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.

Short answer

The most suitable explanation for the observed decrease in pressure at constant temperature in the container, despite no mass change, is that gas molecules are either adsorbing to the container walls or undergoing a chemical reaction. This reduces the number of gas molecules in the container, causing the pressure to decrease even with constant temperature.

Step-by-step solution

Identify the given information

We know the following from the problem statement: 1. Container mass and volume are known. 2. Known mass of a gas sample is introduced. 3. Pressure drops slowly, but temperature remains constant. 4. Container's mass with the gas remains constant over time (ruling out a leak).

Consider the gas laws

Remembering the ideal gas law, given by \(PV = nRT\), where P is the pressure, V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the temperature. Since temperature is constant in this exercise, we can explore how the other parameters might be influencing the pressure.

Possible explanations for the pressure decrease

Since we know there's no leak, as the container's mass with gas remains constant over time, we can suggest some possible explanations for the observed decrease in pressure. These include: 1. Some of the gas molecules are adsorbing to the container walls, effectively reducing their availability in the gas phase, causing a decrease in the pressure. 2. A chemical reaction might be occurring within the container, either between the gas molecules themselves or with the container walls. This could result in some of the gas molecules converting to solids or liquids, thereby reducing the number of gas molecules and causing a decrease in pressure.

Suggesting an explanation

Since the temperature remains constant and the mass is not changing, it is likely that some of the gas molecules are adsorbing to the container walls or undergoing a chemical reaction. This would reduce the number of gas molecules in the container, causing the pressure to decrease even with constant temperature. As a result, the most suitable explanation for the observations would be the occurrence of adsorption or a chemical reaction.

Key concepts

Gas Adsorption

Gas adsorption is a process where gas molecules accumulate on the surface of a solid or a liquid, known as an adsorbent. Unlike absorption, where the substance is taken up by the volume of the material, adsorption involves the build-up of molecules only on the surface. In the context of the exercise, the observed decrease in pressure within a sealed container, despite a constant temperature and no apparent leak, suggests that gas adsorption could be occurring.

Imagine a sponge representing the interior walls of our container. When you spill water (the gas molecules) on a table, the sponge (container's walls) can soak up the water without changing its overall mass significantly, just like the container with the gas. The number of water droplets (gas molecules) available on the table’s surface (gas phase) lessens, without an actual loss of water (gas).

This phenomenon is particularly important in various industrial applications, such as in gas masks where hazardous gases are adsorbed onto activated charcoal, or in catalytic converters where pollutants are adsorbed and then chemically transformed. Moreover, adsorption is reversible, which means the gas can be released from the adsorbent under certain conditions, a principle used in gas storage solutions.

Chemical Reactions in Gases

Chemical reactions involving gases can significantly affect their physical properties, such as pressure. In a contained environment, a chemical reaction might cause gas molecules to recombine into different compounds, possibly solids or liquids, removing them from the gaseous phase.

Let's picture a group of free dancers (gas molecules) at a party (container). As the night progresses, some decide to pair up and sit down (chemical reaction to form a different compound). Fewer dancers are now available to keep the energy (pressure) up in the dance area (gas phase). This analogy helps us understand that as the chemical reaction proceeds, the number of gas molecules decreases, leading to a decrease in pressure, given that the volume and temperature remain constant.

Such reactions can be simple, like a gas reacting with the container's material, or complex, like hydrocarbons breaking down in the presence of a catalyst. In environmental engineering, this principle is used for removing pollutants from the air, where reactive gases undergo chemical changes to become less harmful substances. Understanding chemical reactions in gases is crucial for fields such as atmospheric science, combustion engineering, and the synthesis of new materials.

Pressure Volume Temperature Relationships

The pressure, volume, and temperature of a gas are related through the ideal gas law (\(PV = nRT\), where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature). This law allows us to predict how one property will change as we alter another, provided the amount of gas remains constant.

In a situation like our exercise, if no gas is escaping or being added—the number of moles (n) stays the same—then, under constant temperature, any decrease in pressure must be due to a change in volume or a decrease in the effective number of gas molecules that can exert pressure (due to adsorption or reaction).

For instance, if we were to increase the temperature while keeping the volume constant, we would expect the pressure inside the container to increase as the gas molecules move faster and collide more frequently with the walls. This principle underlines much of thermodynamics and is vital for applications as diverse as predicting weather patterns, designing engines, and even calculating the correct dosage of gas anesthesia in medicine.