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? (Vapour pressure of water at \(28^{\circ} \mathrm{C}=28.3 \mathrm{mmHg}\) ) (a) \(348.7 \mathrm{mmHg}\) (b) \(377 \mathrm{mmHg}\) (c) \(384.7 \mathrm{mmHg}\) (d) none of these

Short answer

348.7 mmHg

Step-by-step solution

- Total Pressure of Gas Mixture

Note down the total pressure of the gas mixture collected over water, which is given as 745 mmHg.

- Pressure of Helium

Record the partial pressure of helium in the mixture, which is 368 mmHg.

- Vapour Pressure of Water

Vapour pressure of water at 28.0°C is 28.3 mmHg. This pressure is due to the water vapour present in the collected gas mixture.

- Calculate Neon's Partial Pressure

Use Dalton's Law of Partial Pressures which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. Subtract the partial pressure of helium and the vapour pressure of water from the total pressure to find the partial pressure of neon: Neon's Partial Pressure = Total Pressure - Helium's Partial Pressure - Water Vapour Pressure

Key concepts

Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures is a fundamental principle in physical chemistry, particularly when dealing with mixtures of gases. According to this law, in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases. This can be expressed mathematically as \[ P_{total} = P_1 + P_2 + P_3 + ... + P_n \] where \( P_{total} \) represents the total pressure of the mixture, and \( P_1, P_2, P_3,..., P_n \) represent the partial pressures of the individual gases in the mixture.

For instance, if we consider a container filled with a mixture of helium and neon, the pressure inside the container is the sum of the pressure that would be exerted by each gas if it were alone in the container. Dalton's Law is particularly useful in scenarios where gases are collected over water since the vapor pressure of water needs to be considered as one of the partial pressures in the system.

Gas Mixture

A gas mixture is composed of two or more different gases that are mixed together without any chemical reaction between them. These gases retain their individual properties, such as mass and partial pressure. In our context, the gas mixture refers to a particular combination of helium and neon gases, along with water vapor, which is inherently present due to the collection method over water.

In the context of partial pressure calculations, the behavior of gas mixtures is described by the ideal gas law when each gas behaves ideally. However, in reality, factors such as non-ideal behavior at high pressures or low temperatures can complicate the situation. For educational exercises and most practical purposes, the ideal gas behavior is a sufficient approximation.

Vapor Pressure of Water

The vapor pressure of water is the pressure exerted by water vapor when it is in equilibrium with its liquid or solid phase. At any given temperature, there is a specific vapor pressure for water. This value is crucial for solving problems involving gas collections over water because it represents the part of the total pressure that is due to water vapor.

For example, at \(28.0^\circ\mathrm{C}\), water has a vapor pressure of \(28.3 \mathrm{mmHg}\). This means that even in the absence of any other gas, water vapor would exert a pressure of \(28.3 \mathrm{mmHg}\) at this temperature. In partial pressure problems, it is essential to subtract the vapor pressure of water from the total pressure to obtain the pressure that is solely due to the other gases in the mixture.

JEE Physical Chemistry Problems

JEE (Joint Entrance Examination) is a highly competitive exam in India for students who wish to pursue engineering at the undergraduate level. Physical chemistry problems in the JEE often test a student's understanding of fundamental concepts like partial pressures in gas mixtures, which are a key part of the JEE Physical Chemistry syllabus.

Problems related to Dalton's Law of Partial Pressures require a clear understanding of the law and its application to solve for unknown pressures. Exercises often include collecting gases over water, which introduces the concept of vapor pressure and necessitates its inclusion in calculations. Students are expected to perform these calculations with precision and accuracy to arrive at the correct answer, as seen in the given problem where students must calculate the partial pressure of neon in a gas mixture.