Question

A deep-sea scuba tank contains oxygen and helium gases. If the partial pressures of the gases are 35 atm and 125 atm, what is the total pressure (in psi)?

Short answer

The total pressure is 2352 psi.

Step-by-step solution

Understand the Problem

We need to find the total pressure inside a scuba tank that contains oxygen and helium gases, using their given partial pressures. The problem asks for the total pressure in units of psi.

Calculate Total Pressure in atm

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. Here, the total pressure in atm is calculated by adding the partial pressures of oxygen and helium:\[P_{total} = P_{O2} + P_{He} = 35\, \text{atm} + 125\, \text{atm}\]Calculating this gives us:\[P_{total} = 160\, \text{atm}\]

Convert Total Pressure to psi

We have the total pressure in atm, and we need to convert it to psi using the conversion factor. We know that \(1\, \text{atm} = 14.7\, \text{psi}\). Thus, the total pressure in psi is:\[P_{total(\text{psi})} = P_{total} \times 14.7 = 160 \times 14.7\]Calculating this gives:\[P_{total(\text{psi})} = 2352\, \text{psi}\]

Key concepts

Understanding Partial Pressure

Partial pressure is a fundamental concept in gas laws, particularly in Dalton's Law of Partial Pressures. It refers to the pressure that a single type of gas in a mixture would exert if it alone occupied the entire volume. This means that for any gas mixture, such as the oxygen and helium in a scuba tank, each gas contributes to the total pressure independently of the others.

• The partial pressure of oxygen in this case is 35 atm.
• The partial pressure of helium is 125 atm.

Dalton's law simply adds these to get the total pressure. It's helpful to think of partial pressures as the unique footprint each gas leaves in the space it occupies. This individual pressure helps to predict the behavior of the gas, such as how it will diffuse and react in the mixture.

Calculating Total Pressure

The process of calculating total pressure in a gas mixture is straightforward with Dalton's Law of Partial Pressures. This law states:

• The total pressure exerted by a mixture of gases is the sum of the partial pressures of each gas present.
• This can be mathematically expressed as: \(P_{total} = P_{gas1} + P_{gas2} + ... + P_{gasn}\).

For our scuba tank, the calculation was simple:

• For oxygen (P_{O2}), the partial pressure was 35 atm.
• For helium (P_{He}), it was 125 atm.
• This gives: \(P_{total} = 35 \, \text{atm} + 125 \, \text{atm} = 160 \, \text{atm}\).

Add these two values up, and you have 160 atm as the total pressure that's acting on the walls of the scuba tank.

Converting Pressure Units

Pressure conversion is an important skill, especially in different scientific and engineering fields where pressure is measured in various units. In our exercise, pressure conversion was necessary to express the total pressure in psi instead of atm.

• We use the conversion factor where \(1 \, \text{atm} = 14.7 \, \text{psi}\).

To convert 160 atm to psi:

• You multiply the atm value by the conversion factor: \(160 \, \text{atm} \times 14.7 \, \text{psi/atm} = 2352 \, \text{psi}\).

The step ensures that if you need to express pressure in a different unit, you can find the correct equivalent. This practice is crucial for projects that demand precision between metric and imperial units, such as engineering designs and weather forecasting.