How to calculate partial pressure?

To calculate partial pressure you can:Use the equation of Dalton's Law if you have the total pressure of the mixture and the partial pressures of other gases present in the same mixture.Use the equation that relates partial pressure to the total pressure and the number of moles.

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If you have ever traveled to an area of high altitude, you might have experienced the feeling of not being able to breathe properly. Guess what? There is a reason why that happens, and you can thank partial pressure for making your life more difficult.

At higher altitudes, the partial pressure of oxygen decreases, making it more difficult for oxygen to get to the bloodstream. So, your body responds to the low amount of oxygen available by increasing your breathing rate and the volume of each breath you take.

Without further ado, let's dive into the world of Partial pressure!

First, we will define partial pressure.
Then, we will look at some properties related to partial pressure.
We will also dive into Dalton's law of partial pressure and Henry's Law.
Next, we will solve some problems involving partial pressure.
Lastly, we will talk about the importance of partial pressure and give some examples.

Definition of Partial Pressure of Gases

Before diving into partial pressure. Let's talk a little about pressure and its meaning.

Pressure is defined as the force exerted per unit area. Pressure is dependent on the magnitude of the applied force and the area to which the force is being applied. This pressure is produced by collisions on the walls of the container due to kinetic energy.

The greater the force exerted, the higher the pressure and the smaller the surface area.

The general formula for pressure is:

$P = \frac{Force (N)}{Area (m^{2})}$

Let's take a look at the following example!

What would happen to the pressure if the same amount of gas molecules was transferred from a 10.5 L container to a 5.0 L container?

We know that the formula for pressure is force divided by area. So, if we were to decrease the area of the container, then the pressure inside the container would increase.

You could also apply your understanding of Boyle's law here and say that since pressure and volume are inversely proportional to one another, decreasing the volume would increase the pressure!

The pressure of a gas can also be calculated by using the Ideal Gas Law (assuming the gases behave ideally). The Ideal Gas Law relates temperature, volume, and the number of moles of gas. A gas is considered an ideal gas if they behave according to the Kinetic Molecular Theory.

The Ideal Gas Law describes the properties of gases by analyzing the pressure, volume, temperature, and moles of gas.

If you need a refresher on the Kinetic Molecular Theory, you can read about it in Kinetic Molecular Theory!

The formula for the ideal gas law is:

$PV = nRT$

Where,

P = pressure in Pa
V = volume of gas in liters
n = amount of gas in moles
R = universal Gas Constant = 0.082057 L·atm / (mol·K)
T = temperature of the gas in Kelvin (K)

Check out this example on how to apply the ideal gas law to calculate pressure!

You have a 3 L container with 132 g of C₃H₈at a temperature of 310 K. Find the pressure in the container.

First, we need to calculate the number of moles of C₃H₈.

$132 g C_{3} H_{8} \times \frac{1 mol C_{3} H_{8}}{44.1 g C_{3} H_{8}} = 2.99 mol C_{3} H_{8}$

Now, we can use the ideal gas law formula to solve for the pressure of C₃H₈.

$P = \frac{nRT}{V} P = \frac{2.99 mol C 3 H 8 \times 0.082057 \times 310 K}{3.00 L} = 25.4 atm$

Have you ever thought about how pressure cookers work, and why does it cook your food faster than conventional ways? Compared to conventional cooking, pressure cookers prevent the heat from escaping as vapor. Pressure cookers can trap the heat and steam inside the container, increasing pressure inside the cooker. This increase in pressure causes the temperature to rise, making your food cook faster! Pretty cool right?

Now that you are more familiar with pressure, let's look at partial pressures!

Partial pressure is defined as the pressure an individual gas exerts within a mixture. The total pressure of a gas is the sum of all the partial pressures in the mixture.

Partial pressure is the pressure exerted by an individual gas within a mixture of gases.

Let's look at an example!

A gas mixture containing Nitrogen and oxygen has a total pressure of 900 torr. One-third of the total pressure is contributed by oxygen molecules. Find the partial pressure contributed by Nitrogen.

If oxygen is responsible for 1/3 of the total pressure, then that means that Nitrogen contributes to the remaining 2/3 of the total pressure. First, you need to find the partial pressure of oxygen. Then, you subtract the partial pressure of oxygen from the total pressure to find the partial pressure of Nitrogen.

$Partial Presurre of Oxygen = \frac{1}{3} \times 900 torr = 300 torr 900 torr = 300 torr + Partial pressure of Nitrogen Partial pressure of nitrogen = 900 torr - 300 torr = 600 torr$

Properties of Partial Pressure

The partial pressure of gases is also affected by temperature, volume, and the number of moles of gas in a container.

Pressure is directly proportional to temperature. Therefore, if you increase one of them, the other variable will also increase (Charles's Law).
Pressure is inversely proportional to the volume. Increasing one variable will cause the other variable to decrease (Boyle's Law).
Pressure is directly proportional to the number of moles of gas inside a container (Avogadro's law)

If you want to learn more about gas laws and their applications, check out "Ideal Gas Law"

Dalton's Law of Partial Pressure

Dalton's law of partial pressure shows the relationship between partial pressures in a mixture. Being able to determine the partial pressure of gases is very useful in the analysis of mixtures.

