Question

What is the total pressure of a gas mixture containing these partial pressures: \(P_{\mathrm{Ne}}=312\) torr, \(P_{\mathrm{He}}=799\) torr, and \(P_{\mathrm{Ar}}=831\) torr?

Short answer

The total pressure of the gas mixture is 1942 torr.

Step-by-step solution

Understanding Partial and Total Pressure

When dealing with gas mixtures, the total pressure is the sum of the partial pressures of each individual gas in the mixture. This follows Dalton's Law of Partial Pressures, which states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases present in the mixture.

Identify the Partial Pressures

From the problem, we have three partial pressures: - The partial pressure of neon ( P_{ ext{Ne}} ) is 312 torr. - The partial pressure of helium ( P_{ ext{He}} ) is 799 torr. - The partial pressure of argon ( P_{ ext{Ar}} ) is 831 torr.

Apply Dalton's Law of Partial Pressures

According to Dalton's Law, the total pressure (P_{ ext{total}}) of the gas mixture can be calculated by adding the partial pressures of the individual gases: \[ P_{ ext{total}} = P_{ ext{Ne}} + P_{ ext{He}} + P_{ ext{Ar}} \] Substituting the values, we have: \[ P_{ ext{total}} = 312 ext{ torr} + 799 ext{ torr} + 831 ext{ torr} \]

Calculate the Total Pressure

Perform the arithmetic to find the total pressure: \[ P_{ ext{total}} = 312 + 799 + 831 \] \[ P_{ ext{total}} = 1942 ext{ torr} \]

Key concepts

Total Pressure

Imagine you have a box filled with different kinds of gas. Each type of gas in this box contributes to the force they exert on the walls, and this force is what we call pressure. To find the total pressure, you need to add up all these forces from each gas. This idea is expressed in Dalton's Law of Partial Pressures. This law is very helpful when you have a mixture of different gases.

Dalton's Law tells us that the total pressure of a gas mixture is simply the sum of the pressures each gas would exert if it were alone. So, if we have neon, helium, and argon all together in a container, each one presses against the container walls. Adding these pressures gives you the total pressure exerted by the gas mixture. This total pressure helps us understand how much force the entire mixture is applying, which can be useful in many scientific and industrial applications.

Partial Pressure

Each gas in a mixture can be thought of as if it occupies the whole volume by itself. This makes calculating its pressure straightforward. The pressure it exerts in this scenario is its partial pressure.

Partial pressure depends on the amount of gas present and is independent of the presence of other gases in the mixture. For the exercise at hand, we have three gases:

• Neon with a partial pressure of 312 torr.
• Helium with a partial pressure of 799 torr.
• Argon with a partial pressure of 831 torr.

Dalton's Law makes these partial pressures easy to handle. Even if more gases were added, you would only need to add each new gas's partial pressure to find the new total. Understanding partial pressures helps chemists and engineers predict how gases in a mixture will behave under different conditions.

Gas Mixture

A gas mixture refers to a combination of different gases within a single container. This mixture behaves predictably thanks to laws like Dalton's Law of Partial Pressures. Different gases in a mixture don't react with each other in ways that could complicate calculations of pressure. This makes it easier to measure and predict how the mixture will behave overall.

When you look at a gas mixture, each type of gas contributes to the mixture's overall properties, including pressure. This is particularly important in environments where precise pressure control is needed, like in medical breathing systems or chemical reactions that require specific conditions. Understanding how each gas adds to the total is critical in these settings. By grasping how gas mixtures work, you gain insight into areas like

• industrial chemical processes,
• brewing, and even space exploration.

In every case, the predictable way gas mixtures behave helps us manipulate and utilize them effectively.