Question

A sample of neon gas is placed into a \(22.4-\mathrm{L}\) rigid container that already contains \(1.00 \mathrm{~mol}\) of nitrogen gas. Indicate which statement is correct in describing the change that occurs when the neon gas is added to the container. Assume ideal gas behavior. The partial pressure of the nitrogen gas in the container would double. The partial pressure of the nitrogen gas would increase by some amount, but we cannot know the exact amount without more information. ci The partial pressure of the nitrogen gas in the container would decrease by \(1 / 2(50 \%)\). d) The partial pressure of the nitrogen gas in the container would decrease by some amount, but we cannot know-the exat amount without more information. e The partial pressure of the nitrogen gas would not change.

Short answer

The partial pressure of the nitrogen gas would not change.

Step-by-step solution

Understand the Scenario

We have a 22.4 L container with 1.00 mol of nitrogen gas (N₂), and we're adding neon gas (Ne) to this container. The container volume is rigid, meaning it cannot expand or contract. We assume ideal gas behavior.

Analyze Partial Pressure Concept

Partial pressure is the pressure that one component of a mixture of gases would exert if it were alone in the container. For ideal gases, the partial pressure is directly proportional to the molar amount of the gas.

Evaluate the Effect of Adding Neon Gas

Adding neon gas to the container only changes the total pressure inside the container but does not directly affect the partial pressure of the nitrogen gas, since the number of moles of nitrogen gas has not changed.

Conclusion Based on Gas Laws

According to Dalton's Law of Partial Pressures, each gas in a mixture exerts the same pressure it would exert if it were alone. Thus, the partial pressure of nitrogen will remain unchanged because its amount and the container's volume remain the same.

Key concepts

Ideal Gas Behavior

Ideal gas behavior is an important concept in understanding how gases interact in a closed environment. An ideal gas is a theoretical gas whose molecules occupy negligible space and have no interactions, therefore the gas follows the ideal gas law perfectly. This means it applies the equation \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature.

In our exercise, we assume that both the nitrogen and neon gases behave ideally. This allows us to make predictions using this formula. Because ideal gases are expected to expand and fill the entire volume of the container uniformly, they make it easy to calculate changes in conditions like pressure and volume. The assumption of ideal behavior simplifies the math but may not perfectly match real-world cases where gas molecules interact with one another.

Partial Pressure

Partial pressure is a core idea when dealing with gases in a mixture. It refers to the pressure exerted by a single type of gas in a mixture of gases. Each gas in a mixture behaves as if it is the only gas present.

Dalton's Law of Partial Pressures explains this further by stating that the total pressure exerted by a mixture of gases is the sum of the partial pressures of each individual gas. Mathematically, it's expressed as:

• \( P_{total} = P_1 + P_2 + P_3 + \, \dots \)

So, if we have two gases in a container, such as nitrogen and neon, the total pressure is simply the sum of their individual partial pressures. In the exercise scenario, even after adding neon gas, the partial pressure of nitrogen remains the same since its mole quantity remains constant.'

Mixture of Gases

A mixture of gases consists of two or more different gases occupying the same container. In our case, we have neon and nitrogen gases. Each gas behaves independently and contributes to the total pressure in the container.

When dealing with a gaseous mixture, it is important to take each gas's mole fraction into account to understand its contribution to the partial pressure. However, as per Dalton's Law, each gas in a mixture exerts its pressure independently, which doesn't change unless the amount of that specific gas changes. Thus, when adding a different gas like neon, only the total pressure in the container increases, while the partial pressures depend on the quantity of individual gases.

Rigid Container

A rigid container is one that does not change its shape, volume, or size regardless of the contents inside it. This plays an important role in our scenario because it establishes that the volume of the container is fixed at 22.4 L.

The unchanging volume allows the calculations of gas behavior under constant volume conditions. In our problem, the fact that the container is rigid means that introducing another gas (neon in this case) does not change the space available for the existing nitrogen gas. This immutability ensures that the partial pressure of nitrogen remains unchanged, following Dalton’s Law of Partial Pressures, even as the total pressure of the mixture increases with the addition of neon.