Question

Air contains nitrogen, oxygen, argon, and trace gases. If the partial pressure of nitrogen is \(587 \mathrm{~mm} \mathrm{Hg}\), oxygen is \(158 \mathrm{~mm} \mathrm{Hg}\), argon is \(7 \mathrm{~mm} \mathrm{Hg}\), and trace gas pressure is negligible, what is the atmospheric pressure?

Short answer

Atmospheric pressure is 752 mm Hg.

Step-by-step solution

Understand Partial Pressure

Partial pressure refers to the pressure exerted by an individual gas in a mixture. In this problem, we're given the partial pressures of nitrogen, oxygen, and argon.

List Given Partial Pressures

The partial pressures are: Nitrogen = 587 mm Hg, Oxygen = 158 mm Hg, Argon = 7 mm Hg. Trace gas pressure is negligible, so we don't include it in our calculation.

Sum the Partial Pressures

The atmospheric pressure is the sum of all the partial pressures. Therefore, calculate the sum as follows: \[ 587 \, \text{mm Hg (Nitrogen)} + 158 \, \text{mm Hg (Oxygen)} + 7 \, \text{mm Hg (Argon)} \]

Calculate the Atmospheric Pressure

Add the partial pressures: \[ 587 + 158 + 7 = 752 \, \text{mm Hg} \] Thus, the atmospheric pressure is 752 mm Hg.

Key concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air above us. This pressure is due to a combination of gases in the atmosphere. Each type of gas contributes to the total atmospheric pressure based on its percentage or proportion.
The standard atmospheric pressure at sea level is approximately 760 mm Hg. This value can change based on altitude and weather conditions. In the given exercise, atmospheric pressure was determined by summing the partial pressures of individual gases present in the air mixture. Understanding atmospheric pressure helps us grasp how we experience weather changes and how air behaves in different conditions.

Mixture of Gases

A mixture of gases means that multiple gases exist together in the same space and exert a combined pressure. Air is a perfect example of a gas mixture, mainly composed of nitrogen, oxygen, argon, and small amounts of other gases called trace gases.
These gases do not react chemically within the atmosphere under normal conditions but contribute their partial pressures independently. Partial pressure is crucial because it allows us to calculate the contribution of each gas to the total pressure. When combined, like in the exercise, these partial pressures give us the total atmospheric pressure.
It's interesting to note that although nitrogen is the most abundant, having various gases in the atmosphere plays a vital role in sustaining life and maintaining environmental balances.

Gas Laws

Gas laws are fundamental principles describing how gases behave in relation to pressure, volume, and temperature. These laws help us predict the behavior of gases in different conditions.
Boyle's Law, Charles's Law, and the Ideal Gas Law are among the most relevant. Boyle's Law relates pressure and volume, explaining how gas expands as pressure decreases. Charles's Law connects temperature and volume, noting that gases expand when heated.
The Ideal Gas Law combines these relationships into a single equation, \[ PV = nRT \]where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.
Although the exercise primarily focuses on partial pressures, gas laws provide a deeper understanding of the properties and behaviors of gases in various conditions.