Dalton's Law: Partial Pressure (Simplified): Study with Video Lessons, Practice Problems & Examples

Partial pressure refers to the pressure exerted by an individual gas in a mixture, contributing to the total pressure in a container, as described by Dalton's law of partial pressures. The partial pressure of a gas can be calculated using the ideal gas law, where $P=\frac{nRT}{V}$. Additionally, the fractional composition of a gas aids in determining its partial pressure through the formula: $P=fP\_\mathrm{total}$, where f is the fractional composition.

Dalton's Law: Partial Pressure (Simplified) Concept 1

Partial pressure is the pressure exerted by an individual gas within a mixture. Think of it as the gas's individual pressure. We're going to say that in a container of unreacting gases, the total pressure of the container is the sum of the partial pressures of each gas. Now, this is known as the law of partial pressures. Basically, the total pressure inside a container comes from adding up all the pressures of each individual gas. So the total pressure would equal the pressure of gas 1, plus the pressure of gas 2, plus the pressure of gas 3, and so on, if there are additional gases. Just remember, the total pressure that a container is experiencing is contributed by each of the individual gases within it.

Dalton's Law: Partial Pressure (Simplified) Example 1

Here we're told that a sample of neon gas exerts a pressure of 1.85 atmospheres inside a cylinder. Some nitrogen gas is also present at a pressure of 500 Torr. 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 torrs.

Since atmospheres is a standard unit we usually use for pressure, let's convert the torr into atmospheres. So we're going to have 500 torr, and remember that for every 1 atmosphere, that's 760. So when we do that, we're going to get as our conversion 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 3 significant figures, 500 only has 1 significant figure. Here, if we want to abide by 1 significant figure, this would round up to 3, which is a pretty big round there in terms of our value. So, it's just better to go let's go with the 3 significant figures in this 1.85. Again the question isn't asking for the number of significant figures in your final answer, we're doing this as continuous practice in terms of determining significant figures. Again, better to go with 3 significant figures. I know it's not the least number of significant figures but going from 2.5 to 3 atmospheres is such a big increase. Better just to go with 3 significant figures and then we have 2.51 atmospheres at the end. So, now that we've seen this question, let's move on to the next video.

Dalton's Law: Partial Pressure (Simplified) Concept 2

So we know at this point that the total pressure felt within a container is a 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 its moles, its temperature, and its volume, we can also find its partial pressure. Now we're going to say here if you assume that the gases behave ideally, then their 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 1, we can find its partial pressure if we know its moles, so moles 1, \( r \) 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.

The ideal gas law equation in MathML is:

P = n • R • T V

Dalton's Law: Partial Pressure (Simplified) Example 2

If 12 grams of helium and 20 grams of oxygen are placed inside a 5-liter cylinder at 30 degrees Celsius, what is the partial pressure of the helium gas? Alright. So, they're giving us information on 2 gases: helium and oxygen. But realize they're only asking for information in terms of partial pressure for the helium. With the helium, I have its 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 the 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 times T divided by V. We don't even need to look at the grams of oxygen because the question again is only asking about the partial pressure of helium.

Alright. 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 4.003 grams of helium for every 1 mole of helium. Grams here cancel out and I'll have my moles as 12 4.003 moles of helium, approximately 2.998 moles of helium. So take that, plug it into the formula. So 2.998 moles of helium. Multiply by my gas law or my gas constant, 0.08206 liters times atmospheres over moles times K. Remember, temperature must be in Kelvin. So the 30 degrees Celsius, I'm going to add 273.15 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. Liters cancel out with liters, kelvins cancel out with kelvins, moles cancel out with moles. And at the end, what we have left is atmospheres. So we plug that in and we'll get 2.998×0.08206×303.155 atmospheres, equals 14.9149 atmospheres.

If we look at the significant figures within our question, we have 3 sig figs, 3 sig figs, 2 sig figs, and 1 sig fig. Here if we wanted 1 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 to round 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. Going from 14.9 to 10 is such a big difference. So here, we're just going to go with 3 significant figures. 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.

Dalton's Law: Partial Pressure (Simplified) Concept 3

Now, when the percent composition of a gas is given, first determine its fractional composition. By fractional composition, we mean that it represents the percent composition of a gas divided by the total percent. So here we have our fractional composition formula. We're going to say fractional composition, which we're going to use m as a stand-in for the variable, equals the percentage of your particular gas you're looking at divided by the total percent, which is 100%. Then, we're going to say that we can calculate the partial pressure of a gas using its fractional composition and the total pressure. So that feeds into Dalton's Law. And Dalton's Law says that the partial pressure of a gas, let's call it gas A, equals the fractional composition of gas A times the total pressure. Using fractional composition allows us to step into Dalton's Law to help us figure out the partial pressure of gases within any given container.

