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

Short answer

The pressure becomes half of 740 mm, which is 370 mm.

Step-by-step solution

Understand Initial Conditions

Initially, the container has an equal number of oxygen and hydrogen molecules. This means the total pressure is contributed equally by both gases. The given total pressure is 740 mm.

Calculate Partial Pressure of Each Gas

Since both gases contribute equally, the partial pressures of oxygen and hydrogen are each half of the total pressure. Thus, the partial pressure of oxygen is \( \frac{740}{2} = 370 \mathrm{~mm} \) and the same for hydrogen.

Analyze Effect of Removing Oxygen

When the oxygen is removed, only hydrogen remains. The pressure now is only due to hydrogen, which initially was 370 mm.

Compare Remaining Pressure with Initial Condition

Originally, together the oxygen and hydrogen made a pressure of 740 mm. After removing oxygen, the remaining pressure is the partial pressure of hydrogen, which is 370 mm. This is half of the initial total pressure.

Key concepts

Partial Pressure

In a gas mixture, each gas contributes to the overall pressure, a concept known as partial pressure. Imagine it like how each person in a group contributes to the noise level in a quiet room. Each gas has its own individual pressure, known as the partial pressure. - The sum of all these partial pressures equals the total pressure of the gas mixture.- The formula to calculate the partial pressure of a gas is: \[ P_i = \frac{n_i}{n_{total}} \times P_{total} \] Where: - \(P_i\) is the partial pressure of gas \(i\). - \(n_i\) is the number of moles of gas \(i\). - \(n_{total}\) is the total number of moles of the gas mixture. - \(P_{total}\) is the total pressure of the gas mixture.In our exercise, the container holds an equal number of oxygen and hydrogen molecules, simplifying the partial pressure calculation to be equal for both gases.

Ideal Gas Law

The Ideal Gas Law is a fundamental concept that helps us understand the behavior of gases in different conditions. It is represented by the equation:\[ PV = nRT \]- \(P\) is the pressure of the gas.- \(V\) is the volume of the gas.- \(n\) is the number of moles of gas.- \(R\) is the universal gas constant.- \(T\) is the temperature in Kelvin.This law assumes that gases are made up of tiny particles and that these particles are in constant, random motion. Therefore, the behavior of real gases can closely approximate the predictions of the Ideal Gas Law under most conditions.

Molecular Composition

The molecular composition of a gas refers to the types and numbers of molecules that make up the gas. This concept is important because the properties of a gas such as density, molar mass, and behavior under different conditions depend highly on its molecular composition.- Oxygen molecules \((O_2)\) and hydrogen molecules \((H_2)\) are different in both mass and size.- Despite these differences, in a closed container, if both gases have an equal number of molecules, they contribute equally to the total pressure of the gas mixture.When oxygen is removed from the container in this exercise, we see a direct impact on the pressure due to a change in molecular composition. This also affects the calculated partial pressure after the removal.

Pressure Changes

Pressure changes in a gas system can occur due to several factors, such as temperature changes, volume changes, or alterations in the number of molecules present. In our example, removing oxygen gas from the container is akin to reducing the number of molecules exerting pressure inside the container, resulting in a decrease in the total pressure. - Initially, the total pressure was contributed equally by oxygen and hydrogen. - Upon removing the oxygen, hydrogen is left to exert its partial pressure alone, decreasing the total pressure by half. Understanding pressure change is crucial because many processes in real-life applications such as chemical reactions and industrial operations involve handling gases.