Problem 17 - A Complete Resource Book in Chemistry for JEE Main

Question

A closed container contains equal number of oxygen and hydrogen molecules at a total pressure of \(740 \mathrm{~mm}\). If oxygen is removed from the system then pressure will (a) become double of \(740 \mathrm{~mm}\) (b) become half of \(740 \mathrm{~mm}\) (c) become \(1 / 9\) of \(740 \mathrm{~mm}\) (d) remain unchanged

Step-by-Step Solution

Answer

The pressure will become half of 740 mm, i.e., 370 mm Hg.

Step 1: Understanding the Problem

We have a closed container with equal numbers of oxygen and hydrogen molecules, resulting in a total pressure of 740 mm Hg due to both gases. The question asks what happens to the pressure if the oxygen is removed, leaving only hydrogen.

Step 2: Identify the Contribution of Each Gas

Since there are equal numbers of oxygen and hydrogen molecules, and according to Dalton's Law of Partial Pressures, each gas contributes equally to the total pressure. Hence, each gas contributes half of the total pressure. Therefore, the pressure contributed by oxygen is \( \frac{740}{2} = 370 \mathrm{~mmHg} \) and the pressure contributed by hydrogen is also \( 370 \mathrm{~mmHg} \).

Step 3: Effect of Removing Oxygen

Removing the oxygen molecules from the container means that only hydrogen molecules remain. Therefore, the pressure will now be solely due to the hydrogen molecules, which contribute \( 370 \mathrm{~mmHg} \).

Step 4: Conclusion Based on Options

The new pressure is \( 370 \mathrm{~mmHg} \), which is half of the initial total pressure. Therefore, the correct choice is (b) become half of \( 740 \mathrm{~mm} \).

Key Concepts

Partial Pressure

When examining a gas mixture, it's important to understand the concept of partial pressure. This term refers to the pressure that an individual gas in a mixture would exert if it were the only gas in that volume. According to Dalton's Law of Partial Pressures, the total pressure in a mixture is the sum of the partial pressures of each component gas.

For example, consider oxygen and hydrogen dispersed equally in a closed container. Both gases exert a pressure, and this contributes equally to the overall pressure reading. Hence, if the total pressure is measured at 740 mm Hg and the gases are equal in number, each gas, including oxygen and hydrogen, contributes 370 mm Hg as their partial pressure. This is essential to calculate any individual gas pressure when other gases are mixed with it.

This principle is particularly useful when dealing with gases in laboratory settings or industrial applications where gas interactions are critical.

Gas Laws

Gas laws are critical to understanding how gases behave under various conditions. A key principle among these laws is Dalton's Law of Partial Pressures. This law states that the total pressure exerted by a mixture of non-reacting gases equals the sum of the partial pressures of each individual gas.

In our example of oxygen and hydrogen, both gases abide by these laws in the closed container. Considering they are present in equal amounts, each behaves ideally, contributing equally to the total pressure within the vessel. Gas laws provide the foundation to predict how changes in volume, temperature, or gas quantity will impact the total pressure.

Understanding these gas laws can aid in a variety of scientific investigations, from calculating the results of chemical reactions to determining the pressure changes when one component of a gas mixture is altered.

Pressure Calculation

Calculating pressure in a mixture of gases involves breaking down the contributions of each individual gas. According to Dalton's Law, it is quite straightforward to determine each gas's influence on the total pressure.

In the scenario with a total pressure of 740 mm Hg, removing oxygen allows us to see the direct impact on pressure. By eliminating the 370 mm Hg contributed by oxygen, the pressure recalibrates to just the hydrogen's original contribution. Hence, the pressure falls to 370 mm Hg. This clear example shows how partial pressures operate independently but cohesively to form the total pressure in any gas mixture.

Being able to break down and execute such pressure calculations is vital in fields that manipulate gases, ranging from medical oxygen supply to scuba diving mixtures.