Problem 70 - Chemistry

Question

A mixture of helium and neon gases is collected over water at \(28.0^{\circ} \mathrm{C}\) and \(745 \mathrm{mmHg} .\) If the partial pressure of helium is \(368 \mathrm{mmHg}\), what is the partial pressure of neon? (Vapor pressure of water at \(28^{\circ} \mathrm{C}=\) \(28.3 \mathrm{mmHg} .\) )

Step-by-Step Solution

Answer

The partial pressure of neon is \(348.7 \, \mathrm{mmHg}\).

Step 1: Identify Given Variables

The total pressure in the system is given as \(745 \, \mathrm{mmHg}\). The partial pressure of helium in the system is given as \(368 \, \mathrm{mmHg}\). The pressure of water in the system is given as \(28.3 \, \mathrm{mmHg}\).

Step 2: Apply Dalton's Law of Partial Pressures

According to Dalton's Law of Partial Pressures, the total pressure is equal to the sum of the partial pressures of individual gases. In this case, the total pressure will be the sum of the pressure of helium, neon, and water. With the given data, the equation can be formed as: \(745 = 368 + P_{Ne} + 28.3\) where \(P_{Ne}\) denotes the pressure of neon.

Step 3: Solve for Neon's Partial Pressure

Reorder the equation to solve for \(P_{Ne}\) which gives: \(P_{Ne} = 745 - 368 - 28.3\).

Step 4: Perform the Calculation

By solving, the value of \(P_{Ne}\) will be: \(P_{Ne} = 348.7 \, \mathrm{mmHg}\).

Key Concepts

Partial Pressure

In any mixture of gases, each gas exerts its own pressure independently of the others. This individual pressure is known as the partial pressure. Dalton's Law of Partial Pressures states that the total pressure of a mixture is the sum of the partial pressures of each gas. For example, if you have a mixture containing helium and neon, each will contribute to the overall pressure based on its proportion in the mixture. If helium's partial pressure is given as 368 mmHg, that means helium alone exerts this much pressure out of the total. Calculating partial pressures helps understand how different gases interact collectively in a confined space.

Vapor Pressure

Vapor pressure is the pressure exerted by the vapor of a liquid in equilibrium with its liquid phase at a given temperature. For example, water at a specific temperature will have a consistent vapor pressure known as the vapor pressure of water. This arises because molecules in the liquid phase constantly escape into the gas phase until equilibrium is reached. In our exercise, the vapor pressure of water at 28°C is 28.3 mmHg. This means that, in addition to the gases present, water vapor contributes 28.3 mmHg to the total pressure inside the container holding the gas mixture. Understanding vapor pressure is vital in calculating the total pressure and the remaining pressure exerted by the gases alone.

Mixture of Gases

A mixture of gases can consist of any number of different gases sharing a common volume, like helium and neon in our scenario. Each gas in a mixture behaves independently and fills the entire volume of the container, even when combined with others. This means that each gas's behavior can be explained using the same principles that describe a single gas. The gases do not interact chemically in the scenario considered here, which allows us to treat and measure their pressures separately as shown in the exercise. The total pressure is thus the sum of the components' pressures, including any contributions from water vapor if over water.

Pressure Calculation

Pressure calculation is crucial for predicting the behavior of gases in a system. By applying Dalton's Law of Partial Pressures, we can calculate the unknown partial pressure from the total and known partial pressures. From our example, we know the total pressure and the partial pressures of helium and water vapor. By subtracting the sum of these known values from the total pressure, we can find neon's pressure. Simplified, the calculation is:

• Take the total pressure: 745 mmHg
• Subtract helium's partial pressure: \(745 - 368 = 377 \, \text{mmHg}\)
• Subtract water's vapor pressure: \(377 - 28.3 = 348.7 \, \text{mmHg}\)

Thus, by understanding and organizing calculations properly, we find the partial pressure of the remaining gas.