Dalton's Law of Partial Pressure Problems & Examples - Chemistry

The Organic Chemistry Tutor
27 Oct 201611:44
EducationalLearning
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TLDRThis video delves into Dalton's Law of Partial Pressure, explaining that the total gas pressure is the sum of individual gases' pressures. It covers calculating partial pressures using the ideal gas law and mole fractions, demonstrating with examples including a storage tank scenario with argon, oxygen, and nitrogen. The video also solves problems involving nitrogen, oxygen, and carbon dioxide, illustrating how to find unknown partial pressures and mole fractions, reinforcing the concept with practical applications.

Takeaways
  • 📚 Dalton's Law of Partial Pressure states that the total pressure of a gas mixture is the sum of the individual partial pressures of the gases.
  • 🧪 The partial pressure of a gas can be calculated using the ideal gas law equation \( PV = nRT \), where \( n \) represents the moles of the specific gas.
  • 🔍 If \( n \) represents the total moles of all gases in a container, \( p \) represents the total pressure of all gases.
  • 📈 The mole fraction of a gas is calculated by dividing the moles of that gas by the total moles in the container.
  • 🔄 The mole fraction can also be found by dividing the partial pressure of a gas by the total pressure, and all mole fractions in a mixture must sum up to one.
  • 📉 The mole fraction represents the percentage of a gas in a mixture in decimal form.
  • 📚 Example problem: In a storage tank with 2 moles of argon, 3 moles of O2, and 5 moles of N2 at a total pressure of 1000 torr, the partial pressures are calculated using mole fractions.
  • 🔢 For the example, the partial pressures are 200 torr for argon, 300 torr for O2, and 500 torr for N2, summing up to the total pressure of 1000 torr.
  • 🌡️ Another example involves calculating partial pressures using the ideal gas law with given masses of N2 and O2 in a 2-liter container at 300 K.
  • 🔎 The partial pressures of N2 and O2 are calculated as 24.6 atm and 36.9 atm, respectively, and the total pressure is 61.5 atm.
Q & A

  • What is Dalton's Law of Partial Pressure?

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

  • How can you calculate the partial pressure of a gas using the Ideal Gas Law equation?

    -You can calculate the partial pressure of a gas using the Ideal Gas Law equation (PV = nRT) by setting n to represent the moles of the specific gas and P to represent its partial pressure.

  • What is the relationship between mole fraction and partial pressure?

    -The partial pressure of a substance is equal to the mole fraction of that substance multiplied by the total pressure of the gas mixture.

  • How do you calculate the mole fraction of a gas in a mixture?

    -The mole fraction of a gas is calculated by dividing the moles of that specific gas by the total moles of all gases in the container.

  • What is the sum of all mole fractions in a gas mixture?

    -The sum of all mole fractions in a gas mixture must add up to one, as they represent the proportions of the total moles.

  • In the given problem with a storage tank containing argon, oxygen, and nitrogen, what is the mole fraction of argon?

    -The mole fraction of argon in the storage tank is one over five (0.2), as there are two moles of argon out of a total of ten moles of gas.

  • What is the partial pressure of argon in the storage tank problem, given a total pressure of 1000 torr?

    -The partial pressure of argon is 200 torr, which is calculated by multiplying the mole fraction of argon (0.2) by the total pressure (1000 torr).

  • How can you find the total pressure of a gas mixture using Dalton's Law?

    -According to Dalton's Law, the total pressure of a gas mixture is the sum of the individual partial pressures of each gas in the mixture.

  • In the second problem with nitrogen and oxygen in a container, what is the partial pressure of nitrogen calculated using the Ideal Gas Law?

    -The partial pressure of nitrogen is 24.6 atm, calculated using the formula P = (nRT/V) with n = 2 moles, R = 0.08206 L·atm/mol·K, T = 300 K, and V = 2 L.

  • How can you determine the partial pressure of a gas if you know the partial pressures of the other gases and the total pressure?

