Question

What is partial pressure? What is the relationship between the partial pressures of each gas in a sample and the total pressure of gas in the sample?

Short answer

Partial pressure is the pressure that one gas in a mixture would exert if it alone occupied the entire volume. The relationship between partial pressures and total pressure is given by Dalton's Law, stating that the total pressure is the sum of all individual partial pressures.

Step-by-step solution

Understanding Partial Pressure

Partial pressure refers to the pressure that would be exerted by one of the gases in a mixture if it occupied the entire volume of the mixture alone at the same temperature. It is a measure of the contribution of each gas in a mixture to the overall pressure.

Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual component gases. Mathematically, this can be expressed as: \[ P_{total} = P_1 + P_2 + P_3 + \ldots + P_n \] where \( P_{total} \) is the total pressure, and \( P_1, P_2, P_3, ..., P_n \) are the partial pressures of the gases 1, 2, 3, ..., n in the mixture.

Key concepts

Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures is a principle in chemistry and physics that helps us understand how gases behave when they are mixed. Imagine you have different gases, each in separate containers. Each gas has its own pressure based on how many molecules it has and how much they are moving around.

Now, if you were to mix all those gases into one container, each gas would still exert its own pressure as if it were alone in the container, ignoring the presence of other gases. This individual pressure is what we call the partial pressure. So, Dalton's Law tells us that if you want to find the total pressure of this new mixture, you simply add up all the partial pressures.

This is crucial for a wide range of scientific and practical applications, such as understanding the behavior of gases in the atmosphere, calculating the required proportions of gas mixtures for industrial processes, or even determining the right mixture of breathing gases for deep-sea divers.

Gas Mixture

When we talk about a gas mixture, we’re referring to a combination of different gases occupying the same space without any chemical reaction taking place between them. Each gas within the mixture continues to act independently, which means that it exerts its own pressure, volume, and temperature. In a classroom setting, you could compare this to a group project where each student works on their part. They all contribute to the final project, but their parts are completed separately.

It's also worth noting that gases mix very well due to their high energy and motion, becoming evenly distributed throughout the mixture's volume. This principle of gas mixtures is important because it allows us to predict gas behavior using other laws of thermodynamics and to calculate each gas's partial pressure within the mixture easily.

Total Pressure in a Gas Mixture

Understanding the total pressure in a gas mixture is essential for many industrial and environmental applications. Imagine a balloon filled with helium, oxygen, and nitrogen; each of these gases contributes to filling out the balloon. But how much each one pushes against the balloon's walls is its partial pressure. The total pressure is simply the sum of these individual pressures.

Real-Life Importance

Knowing how to compute total pressure is critically important in fields such as meteorology, respiratory therapy, and engineering. For instance, weather prediction relies on understanding the pressure changes in the atmosphere, while respiratory therapists must know how to mix gases for patients to breathe correctly. Engineers, on the other hand, might use this concept while designing pressure-dependent systems.

In conclusion, the total pressure is like the sum of individual efforts contributing to a team's success, each gas doing its part.