Question

For a mixture of gases in the same container, the total pressure exerted by the mixture of gases is the \(\quad\) of the pressures that those gases would exert if they were alone in the container under the same conditions.

Short answer

For a mixture of gases in the same container, the total pressure exerted by the mixture of gases is the \(\textbf{sum}\) of the pressures that those gases would exert if they were alone in the container under the same conditions.

Step-by-step solution

Recall Dalton's Law of Partial Pressures

According to Dalton's Law of Partial Pressures, the total pressure exerted by a mixture of non-reacting gases in a container is equal to the sum of their individual partial pressures when they are occupying the same volume and under the same temperature and pressure conditions. Mathematically, this can be represented as: \[P_\text{total} = P_1 + P_2 + P_3 + \dots + P_n\] Where \(P_\text{total}\) is the total pressure exerted by the mixture of gases, and \(P_1\), \(P_2\), \(P_3\), ..., \(P_n\) are the partial pressures exerted by each individual gas in the mixture.

Complete the Statement

Now, let's complete the statement using Dalton's Law: For a mixture of gases in the same container, the total pressure exerted by the mixture of gases is the \(\textbf{sum}\) of the pressures that those gases would exert if they were alone in the container under the same conditions.

Key concepts

Total Pressure of Gas Mixture

Understanding the concept of the total pressure of a gas mixture is fundamental when studying gas laws in chemistry. This total pressure is essentially the collective force that a mixture of gases applies on the walls of its container. Picture this as a team of individuals each pushing on a wall; the total pressure is like the combined effort of all the team members.

According to Dalton's Law of Partial Pressures, which is a cornerstone in chemical thermodynamics, when you have different gases mixed in a container, they behave as if they are alone. Each gas contributes a part of the total pressure, and the sum of these individual contributions gives you the total pressure exerted by the mixture. This is crucial for predicting how gases will behave under different conditions and is used extensively in fields such as environmental science, engineering, and medicine.

Partial Pressure

If we dive deeper into the concept of partial pressure, we can view it as the pressure a gas would exert if it alone occupied the entire volume of the mixture at the same temperature. This is a virtual scenario, as in reality, gases are mixed together. But what Dalton's Law tells us is that gases don't intrude on each other's 'personal space' - they act independently when it comes to pressure. This independent behavior simplifies how we can calculate the pressure of each gas in a mixture. Just isolate each gas and consider its contribution to the total pressure, as shown in the mathematical representation \(P_\text{total} = P_1 + P_2 + P_3 + \dots + P_n\).

When you're dealing with practical applications, such as respiratory therapy or chemical reactions in the industry, you often need to know how much of a particular gas is present. That's where understanding partial pressures becomes valuable.

Gas Laws in Chemistry

Gas laws in chemistry are a series of fundamental principles that describe how gases behave under various conditions of pressure, volume, and temperature. These laws provide the framework within which the behavior of gases can be predicted and manipulated.

The most well-known gas laws include Boyle's Law, which tells us about the pressure-volume relationship at constant temperature, and Charles's Law, which explains how gas volume changes with temperature. However, there are several others like Avogadro's Law and the Ideal Gas Law, which further explain the relationships between gas physical quantities.

Dalton's Law fits into this assortment as a way to handle mixtures of gases by considering each gas's individual pressure contribution. It’s like having a collaborative project with several team-members, and each one's input is evaluated independently to gauge the total outcome. Dalton's Law allows us to apply these individual properties to complex systems, which can be encountered in real-world scenarios, from the science of diving to aerospace engineering and beyond. With gas laws, chemistry gives us the tools to both understand nature and harness it for various applications.