    -You can determine the partial pressure of a specific gas by subtracting the sum of the known partial pressures from the total pressure.

  • In the final problem with nitrogen, oxygen, and carbon dioxide, what is the mole fraction of carbon dioxide?

    -The mole fraction of carbon dioxide is approximately 0.091, calculated by dividing its partial pressure (75 torr) by the total pressure (825 torr).

Outlines
00:00
🌟 Dalton's Law of Partial Pressures Explained

This paragraph introduces Dalton's Law of Partial Pressures, which states that the total pressure of a gaseous mixture is the sum of the partial pressures of its individual components. It explains how to calculate partial pressures using the ideal gas law equation (PV=nRT) and mole fractions. The mole fraction is the ratio of moles of a particular gas to the total moles in the mixture, and it's used to find the partial pressure when multiplied by the total pressure. The paragraph also clarifies that the sum of all mole fractions in a mixture must equal one, and provides an example problem involving a storage tank with argon, oxygen, and nitrogen gases to illustrate the calculation process.

05:01
🔬 Applying Dalton's Law to Calculate Partial Pressures

This section delves deeper into the application of Dalton's Law by using the ideal gas law to calculate the partial pressures of nitrogen (N2) and oxygen (O2) in a two-liter container at 300 Kelvin. It outlines the process of converting mass to moles using molar mass, and then using these moles to find the partial pressures by dividing nRT by volume (V). The paragraph demonstrates the calculation for both N2 and O2, resulting in partial pressures of 24.6 atm and 36.9 atm, respectively. It concludes by showing how to use these partial pressures to determine the total pressure of the gas mixture, either by summing the individual partial pressures or by using the total moles in the ideal gas law equation.

10:02
📚 Finding Partial Pressure and Mole Fraction of CO2

The final paragraph presents a problem-solving scenario where the partial pressures of nitrogen (N2) and oxygen (O2), along with the total pressure, are known, and the task is to find the partial pressure and mole fraction of carbon dioxide (CO2). It uses Dalton's Law to subtract the known partial pressures of N2 and O2 from the total pressure to isolate the partial pressure of CO2. After calculating the partial pressure of CO2 as 75 torr, the paragraph explains how to determine the mole fraction of CO2 by dividing its partial pressure by the total pressure, resulting in approximately 9.1%. This indicates that about 9.1% of the molecules in the container are carbon dioxide, concluding the video with a practical application of the concepts discussed.

