Question

A bicycle tire contains nitrogen, oxygen, and argon gases. If the partial pressures are $51.0\mathrm{psi},13.5\mathrm{psi},$ and $0.5\mathrm{psi},$ what is the total pressure (in atm)?

Short answer

The total pressure is approximately 4.42 atm.

Step-by-step solution

Understanding Partial Pressure

The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture. Each gas exerts its own pressure, which contributes to the total pressure.

Adding Partial Pressures

To find the total pressure, add the partial pressures of nitrogen, oxygen, and argon gases. Calculate by adding: $51.0\text{psi}+13.5\text{psi}+0.5\text{psi}$. This results in a total pressure of $65.0\text{psi}$.

Converting psi to atm

To convert psi (pounds per square inch) to atm (atmospheres), use the conversion factor: $1\text{atm}=14.696\text{psi}$. Divide the total pressure in psi by the conversion factor: $\frac{65.0\text{psi}}{14.696\text{psi/atm}}$.

Calculating Total Pressure in atm

Perform the division to get the total pressure in atm: $\frac{65.0}{14.696}=4.42\text{atm}$. So, the total pressure in the tire is approximately $4.42\text{atm}$.

Key concepts

Total Pressure Calculation

The total pressure in a gas mixture is derived by adding up the partial pressures of the individual gases within the mixture. This is because each gas in a mixture behaves independently, contributing its own pressure to the total. For example, if you have nitrogen, oxygen, and argon in a bicycle tire, each of these gases will exert its specific partial pressure, and the cumulative effect is the total pressure. To calculate it, simply sum up these values:

In the given exercise, you have:

• Nitrogen: 51.0 psi
• Oxygen: 13.5 psi
• Argon: 0.5 psi

The calculation would be:

$$51.0extpsi+13.5extpsi+0.5extpsi=65.0extpsi$$This means that the total pressure exerted by the gas mixture is 65.0 psi.

Psi to Atm Conversion

Converting from psi to atm is a simple yet crucial step when dealing with gas pressure calculations in different units. The conversion factor between psi (pounds per square inch) and atm (atmospheres) is important to remember: $1extatm=14.696extpsi$.

When you need to convert pressure from psi to atm, you use this conversion factor by dividing the pressure in psi by 14.696:

For instance, with a total pressure of 65.0 psi, you calculate:

$$\frac{65.0extpsi}{14.696extpsi/atm}$$
This results in approximately 4.42 atm, meaning the total pressure in the tire, when converted, is 4.42 atm. This process is key in ensuring that you have the correct unit for various scientific calculations.

Gas Mixture Pressure

In a mixture of gases, each type of gas contributes to the total pressure in a way governed by Dalton's Law of Partial Pressures. This principle states that the total pressure of a gas mixture is equal to the sum of the partial pressures of all individual gases in the mixture.

Let's break this down:

• It's similar to how multiple contributors can add money to a shared account, where each person's contribution adds to the total sum.
• The partial pressure of a gas is essentially the pressure it would exert if it alone occupied the entire volume of the mixture at the same temperature.

So, in the example with nitrogen, oxygen, and argon in the bicycle tire, their respective pressures add up to make the total pressure. Understanding gas mixture pressures helps to predict and control how gases behave when combined, which is essential in fields like chemistry and engineering.