Question

Air contains nitrogen, oxygen, argon, and trace gases. If the partial pressure of nitrogen is \(592 \mathrm{~mm} \mathrm{Hg}\), oxygen is \(160 \mathrm{~mm} \mathrm{Hg}\), argon is \(7 \mathrm{~mm} \mathrm{Hg}\), and trace gas is \(1 \mathrm{~mm} \mathrm{Hg}\), what is the atmospheric pressure?

Short answer

The atmospheric pressure is 760 mm Hg.

Step-by-step solution

Understand the Concept

Atmospheric pressure is the sum of the partial pressures of all the gases present in the atmosphere. This means we need to add together the partial pressures of nitrogen, oxygen, argon, and trace gases to find the total atmospheric pressure.

Identify Gases and Pressures

The partial pressures are given as follows: - Nitrogen: 592 mm Hg - Oxygen: 160 mm Hg - Argon: 7 mm Hg - Trace gases: 1 mm Hg.

Add the Partial Pressures

To find the total atmospheric pressure, add the partial pressures of all the gases:\[\text{Total Pressure} = 592 \text{ mm Hg (Nitrogen)} + 160 \text{ mm Hg (Oxygen)} + 7 \text{ mm Hg (Argon)} + 1 \text{ mm Hg (Trace gases)}\]

Calculate the Total Pressure

Perform the addition:\[\text{Total Pressure} = 592 + 160 + 7 + 1 = 760 \text{ mm Hg}\]. Therefore, the atmospheric pressure is 760 mm Hg.

Key concepts

Partial Pressure in Gaseous Mixtures

The concept of partial pressure is crucial in understanding gas mixtures, especially when it comes to atmospheric gases. Each gas within a mixture exerts its own pressure that contributes to the total pressure of the system. This is what we call the partial pressure. In simple terms, the partial pressure of a gas is the pressure it would exert if it occupied the entire volume by itself.
When dealing with atmospheric gases, their partial pressures collectively make up the atmospheric pressure we experience daily. Henry's Law and Dalton's Law are often key principles in calculating and understanding these pressures. Dalton's Law of Partial Pressures, in particular, states that the total pressure of a gas mixture is equal to the sum of the partial pressures of the individual gases.
For instance, in the original exercise, we calculated the atmospheric pressure by adding the partial pressures of nitrogen, oxygen, argon, and trace gases since atmospheric pressure is essentially the sum of these partial pressures. By understanding partial pressures, we can better predict gas behavior and properties in various atmospheric conditions.

Fundamentals of Gas Laws

Gas laws are fundamental rules that describe the behavior of gases in different scenarios. These laws help in understanding how gas particles interact with each other and the physical conditions affecting them, such as pressure, temperature, and volume.
Some of the main gas laws include:

• Boyle's Law - Relates pressure and volume at a constant temperature.
• Charles's Law - Relates volume and temperature at constant pressure.
• Avogadro's Law - Connects gas volume with the number of moles at a fixed temperature and pressure.
• Dalton's Law - Focuses on partial pressures in gas mixtures.

These laws are interrelated, consolidating into the Ideal Gas Law, represented by the equation: \[ PV = nRT \] where \( P \) is pressure, \( V \) is volume, \( n \) is the amount of substance, \( R \) is the gas constant, and \( T \) is temperature. This law is invaluable in chemistry problem-solving, allowing us to reason through gas behavior in diverse settings. Understanding these laws lays the groundwork for grasping how gases behave under varying environmental conditions.

Effective Chemistry Problem-Solving

Chemistry problem-solving, particularly in tasks involving gases, requires a strategic approach to efficiently tackle and resolve questions. Focus on understanding the problem, recognizing the relevant concepts, and applying the correct formulas or principles.
In our example of calculating atmospheric pressure, effective problem-solving involved recognizing that partial pressures needed to be summed to determine the total pressure. Here are some steps to enhance chemistry problem-solving skills:

• Read and understand the problem carefully to identify what is known and what needs to be determined.
• Identify the key concepts or laws applicable to the problem, such as Dalton's Law for partial pressures.
• Organize the information clearly, listing out given data such as pressure readings for different gases.
• Apply the appropriate formulas systematically and ensure each calculation step is logical and checks out.
• Review the solution to ensure all aspects of the problem have been addressed.

By following these strategies, students can improve their ability to solve chemistry problems related to gas laws and beyond, fostering better comprehension and application of scientific principles.