Mindmap
Keywords
💡Dalton's Law of Partial Pressure
Dalton's Law of Partial Pressure is a fundamental principle in chemistry that states the total pressure of a gaseous mixture is the sum of the partial pressures of the individual gases. This law is central to the video's theme, as it provides the foundation for understanding how gases behave in mixtures. The script uses this law to calculate the partial pressures of different gases in various examples, such as in a storage tank containing argon, oxygen, and nitrogen.
💡Partial Pressure
Partial pressure refers to the pressure exerted by an individual gas in a mixture of gases. It is a key concept in the script, as it is used to determine the individual contributions of each gas to the total pressure. The video explains how to calculate partial pressures using both the ideal gas law and mole fractions, as seen in the example with argon, oxygen, and nitrogen in a storage tank.
💡Ideal Gas Law
The Ideal Gas Law is a mathematical equation of state for a hypothetical ideal gas, expressed as PV = nRT. It is a crucial concept in the script, as it is used to calculate the partial pressures of gases when the number of moles and other variables are known. The video demonstrates its application in determining the partial pressures of nitrogen and oxygen in a two-liter container at 300 Kelvin.
💡Mole Fraction
Mole fraction is the ratio of the number of moles of a component in a mixture to the total number of moles of all components. It is a key term in the script, as it is used to relate the composition of a gas mixture to its partial pressures. The video shows how mole fractions are calculated and used to find the partial pressures of gases, such as in the storage tank example with argon, oxygen, and nitrogen.
💡Total Pressure
Total pressure is the sum of the partial pressures of all the gases in a mixture. It is a central concept in the script, as it represents the overall pressure exerted by a mixture of gases. The video explains how to calculate total pressure using both the sum of individual partial pressures and the ideal gas law, as demonstrated in the examples provided.
💡Moles
Moles are a measure of the amount of substance, typically used in chemistry to quantify the number of atoms, molecules, or ions. In the script, moles are used to calculate partial pressures using the ideal gas law and to determine mole fractions. The video shows how to convert mass to moles using molar mass and how this relates to the calculation of partial pressures.
💡Molar Mass
Molar mass is the mass of one mole of a substance, usually expressed in grams per mole. It is an important concept in the script, as it is used to convert the mass of a gas into moles, which is necessary for applying the ideal gas law. The video demonstrates this conversion for nitrogen and oxygen to find their respective moles in a gas mixture.
💡Gas Constant (R)
The gas constant (R) is a physical constant that appears in the ideal gas law and is used to relate the pressure, volume, and temperature of a gas. In the script, the gas constant is used in the ideal gas law equation to calculate partial pressures of gases. The video provides the value of R and shows its use in calculations for nitrogen and oxygen.
💡Temperature (Kelvin)
Temperature in Kelvin is an absolute temperature scale used in the ideal gas law. It is an essential parameter in the script, as it affects the pressure and volume relationship of gases. The video uses a temperature of 300 Kelvin to demonstrate the calculation of partial pressures for nitrogen and oxygen in a container.
💡Volume
Volume is the amount of space that a substance occupies. In the script, volume is a critical variable in the ideal gas law, as it is used to calculate the pressure of gases. The video uses a volume of two liters to demonstrate how the volume of a container affects the partial pressures of nitrogen and oxygen.
💡Percent
Percent is a way to express a number as a fraction of 100. In the script, percent is used to describe the proportion of different gases in a mixture, such as the mole fraction of nitrogen being equivalent to 20% of the total molecules in a container. The video explains how to convert mole fractions to percentages and vice versa.
Highlights

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

The partial pressure of a gas can be calculated using the ideal gas law equation, PV = nRT.

If n represents the moles of substance A, then P represents the partial pressure of substance A.

If n represents the total moles of all gas molecules in a container, then P represents the total pressure of all the gas molecules in that container.

The subscripts between n and P must match in the ideal gas law equation.

The partial pressure of a gas can also be calculated using the mole fraction and the total pressure.

The mole fraction is the ratio of the moles of a substance to the total moles in the container.

The sum of all mole fractions must add up to one.

Example problem: Calculating the partial pressure of each gas in a storage tank containing two moles of argon, three moles of O2, and five moles of N2 at a total pressure of 1000 torr.

The mole fraction of argon is 0.2, O2 is 0.3, and N2 is 0.5.

The partial pressure of argon is 200 torr, O2 is 300 torr, and N2 is 500 torr, adding up to the total pressure of 1000 torr.

Example problem: Calculating the partial pressure of each gas in a 2-liter container at 300 Kelvin with 56 grams of N2 and 96 grams of O2.

The molar mass of N2 is 28 grams per mole, and O2 is 32 grams per mole, resulting in 2 moles of N2 and 3 moles of O2.

The partial pressure of N2 is 24.6 atm, and O2 is 36.9 atm, with a total pressure of 61.5 atm.

Example problem: Calculating the partial pressure and mole fraction of CO2 in a storage tank with a total pressure of 825 torr, given the partial pressures of N2 and O2.

The partial pressure of CO2 is 75 torr, and its mole fraction is approximately 0.091.

Transcripts

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Dalton's LawPartial PressureIdeal Gas LawGas MoleculesMole FractionTotal PressureArgon GasOxygen GasNitrogen GasStorage TankGas Calculations