Question

A gas mixture containing oxygen, nitrogen, and helium exerts a total pressure of 925 torr. If the partial pressures are oxygen 425 torr and helium 75 torr, what is the partial pressure (torr) of the nitrogen in the mixture?

Short answer

The partial pressure of nitrogen is 425 torr.

Step-by-step solution

- Understand the given data

Identify the total pressure and the given partial pressures. Total pressure: 925 torr, partial pressure of oxygen: 425 torr, partial pressure of helium: 75 torr.

- Recall the formula for total pressure

The total pressure of a gas mixture is the sum of the partial pressures of the individual gases. This is expressed as: \( P_{total} = P_{O_2} + P_{N_2} + P_{He} \)

- Calculate the partial pressure of nitrogen

Subtract the partial pressures of oxygen and helium from the total pressure to find the partial pressure of nitrogen: \( P_{N_2} = P_{total} - P_{O_2} - P_{He} \) \( P_{N_2} = 925 \text{ torr} - 425 \text{ torr} - 75 \text{ torr} \) Calculate the result.

- Simplify

Perform the subtraction to find the partial pressure of nitrogen: \( P_{N_2} = 925 - 425 - 75 = 425 \)

Key concepts

Partial Pressure

Partial pressure is a key concept when dealing with gas mixtures. It represents the pressure that each gas in a mixture would exert if it were alone in the same volume. For example, in our exercise, the partial pressures are given for oxygen and helium, which are 425 torr and 75 torr respectively. Understanding partial pressure helps us determine the contribution of each gas to the total pressure in a mixture.

Dalton's Law

Dalton's Law of Partial Pressures is crucial for solving problems involving gas mixtures. Dalton's Law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases. Mathematically, this can be expressed as:

\( P_{total} = P_{1} + P_{2} + P_{3} + \text{...} \ \)where \( P_{total} \) is the total pressure, and \( P_{1}, P_{2}, P_{3}, \text{...}\) are the partial pressures of the gases in the mixture.
In our exercise, Dalton's Law helps us find the missing partial pressure of nitrogen by rearranging the formula to isolate the unknown partial pressure.

\( P_{N_2} = P_{total} - P_{O_2} - P_{He} \)We then plug in the numbers to find that the partial pressure of nitrogen is 425 torr.

Gas Laws

Gas laws are a set of rules that describe the behavior of gases. They include Boyle's Law, Charles's Law, and Avogadro's Law, among others. These laws help us predict how gases will react under different conditions of temperature, volume, and pressure. Dalton's Law, which we discussed earlier, is one of these gas laws. In our exercise, applying Dalton's Law helps us find the partial pressures and understand the contributions of each gas to the total pressure.

Understanding gas laws is essential in fields like chemistry, physics, and engineering, where gas behavior must be taken into account for various applications. These laws simplify complex mixtures into manageable steps, as seen in how we calculated the unknown partial pressure of nitrogen.

Chemistry

Chemistry is the study of matter, its properties, and the changes it undergoes. When it comes to gas mixtures, chemistry helps us understand the interactions between different gases and predict their behaviors. The concepts of partial pressure and Dalton's Law, for instance, are fundamental in the field of chemistry.

Imagine a scenario where we have a mixture of gases in a laboratory. By applying your knowledge of chemistry and the gas laws, you can calculate important metrics like total pressure, partial pressures, and more. This is crucial for experiments that require precise control over conditions. Our exercise is a perfect illustration of how these principles come into play in practical chemistry problems.