Partial Pressure - Online Tutor, Practice Problems & Exam Prep

Partial pressure is the individual pressure exerted by a gas within a mixture, and the total pressure inside a container is the sum of the partial pressures of each gas, as stated by Dalton's Law of Partial Pressures. To calculate the partial pressure of a specific gas, one can use the ideal gas law if the gas behaves ideally. The formula involves the number of moles of the gas, the gas constant, the temperature, and the volume of the container. Additionally, Dalton's Law allows for the use of mole fraction to find a gas's partial pressure by multiplying the mole fraction by the total pressure. Understanding these concepts is crucial for analyzing gas mixtures and their behaviors under various conditions.

Partial Pressure

Partial pressure is the pressure exerted by an individual gas within a mixture. So think of it as the gas's individual pressure. We're going to say in a container of unreacting gases, the total pressure of the container is the sum of partial pressures of each gas.

Now this is known as the law of partial pressures. So basically, the total pressure inside of a container comes from adding up all the pressures of each individual gas. Total pressure would equal the pressure of gas one plus gas two plus gas three and so on if there are additional gases.

So just remember, the total pressure that a container is experiencing is contributed by each of the individual gases within it.

Partial Pressure Example 1

Here we're told that a sample of neon gas exerts a pressure of 1.85 atmospheres inside a cylinder. Some nitrogen gases also present at a pressure of 500 tour. What is the total pressure inside the cylinder? So remember we just learned about the law of partial pressures, which tells us that the total pressure felt inside of a container, or in this case a cylinder, comes from adding up the partial pressures of each gas present.

So in the container we have neon gas and we also have nitrogen gas. The total pressure is when you add their partial pressures together. Now the issue is we don't have the same units for these gases. Neon is in atmospheres but nitrogen is in tours. Since atmospheres is a standard unit we usually use for pressure, let's convert the Tor into atmospheres. So we're going to have 500 Tor and remember that for everyone atmosphere that's 760 tour.

So when we do that, we're going to get as our atmospheres 0.65789 atmospheres, take that and plug it in. And when we do that, we're going to get a total pressure of 2.50789 atmospheres. Within our question, 1.85 has three sig figs, 500 only has one sig fig here. If we went by one sig fig, this would round up to three, which is a pretty big round there in terms of our value.

So it's just better to go. Let's go with the three sig figs in this 1.85. Again, the question isn't asking for a number of sig figs in your final answer. We're doing this as continuous practice in terms of determining sigfigs. Again, better to go with three sig figs. I know it's not the least number of sig figs, but going from 2.5 to 3 three atmospheres is such a big increase. Better just to go with three sig figs and then we have 2.51 atmospheres at the end.

So now that we've seen this question, let's move on to a next video.

Partial Pressure

So we know at this point that the total pressure felt within a container is the result of adding up all the partial pressures of the gases present. Now if we can focus on one of these gases and we know it's moles, its temperature and its volume, we could also find its partial pressure.

Now we're going to say here, if you assume that the gases behave ideally, then there are partial pressures can be calculated from the ideal gas law. We're going to say here that the pressure of that gas that I'm focusing on, so let's call it gas one, we can find its partial pressure if we know its moles.

So moles n1 is our gas constant times the temperature of the container divided by the volume of the container. So here we're using the ideal gas law to just focus in on one gas and from it determine its partial pressure.

Partial Pressure Example 2

If 12 grams of helium and 20 grams of oxygen are placed inside a 5 liter cylinder at 30�C, what is the partial pressure of the helium gas? All right, so they're giving us information on 2 gases. They're giving us information on helium and oxygen, but realize they're only asking for information in terms of partial pressure for the helium.

With the helium I have it's grams and from that I can determine its moles. I have the volume of the container and I have the temperature of the container. With this information, I can find a partial pressure of helium gas by utilizing the ideal gas law. So we're going to say here pressure of helium equals moles of helium times R * T / V. We don't even need to look at the grants of oxygen because the question again is only asking about the partial pressure of helium.

All right, so let's take the 12 grams of helium. We look on the periodic table. You'll see that the atomic mass of helium is approximately 4.003g helium for everyone. More of helium grams here cancel out, and I'll have my moles as 2.9978 moles of helium. So take that. Plug it into the formula, so 2.9978 moles of helium multiplied by my gas law or my gas constant .08206 liters times atmospheres over moles times K.

Temperature must be in Kelvin, so the 30�C I'm going to add 273.5 to it and that gives me 303.15 Kelvin. Then we take the volume which is 5 liters and we just plug it in. Look at the units. Leaders cancel out with liters, Kelvin's cancel out with Kelvin's moles cancel out with moles. And at the end what we have left is atmospheres. So we plug that in and we'll get 14.9149 atmospheres.

If we look at the sig figs within our question, we have three sig figs, 3 sig figs, 2 sig figs, and one sig fig here. If we wanted one sig fig, it would round down to 10 atmospheres. Again, that's such a big deviation from our actual number. So let's go with a number that makes more sense because we don't want around so much. We're going to say our answer here is 14.9 atmospheres.

Again, we're constantly trying to remember significant figures play a role in a lot of our questions here. We're not being asked to directly, but when applicable we should alley it here. It wouldn't make sense to apply it because it would round our answer to a number that doesn't quite fit. Going from 14.9 to 10 is such a big difference. So here we're just going to go with three sig figs. 14.9 atmospheres is more reasonable.

It's not a big deviation from our original answer, so just remember if we have the moles, the temperature and the volume, we can find the partial pressure of a gas by using the ideal gas law formula.

