Question

What is the total pressure, in \(\mathrm{mmHg}\), of a gas mixture containing argon gas at \(0.25\) atm, helium gas at \(350 \mathrm{mmHg}\), and nitrogen gas at 360 torr?

Short answer

The total pressure is 900 mmHg.

Step-by-step solution

- Understanding the problem

We need to find the total pressure of a gas mixture. Each gas has its individual pressure, but they are given in different units. First, we need to convert all pressures to the same unit.

- Convert argon gas pressure to mmHg

The pressure of argon gas is given as 0.25 atm. We need to convert this to mmHg. We know that 1 atm = 760 mmHg. Therefore, the pressure of argon gas in mmHg is: \[ 0.25 \text{ atm} \times 760 \text{ mmHg/atm} = 190 \text{ mmHg} \]

- Helium gas pressure is already in mmHg

The pressure of helium gas is given as 350 mmHg. No conversion is needed.

- Convert nitrogen gas pressure to mmHg

The pressure of nitrogen gas is given as 360 torr. We need to convert this to mmHg. Since 1 torr = 1 mmHg, the pressure remains the same: \[ 360 \text{ torr} = 360 \text{ mmHg} \]

- Calculate the total pressure

Now that all pressures are in the same unit (mmHg), we can add them together to find the total pressure: \[ 190 \text{ mmHg (argon)} + 350 \text{ mmHg (helium)} + 360 \text{ mmHg (nitrogen)} = 900 \text{ mmHg} \]

Key concepts

unit conversion

When dealing with problems involving different units of pressure, the first thing to do is to convert them all into a common unit. By doing this, we can add them together easily.

For example, in this exercise, the gas pressures were given in units of atm, mmHg, and torr. To harmonize these:

• The first step is to know the conversion factors: 1 atm = 760 mmHg and 1 torr = 1 mmHg.
• Through these conversions, you can now convert argon’s pressure from atm to mmHg and nitrogen’s pressure from torr to mmHg.
• Remember, unit conversion is crucial for accurate calculations.

Understanding unit conversion ensures that you can work with varied data and still come up with a meaningful result.

partial pressures

The total pressure of a gas mixture is the sum of the partial pressures of the individual gases in that mixture. Each gas in the mixture exerts a pressure independently of the others.

Here's what you need to know about partial pressures:

• A partial pressure is the pressure that each gas would exert if it alone occupied the whole volume of the mixture.
• By adding the partial pressures of argon, helium, and nitrogen, you get the total pressure.
• The concept of partial pressures is fundamental in understanding how gases interact in a mixture.

Diving deeper into partial pressures helps explain why gases behave independently in a mixture, making it easy to calculate the total pressure.

ideal gas law

Understanding the ideal gas law, even briefly, can provide a better picture of gas behavior. The ideal gas law is expressed as \[PV = nRT\]where:

• P is the pressure of the gas,
• V is its volume,
• n is the number of moles,
• R is the ideal gas constant,
• T is the temperature in Kelvin.

This law connects pressure, volume, and temperature of an ideal gas.

In the context of the exercise, knowing this helps in understanding why pressure changes with volumes and temperatures, but isn't directly used for the given problem.

Even when not directly applicable, the ideal gas law is foundational knowledge for advanced gas calculations.

gas mixture

When dealing with a gas mixture, it’s essential to understand the behavior of different gases combined together. Each gas in a mixture behaves as if it’s alone in the container.

Here's a quick rundown:

• Each gas's pressure is unaffected by the type of gases present.
• The total pressure depends on the sum of all partial pressures.
• Examples include air, which is a mixture of nitrogen, oxygen, argon, etc.

Understanding gas mixtures is crucial since many real-world applications involve mixed gases, from breathing air to industrial gas applications.With this knowledge, you can easily determine the total pressure of any gas mixture by summing up individual gas pressures, as demonstrated.