Question

Challenge Air is a mixture of gases. By percentage, it is roughly 78 percent nitrogen, 21 percent oxygen, and 1 percent argon. (There are trace amounts of many other gases in air.) If the atmospheric pressure is 760 mm Hg, what are the partial pressures of nitrogen, oxygen, and argon in the atmosphere?

Short answer

The partial pressures of nitrogen, oxygen, and argon in the atmosphere are 592.8 mm Hg, 159.6 mm Hg, and 7.6 mm Hg, respectively.

Step-by-step solution

Calculate the partial pressure of nitrogen

To calculate the partial pressure of nitrogen, simply multiply the percentage of nitrogen (78%) by the atmospheric pressure (760 mm Hg). Partial Pressure of Nitrogen = 0.78 * 760 mm Hg

Calculate the partial pressure of oxygen

To calculate the partial pressure of oxygen, simply multiply the percentage of oxygen (21%) by the atmospheric pressure (760 mm Hg). Partial Pressure of Oxygen = 0.21 * 760 mm Hg

Calculate the partial pressure of argon

To calculate the partial pressure of argon, simply multiply the percentage of argon (1%) by the atmospheric pressure (760 mm Hg). Partial Pressure of Argon = 0.01 * 760 mm Hg

Calculate the partial pressures

Now, compute the partial pressures by plugging in the values in steps 1, 2, and 3. Partial Pressure of Nitrogen = 0.78 * 760 mm Hg = 592.8 mm Hg Partial Pressure of Oxygen = 0.21 * 760 mm Hg = 159.6 mm Hg Partial Pressure of Argon = 0.01 * 760 mm Hg = 7.6 mm Hg Thus, the partial pressures of nitrogen, oxygen, and argon in the atmosphere are 592.8 mm Hg, 159.6 mm Hg, and 7.6 mm Hg, respectively.

Key concepts

Dalton's Law of Partial Pressures

When studying mixtures of gases, an important principle to understand is Dalton's Law of Partial Pressures. This law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the individual pressures each gas would exert if it were alone. That is, the total pressure (\( P_{total} \)) is a sum of the partial pressures (\( P_{gas1} \) + \( P_{gas2} \) + ... + \( P_{gasn} \) ).

Diving into the concept of partial pressures for our atmospheric example, we can apply Dalton's Law directly. Each gas (_e.g._, nitrogen, oxygen, and argon) has partial pressure proportional to its mole fraction. This relates directly to the percent of each gas in the mixture. For our scenario, to find the partial pressure of a single gas, you multiply its percentage concentration by the total atmospheric pressure. This simple calculation hinges on Dalton's Law, which facilitates understanding of pressure contributions for each gas within a mixture.

Understanding Dalton's Law is vital in various scientific and engineering fields such as chemistry, physics, and environmental science as it influences the behavior of gases under different conditions.

Atmospheric Pressure

Atmospheric pressure, also called barometric pressure, is the force exerted onto a surface by the weight of the air above that surface in the atmosphere of Earth (or that of another planet). At sea level, the average atmospheric pressure is about 760 millimeters of mercury (mm Hg) or 1013.25 millibars. Atmospheric pressure decreases with higher altitudes.

The value of atmospheric pressure is crucial when we calculate partial pressures of gases. As observed in our exercise, knowing that the atmospheric pressure is 760 mm Hg serves as a baseline to determine the partial pressures of nitrogen, oxygen, and argon. It's like putting a pie into slices - the atmospheric pressure is the whole pie, and the partial pressures are the slices, with the size of each slice depending on the gas's relative amount in the total mixture.

Measuring atmospheric pressure is essential in meteorology for weather forecasting, in aviation for altitude setting and also in various scientific research fields that require precision in gas-related experiments.

Gas Composition

Gas composition refers to the breakdown of a gas mixture into its constituent gases and their respective proportions. For example, Earth's atmosphere is composed primarily of nitrogen, oxygen, and argon, with each of these gases present in specific percentages. It's quite similar to a recipe, where each ingredient must be measured and combined in the right proportions to achieve the desired result.

In the given problem, we have percentages of 78% nitrogen, 21% oxygen, and 1% argon. These values are not arbitrary; they are measurements that have been determined through scientific observation and analysis. Knowing the composition is essential because it influences how gases behave, how they interact with other substances, and their overall effect on the environment.

When scientists or engineers work with gases, be it in the laboratory or industry, understanding gas composition is fundamental to safely managing reactivity, toxicity, and efficiency of chemical processes. It's also foundational for environmental monitoring and control strategies.