Partial Pressure

Under Dalton's law, we can use the mole fraction of a gas to find the partial pressure of that gas. Here we're going to say dolphins loss says that the partial pressure of a gas 1 equals the mole fraction of that gas one times the total pressure.

So if you don't quite remember how to calculate mole fraction, I suggest you go back and take a look at my topic videos on mole fractions before proceeding further under Dalton's law.

P 1 = X 1 × P total

Partial Pressure Example 3

Here in this example question, it says a container has 16.7g O₂, 8.1 grams H₂ and three 5.2g N₂ and contains a total pressure of 0.83 atmospheres. We're asked to calculate the mole fraction of O₂ and its partial pressure. All right, to determine the partial pressure of O₂, the pressure of O₂ equals the mole fraction of O₂ times the pressure total. Right now, we already know what the total pressure is. It is 0.83 atmospheres.

So to determine partial pressure, we first have to find the mole fraction of O₂. Remember, the mole fraction of O₂ is equal to moles of O₂ divided by total moles of all the gases together. So we're going to take here. We're going to say we have 16.7g O₂, 8.1 grams H₂, and three 5.2g N₂. We're going to convert each one of these grams into moles, so we look on the periodic table for the atomic masses of oxygen, hydrogen, and nitrogen.

Here, 1 mole of O₂ (2 oxygens) comes out to 32 grams. One mole of H₂ (2 hydrogens) when you add up their atomic masses is 2.016g, and then you have two nitrogens. So 1 mole of N₂ is 28.02g. Here, all of our grams cancel out and we'll have the moles for each one of these gases. So that's going to come out to 0.5219 moles of O₂, 4.0179 moles H₂, and 1.2562 moles of N₂.

So take those and plug them in. So we have 0.5219 moles of O₂. On the bottom, we have the collective moles of everyone, so here we're just adding them all together. OK? And then when you work that out, you'll get your mole fraction for O₂, which comes out to be 0.0900. Take that mole fraction and plug it in here. So here's our mole fraction of O₂. Remember, mole fraction is a unitless number.

So then 0.0900 * 0.83 atmospheres comes out to 0.075 atmospheres. Here our answer has two significant figures because our lowest number of sig figs are 8.1 and 0.83. They both have two sig figs. So just remember, utilizing Dalton's law, we can use the mole fraction of any gas times the pressure total to find the partial pressure of that particular gas.

A sample of 3.51 g argon and an unknown amount of oxygen are mixed in a container at room temperature. The partial pressure of argon was calculated as 71.0 torr and the partial pressure of oxygen as 188 torr. What is the mass of the oxygen within the container?

• A. 4.27 g
• B. 6.18 g
• C. 7.44 g
• D. 9.16 g
• E. 15.2 g

A gas mixture contains 72.8% chlorine and 27.2% neon by mass. What is the partial pressure of neon in the mixture if the total pressure is recorded as 809 mmHg?

• A. 260 mmHg
• B. 289 mmHg
• C. 320 mmHg
• D. 392 mmHg
• E. 459 mmHg

Here’s what students ask on this topic:

How can one find partial pressure?

Partial pressure is the pressure that a gas in a mixture of gases would exert if it alone occupied the entire volume of the mixture at the same temperature. To find the partial pressure of a gas, you can use Dalton's Law of Partial Pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.

The formula to calculate the partial pressure of a gas is:

$P_{\mathrm{gas}}=\left(X_{\mathrm{gas}}\right)P_{\mathrm{total}}$

Where:

• Pgas is the partial pressure of the gas you're interested in.
• Xgas is the mole fraction of the gas in the mixture, which is the ratio of the number of moles of that gas to the total number of moles of all gases in the mixture.
• Ptotal is the total pressure of the gas mixture.

For example, if you have a gas mixture in a container and you know the total pressure of the mixture and the mole fraction of each gas, you can calculate the partial pressure of each gas using the formula above. Remember that the temperature and volume of the container are constant when using this formula.

How do you calculate partial pressure?

To calculate the partial pressure of a gas in a mixture, you can use Dalton's Law of Partial Pressures. According to this law, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases. The partial pressure of each gas is proportional to its mole fraction in the mixture.

Here's how you can calculate it:

1. Determine the mole fraction of the gas: Divide the number of moles of the gas by the total number of moles of all gases in the mixture.

Mole Fraction (_Xgas) = moles of gas / total moles of all gases

2. Multiply the mole fraction by the total pressure of the gas mixture to find the partial pressure:

Partial Pressure (_Pgas) = Mole Fraction (_Xgas) * Total Pressure (_Ptotal)

For example, if you have a mixture of oxygen and nitrogen with a total pressure of 1 atmosphere (atm), and the mole fraction of oxygen is 0.21, the partial pressure of oxygen would be:

_PO2 = 0.21 * 1 atm = 0.21 atm

Remember that the total pressure must be known, and the gases should not react with each other for this calculation to be valid.

What is partial pressure?

Partial pressure is a concept in chemistry and physics that refers to the pressure that a single gas in a mixture of gases would exert if it alone occupied the entire volume of the mixture at the same temperature. This is an important concept in understanding gas behavior and is based on Dalton's Law of Partial Pressures, which states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases.

To put it simply, imagine you have a container filled with a mixture of oxygen and nitrogen. The partial pressure of oxygen is the pressure it would exert if it were the only gas in the container. The same goes for nitrogen. So, if you know the partial pressures of all the gases in a mixture, you can add them up to find the total pressure. This principle is crucial in various scientific fields, including respiratory physiology, where it helps to understand how gases are exchanged in the lungs.