Dalton's Law of Partial Pressure states that the sum of the partial pressures of each individual gas present in a mixture is equal to the total pressure of the gas mixture.

The equation for Dalton's Law of Partial Pressure is simple. The total pressure of a mixture is equal to the partial pressure of gas A, gas B, and so on.

$P_{total = P_{A} + P_{B + . . .}}$

Partial Pressures Dalton's law of Partial Pressure Definition StudySmarter Fig.1-Mixing of gases and partial pressures

Find the total pressure of a mixture containing nitrogen with a partial pressure of 1.250 atm and helium with a partial pressure of 0.760 atm.

$P_{total = P_{A} + P_{B + . . .}} P_{total = 1.250 atm + 0.760 atm = 2.01 atm}$

The partial pressure of gases can also be calculated using an equation that relates partial pressure to the total pressure and the number of moles.

$Partial Pressure of a gas = \frac{n_{gas}}{n_{total}} \times P_{total}$

Where,

P_total is the total pressure of a mixture
n_gasis the number of moles of the individual gas
n_total is the total number of moles of all gases in the mixture
$\frac{n_{gas}}{n_{total}}$ is also known as the mole fraction.

Now, let's look at some examples to make things easier!

You have a mixture of gases exerting a total pressure of 1.105 atm. The mixture contains 0.3 moles of H₂, 0.2 moles for O_2, and 0.7 moles of CO₂. What is the pressure contributed by CO₂?

Use the equation above to calculate the partial pressure of CO₂.

$P_{{CO}_{2}} = \frac{n_{gas}}{n_{total}} \times P_{total} P_{{CO}_{2}} = \frac{0.7 mol {CO}_{2}}{0.7 + 0.3 + 0.2 mol total} \times 1.105 atm = 0.645 atm$

Henry's Law

Another law that relates to partial pressure is Henry's Law. Henry's Law proposes that when a gas is in contact with a liquid, it will dissolve proportionally to its partial pressure, assuming that no chemical reaction occurs between the solute and solvent.

Henry's law states that the amount of gas dissolved in a solution is directly proportional to the partial pressure of the gas. In other words, the Solubility of gas will increase with the increase in the partial pressure of a gas.

The formula for Henry's Law is:

$C = k P$

Where,

C = Concentration of the dissolved gas
K = Henry's constant that depends on the gas solvent.
P = partial pressure of the gaseous solute above the solution.

So, can you apply Henry's Law to all equations involving a gas being and solution? No! Henry's Law is mostly applied to dilute solutions of gases that do not react with the solvent or dissociate in the solvent. For instance, you could apply Henry's Law to an equation between oxygen gas and water because no chemical reaction would happen, but not to an equation between HCl and water because hydrogen chloride dissociates into H⁺ and Cl^-.

$HCl (g) \overset{H_{2} O}{\to} H_{(aq)}^{+} + {Cl}_{(aq)}^{-}$

Importance of Partial Pressure

Partial pressure play a big role in various areas of life. For example, scuba divers are usually very familiar with partial pressure because their tank contains a mixture of gases. When divers decide to dive in deep waters where pressure is high, they need to know how changing partial pressures can affect their bodies. For example, If there are high levels of oxygen, oxygen toxicity may occur. Similarly, if there is too much nitrogen present, and it enters the bloodstream, it can cause nitrogen narcosis, characterized by decreased awareness and loss of consciousness. So, next time you go scuba diving, remember the importance of partial pressure!

Partial pressure also affects the growth of eukaryotic organisms like fungi! A very interesting study showed that when fungi were exposed to the high partial pressure of pure oxygen (10 atm), they stopped growing. But, when this pressure was quickly removed, they went back to growing as if nothing happened!

Examples of Partial Pressure

Practice makes perfect. So, let's solve more problems regarding partial pressure!

Supposed that you have nitrogen, oxygen, and hydrogen gas present in a sealed container. If the partial pressure of nitrogen is 300 torr, the partial pressure of oxygen is 200 torr, and the partial pressure of hydrogen is 150 torr, then what is the total pressure?

$P_{total} = P_{A} + P_{B + . . .} P_{total} = 300 + 200 + 150 = 650 torr$

Now, let's look at one last problem.

Two moles of helium, seven moles of neon, and one mole of argon are present in a vessel whose total pressure is 500torr. What are the partial pressures of helium, neon and argon respectively?

Dalton’s law of partial pressures says that the total pressure is equal to the sum of the partial pressures of each of the gases present. So, Each individual partial pressure is equal to the mole fraction of the gas times the total pressure!

