressure decreases too.

Step 4: Suggesting the explanation

Based on our analysis, we can suggest that the observed pressure drop is likely due to either a chemical reaction involving the gas molecules or adsorption of the gas molecules to the container walls. The fact that the mass of the gas-filled container does not change over time supports the adsorption theory, as the gas molecules are still present in the container (bound to the walls) but not actively contributing to the pressure inside the container.