Question

In a gas mixture, the partial pressures are nitrogen 425 torr, oxygen 115 torr, and helium 225 torr. What is the total pressure (torr) exerted by the gas mixture?

Short answer

The total pressure is 765 torr.

Step-by-step solution

- Identify the Given Partial Pressures

The problem provides the partial pressures of three gases. Nitrogen has a partial pressure of 425 torr, oxygen has a partial pressure of 115 torr, and helium has a partial pressure of 225 torr.

- Recall Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas in the mixture.

- Add the Partial Pressures

Using Dalton's Law, add the partial pressures of nitrogen, oxygen, and helium to find the total pressure: \[ P_{total} = P_{N_2} + P_{O_2} + P_{He} \] where, \( P_{N_2} = 425 \) torr \( P_{O_2} = 115 \) torr and \( P_{He} = 225 \) torr \[ P_{total} = 425 + 115 + 225 = 765 \text{ torr} \]

Key concepts

headline of the respective core concept

Dalton's Law of Partial Pressures is a fundamental concept in chemistry that helps us understand the behavior of gases in a mixture. This law states that the total pressure exerted by a mixture of non-reacting gases is the sum of the partial pressures of each individual gas present. In simple terms, each gas in a mixture acts independently, and the total pressure is the sum of their individual pressures. To find the total pressure, we simply add the partial pressures of all gases involved.

headline of the respective core concept

In a gas mixture, each gas contributes to the overall pressure based on its partial pressure. Partial pressure is the pressure that each gas would exert if it were the only gas present in the volume. Understanding partial pressures is crucial for calculating the total pressure in a gas mixture, as shown by Dalton's Law. To find the partial pressure of a gas, we can use the equation: \ \[P_{i} = (\text{mole fraction of gas } i) \times (\text{total pressure}) \] \ For example, if we know the mole fraction and the total pressure, we can easily calculate the partial pressure of each gas.

headline of the respective core concept

Gas mixtures are common in both natural and industrial processes. A gas mixture is composed of different gases that share the same physical space but do not chemically react with each other. Common examples include air, which is a mixture of nitrogen, oxygen, carbon dioxide, and other trace gases. When dealing with gas mixtures, it is essential to understand how each component behaves individually and in combination with others. This knowledge allows scientists and engineers to predict and manipulate gas behavior for various applications, such as in respiratory therapy, scuba diving, and chemical manufacturing.