Question

In a gas mixture, the partial pressures are argon \(415 \mathrm{mmHg}\), neon \(75 \mathrm{mmHg}\), and nitrogen \(125 \mathrm{mmHg}\). What is the total pressure (atm) exerted by the gas mixture?

Short answer

The total pressure exerted by the gas mixture is approximately 0.81 atm.

Step-by-step solution

- Understand Partial Pressures

In a gas mixture, each gas exerts pressure independently of the others. This independent pressure is known as the partial pressure. To find the total pressure, sum the partial pressures of all the gases.

- Sum the Partial Pressures

Add the partial pressures of argon, neon, and nitrogen: \[ P_{total} = P_{argon} + P_{neon} + P_{nitrogen} \] Given: \[ P_{argon} = 415 \text{ mmHg} \] \[ P_{neon} = 75 \text{ mmHg} \] \[ P_{nitrogen} = 125 \text{ mmHg} \] Adding these values together: \[ P_{total} = 415 \text{ mmHg} + 75 \text{ mmHg} + 125 \text{ mmHg} = 615 \text{ mmHg} \]

- Convert the Total Pressure to atm

There are 760 mmHg in one atmosphere (atm). To convert the total pressure from mmHg to atm, divide the total pressure in mmHg by 760: \[ P_{total} (atm) = \frac{P_{total} (mmHg)}{760} \] Plugging in our total pressure: \[ P_{total} (atm) = \frac{615 \text{ mmHg}}{760 \text{ mmHg/atm}} \approx 0.81 \text{ atm} \]

Key concepts

Partial Pressure

Partial pressure is the pressure that a single gas in a mixture of gases would exert if it occupied the entire volume by itself. Each gas in a mixture behaves independently and contributes to the overall pressure proportionately. For example, in the given exercise, argon, neon, and nitrogen each have their own partial pressures: 415 mmHg, 75 mmHg, and 125 mmHg, respectively. Understanding partial pressure helps us predict how gases in a mixture will behave, and it is a fundamental concept in gas laws, particularly Dalton's Law of Partial Pressures. To find the total pressure of the mixture, you simply add the partial pressures of all the gases together. This gives a clear pathway to sum up and understand the total contributions of each gas in a mixture.

Total Pressure

Total pressure is essentially the sum of all the partial pressures of the gases in a mixture. According to Dalton's Law of Partial Pressures, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas. In the exercise, the total pressure (denoted as \(P_{total}\)) is computed using:

• \(P_{argon} = 415 \text{ mmHg}\)
• \(P_{neon} = 75 \text{ mmHg}\)
• \(P_{nitrogen} = 125 \text{ mmHg}\)

By adding the partial pressures together: \[P_{total} = 415 \text{ mmHg} + 75 \text{ mmHg} + 125 \text{ mmHg} = 615 \text{ mmHg}\] This sum represents the cumulative pressure exerted by the mixture of argon, neon, and nitrogen gases within the given volume.

Pressure Conversion

Converting pressure from one unit to another is a common task in chemistry. In the exercise, we need to convert the total pressure from mmHg to atmospheres (atm). Here, we use the conversion factor where 1 atm = 760 mmHg to make this switch. Given that we have a total pressure of 615 mmHg, we perform the following division to convert to atm: \[P_{total} (atm) = \frac{615 \text{ mmHg}}{760 \text{ mmHg/atm}} \approx 0.81 \text{ atm}\] This conversion is essential in many fields ranging from meteorology to engineering, where different units of pressure might be used. Knowing how to easily navigate between these units ensures accuracy in calculations and better comprehension of the concepts discussed.