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How to calculate total pressure and partial pressures for gas mixtures from Ideal Gas Law. The term partial pressure is used when we have a mixture of two or several gases in the same volume, and it expresses the pressure that is caused by each of the induvidual gases in the mixture.
- Overview
- Key points
- Introduction
- Ideal gases and partial pressure
- Example 1: Calculating the partial pressure of a gas
- Dalton's law of partial pressures
- Example 2: Calculating partial pressures and total pressure
- Step 1: Calculate moles of oxygen and nitrogen gas
- Step 2 (method 1): Calculate partial pressures and use Dalton's law to get PTotal
- Step 2 (method 2): Use ideal gas law to calculate PTotal without partial pressures
- GeneratedCaptionsTabForHeroSec
Definition of partial pressure and using Dalton's law of partial pressures
•The pressure exerted by an individual gas in a mixture is known as its partial pressure.
•Assuming we have a mixture of ideal gases, we can use the ideal gas law to solve problems involving gases in a mixture.
•Dalton's law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases:
PTotal=Pgas 1+Pgas 2+Pgas 3…
•Dalton's law can also be expressed using the mole fraction of a gas, x :
•The pressure exerted by an individual gas in a mixture is known as its partial pressure.
•Assuming we have a mixture of ideal gases, we can use the ideal gas law to solve problems involving gases in a mixture.
•Dalton's law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases:
PTotal=Pgas 1+Pgas 2+Pgas 3…
•Dalton's law can also be expressed using the mole fraction of a gas, x :
Pgas 1=x1PTotal
In day-to-day life, we measure gas pressure when we use a barometer to check the atmospheric pressure outside or a tire gauge to measure the pressure in a bike tube. When we do this, we are measuring a macroscopic physical property of a large number of gas molecules that are invisible to the naked eye. On the molecular level, the pressure we are measuring comes from the force of individual gas molecules colliding with other objects, such as the walls of their container.
Let's take a closer look at pressure from a molecular perspective and learn how Dalton's Law helps us calculate total and partial pressures for mixtures of gases.
In this article, we will be assuming the gases in our mixtures can be approximated as ideal gases. This assumption is generally reasonable as long as the temperature of the gas is not super low (close to 0K ), and the pressure is around 1atm .
[Can we be more specific about when a gas behaves ideally? ]
This means we are making some assumptions about our gas molecules:
•We assume that the gas molecules take up no volume.
•We assume that the molecules have no intermolecular attractions, which means they act independently of other gas molecules.
Based on these assumptions, we can calculate the contribution of different gases in a mixture to the total pressure. We refer to the pressure exerted by a specific gas in a mixture as its partial pressure. The partial pressure of a gas can be calculated using the ideal gas law, which we will cover in the next section, as well as using Dalton's law of partial pressures.
Let's say we have a mixture of hydrogen gas, H2(g) , and oxygen gas, O2(g) . The mixture contains 6.7mol hydrogen gas and 3.3mol oxygen gas. The mixture is in a 300L container at 273K , and the total pressure of the gas mixture is 0.75atm .
The contribution of hydrogen gas to the total pressure is its partial pressure. Since the gas molecules in an ideal gas behave independently of other gases in the mixture, the partial pressure of hydrogen is the same pressure as if there were no other gases in the container. Therefore, if we want to know the partial pressure of hydrogen gas in the mixture, PH2 , we can completely ignore the oxygen gas and use the ideal gas law:
PH2V=nH2RT
Rearranging the ideal gas equation to solve for PH2 , we get:
PH2=nH2RTV=(6.7mol)(0.08206atm⋅Lmol⋅K)(273K)300L=0.50atm
Thus, the ideal gas law tells us that the partial pressure of hydrogen in the mixture is 0.50atm . We can also calculate the partial pressure of hydrogen in this problem using Dalton's law of partial pressures, which will be discussed in the next section.
Dalton's law of partial pressures states that the total pressure of a mixture of gases is the sum of the partial pressures of its components:
PTotal=Pgas 1+Pgas 2+Pgas 3…
where the partial pressure of each gas is the pressure that the gas would exert if it was the only gas in the container. That is because we assume there are no attractive forces between the gases.
Dalton's law of partial pressure can also be expressed in terms of the mole fraction of a gas in the mixture. The mole fraction of a gas is the number of moles of that gas divided by the total moles of gas in the mixture, and it is often abbreviated as x :
x1=mole fraction of gas 1=moles of gas 1total moles of gas
Dalton's law can be rearranged to give the partial pressure of gas 1 in a mixture in terms of the mole fraction of gas 1:
Let's say that we have one container with 24.0L of nitrogen gas at 2.00atm , and another container with 12.0L of oxygen gas at 2.00atm . The temperature of both gases is 273K .
If both gases are mixed in a 10.0L container, what are the partial pressures of nitrogen and oxygen in the resulting mixture? What is the total pressure?
Since we know P , V ,and T for each of the gases before they're combined, we can find the number of moles of nitrogen gas and oxygen gas using the ideal gas law:
n=PVRT
Solving for nitrogen and oxygen, we get:
nN2=(2atm)(24.0L)(0.08206atm⋅Lmol⋅K)(273K)=2.14mol nitrogen
Once we know the number of moles for each gas in our mixture, we can now use the ideal gas law to find the partial pressure of each component in the 10.0L container:
P=nRTV
PN2=(2.14mol)(0.08206atm⋅Lmol⋅K)(273K)10L=4.79atm
PO2=(1.07mol)(0.08206atm⋅Lmol⋅K)(273K)10L=2.40atm
Notice that the partial pressure for each of the gases increased compared to the pressure of the gas in the original container. This makes sense since the volume of both gases decreased, and pressure is inversely proportional to volume.
We can now get the total pressure of the mixture by adding the partial pressures together using Dalton's Law:
Since the pressure of an ideal gas mixture only depends on the number of gas molecules in the container (and not the identity of the gas molecules), we can use the total moles of gas to calculate the total pressure using the ideal gas law:
PTotal=(nN2+nO2)RTV=(2.14mol+1.07mol)(0.08206atm⋅Lmol⋅K)(273K)10L=(3.21mol)(0.08206atm⋅Lmol⋅K)(273K)10L=7.19atm
Once we know the total pressure, we can use the mole fraction version of Dalton's law to calculate the partial pressures:
PN2=xN2PTotal=(2.14mol3.21mol)(7.19atm)=4.79atm
PO2=xO2PTotal=(1.07mol3.21mol)(7.19atm)=2.40atm
Luckily, both methods give the same answers!
Learn how to calculate the partial pressure and total pressure of a gas mixture using Dalton's law and the ideal gas law. See examples, definitions, and key points of this topic.
Use the ideal gas law to calculate the partial pressure of each gas. Then add together the partial pressures to obtain the total pressure of the gaseous mixture.
Dalton’s Law, or the Law of Partial Pressures, states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the gases in the mixture.
27 de jul. de 2023 · To calculate total pressure, simply sum the partial pressures of each gas. How to Calculate Total Pressure? The following two example problems outline how to calculate the Total Pressure.
10 de mai. de 2024 · To calculate the partial pressure of a gas: Divide the dissolved gas moles by the moles of the mixture to find the mole fraction. Multiply the total pressure by the mole fraction to find the partial pressure of the chosen gas. Alternatively, you can use the ideal gas equation or Henry's law, depending on your data.
This law states that in a mixture of two or more gases, the total pressure is the sum of the partial pressures of all the components. The partial pressure of a gas is the pressure that gas would exert if it occupied the container by itself.