Frational composition formula:

fractional composition (m) = percentage of gas 100

Dalton's Law formula:

Partial pressure of gas A = fractional composition of gas A ⋅ total pressure

Dalton's Law: Partial Pressure (Simplified) Example 3

A cylinder of a gas mixture used for calibration of blood gas analyzers in medical laboratories contains 5% carbon dioxide, 12% oxygen, and the remainder nitrogen at a total pressure of 146 atmospheres. What is the partial pressure of each component of this gas? Alright. So, we're going to say we have 5% CO₂, we have 12% oxygen, and if we subtract 5% and 12% from 100%, that will give us the percentage of our nitrogen gas. So, that will come out to 83% nitrogen gas. Now that we know each of their percentages, we can figure out their fractional compositions and by extension their partial pressures.

For CO₂, the pressure of CO₂ equals its fractional composition, which is 5% divided by 100% times the total pressure of 146 atmospheres. This tells me that the partial pressure of CO₂ is about 7.3 atmospheres. For O₂, that'd be 12%, so pressure of O₂ equals 12100 times the total pressure. So that will come out to 17.5 atmospheres. And then finally, we have nitrogen gas, so that would be pressure of nitrogen gas equals 83100 times 146 atmospheres. So this comes out to approximately 121.2 atmospheres. So, this will be the partial pressure of each gas component within the gas mixture of this cylinder.

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. 220 mmHg
• B. 242 mmHg
• C. 588 mmHg
• D. 183 mmHg

The partial pressure of N₂ in the air is 593 mmHg at 1 atm. What is the partial pressure of N₂ in a bubble of air a scuba diver breathes when he is 66 ft below the surface of the water where the pressure is 3.00 atm?

• A. 2.34 mmHg
• B. 1779 mmHg
• C. 593 mmHg
• D. 2.28×10³ mmHg
• E. 7.02 mmHg

Here’s what students ask on this topic:

What is Dalton's Law of Partial Pressures?

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases in a container is equal to the sum of the partial pressures of each individual gas. Mathematically, it can be expressed as:

$P_{\text{total}}=P_1+P_2+P_3+...$

where $P_1$ is the partial pressure of gas 1, $P_2$ is the partial pressure of gas 2, and so on. Each gas in the mixture contributes to the total pressure proportionally to its amount.

How do you calculate the partial pressure of a gas using the ideal gas law?

The partial pressure of a gas in a mixture can be calculated using the ideal gas law, which is:

$P=\frac{nRT}{V}$

Here, $P$ is the partial pressure of the gas, $n$ is the number of moles of the gas, $R$ is the gas constant, $T$ is the temperature in Kelvin, and $V$ is the volume of the container. By knowing the moles, temperature, and volume, you can determine the partial pressure of the gas.

What is fractional composition and how is it used to calculate partial pressure?

Fractional composition represents the ratio of the amount of a particular gas to the total amount of gases in a mixture. It is calculated by dividing the percentage composition of the gas by 100%. The formula is:

$f=\frac{\mathrm{percentage}}{100}$

To find the partial pressure of a gas using its fractional composition, you multiply the fractional composition by the total pressure:

$P_a=f{P}_{\text{total}}$

where $P_a$ is the partial pressure of gas a, $f$ is the fractional composition, and $P_{\text{total}}$ is the total pressure.

How does Dalton's Law apply to real-life situations?

Dalton's Law of Partial Pressures is applicable in various real-life situations, such as calculating the pressure of gases in scuba diving tanks, determining the composition of gases in the atmosphere, and in medical applications like anesthesia delivery. For example, in scuba diving, knowing the partial pressures of oxygen and nitrogen is crucial to avoid conditions like oxygen toxicity and nitrogen narcosis. In the atmosphere, Dalton's Law helps in understanding how different gases like oxygen, nitrogen, and carbon dioxide contribute to the total atmospheric pressure.

What assumptions are made when using Dalton's Law of Partial Pressures?

When using Dalton's Law of Partial Pressures, several assumptions are made: (1) The gases in the mixture do not react with each other. (2) The gases behave ideally, meaning they follow the ideal gas law. (3) The volume of the individual gas molecules is negligible compared to the volume of the container. (4) There are no intermolecular forces between the gas molecules. These assumptions simplify the calculations but may not always hold true in real-world scenarios, especially at high pressures or low temperatures.