$Partial Pressure of a gas = \frac{n_{gas}}{n_{total}} \times P_{total} P_{helium} = \frac{2}{10} \times 500 torr = 100 torr P_{neon} = \frac{7}{10} \times 500 torr = 350 torr P_{Argon} = \frac{1}{10} \times 500 torr = 50 torr$

After reading this article, I hope you have become more familiar with the importance of partial pressures and how to apply this knowledge to situations involving partial pressures!

Partial Pressure - Key takeaways

Partial pressure is the pressure exerted by an individual gas within a mixture of gases.
Dalton's Law of Partial Pressure states that the sum of the partial pressures of each individual gas present in a mixture is equal to the total pressure of the gas mixture.
Pressure is the force exerted per unit area.

References

Moore, J. T., & Langley, R. (2021). McGraw Hill: AP Chemistry, 2022. New York: McGraw-Hill Education.
Post, R., Snyder, C., & Houk, C. C. (2020). Chemistry: A self-teaching guide. Hoboken, NJ: Jossey Bass.
Zumdahl, S. S., Zumdahl, S. A., & DeCoste, D. J. (2017). Chemistry. Boston, MA: Cengage.
Caldwell, J. (1965). Effects of High Partial Pressures of Oxygen on Fungi and Bacteria. Nature, 206(4981), 321–323. https://doi.org/10.1038/206321a0 ‌
Partial Pressure - What is it? (2017, November 8). Scuba Diving Gear. https://www.deepbluediving.org/partial-pressure-what-is-it/ ‌
https://sciencing.com/real-life-applications-gas-laws-5678833.html
https://news.ncsu.edu/2019/02/why-does-food-cook-faster-in-a-pressure-cooker/

Frequently Asked Questions about Partial Pressure

Partial pressure is the pressure exerted by an individual gas within a mixture of gases.

To calculate partial pressure you can:

Use the equation of Dalton's Law if you have the total pressure of the mixture and the partial pressures of other gases present in the same mixture.
Use the equation that relates partial pressure to the total pressure and the number of moles.

Pressure is the force exerted per unit area, whereas partial pressure is the pressure exerted by an individual gas within a mixture containing different gases.

Dalton's law states that the sum of the partial pressures of each individual gas present in a mixture is equal to the total pressure of the gas mixture.

Partial pressure is important because it affects many areas of our lives, from the gas exchange that occurs during respiration to opening a bottle of your favorite carbonated drink!

Final Partial Pressure Quiz

Partial Pressure Quiz - Teste dein Wissen

Question

True or false: pressure is defined as forces exerted per unit area

Show answer

Answer

True

Show question

Question

Which of the following is the definition of Partial pressure?

Show answer

Answer

The pressure exerted by an individual gas within a mixture of gases.

Show question

Question

What does Dalton's law say about the relationship between partial pressures and the total pressure of a mixture?

Show answer

Answer

The sum of the partial pressures of each individual gas is equal to the total pressure of the gas mixture.

Show question

Question

True or false: The greater the force exerted, the higher the pressure and the greater the surface area.

Show answer

Answer

False

Show question

Question

If you decrease the area of a container, then the pressure inside the container will _______.

Show answer

Answer

increase

Show question

Question

True or false: The Ideal gas law describes the properties of gases by analyzing the pressure, volume, temperature, and moles of gas.

Show answer

Answer

True

Show question

Question

At _____ temperatures and _____ pressure, a substance will probably be going to be solid.

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Answer

low; high

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Question

At high temperature and low pressure, a substance will most likely going to be a _____.

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Answer

Gas

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Question

In a phase diagram, the Critical Point of a substance is the point where:

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Answer

Gas cannot be condensed into a liquid anymore.

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Question

The point in a phase diagram where all three states can exist simultaneously is called:

Show answer

Answer

Triple point

Show question

Question

True or false: Phase diagrams are divided into two areas.

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Answer

False

Show question

Question

True or false: The partial pressure of gases can be affected by temperature, volume, and the number of moles of gas in a container.

Show answer

Answer

True

Show question

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True or false: pressure is defined as forces exerted per unit area

True

Which of the following is the definition of Partial pressure?

The pressure exerted by an individual gas within a mixture of gases.

What does Dalton's law say about the relationship between partial pressures and the total pressure of a mixture?

The sum of the partial pressures of each individual gas is equal to the total pressure of the gas mixture.

True or false: The greater the force exerted, the higher the pressure and the greater the surface area.

False

If you decrease the area of a container, then the pressure inside the container will _______.

increase

True or false: The Ideal gas law describes the properties of gases by analyzing the pressure, volume, temperature, and moles of gas.

True

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Partial Pressure

Properties of Partial Pressure

Dalton's Law of Partial Pressure

Henry's Law

Importance of Partial Pressure

Examples of Partial Pressure

Partial Pressure - Key takeaways

References

Frequently Asked Questions about Partial Pressure

What is partial pressure?

How to calculate partial pressure?

What is the difference between pressure and partial pressure?

What is the partial pressure in Dalton's law?

Why is partial pressure important?

Final Partial Pressure Quiz

Partial Pressure Quiz - Teste dein Wissen

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