Partial pressure example | Chemistry | Khan Academy

Khan Academy
28 Aug 200915:08
EducationalLearning
32 Likes 10 Comments

TLDRThis script explores the calculation of total and partial pressures in a container filled with a mixture of gases (oxygen, hydrogen, and nitrogen). It demonstrates how to determine the moles of each gas, calculate the total pressure using the ideal gas law, and find the partial pressures of individual gases, emphasizing the importance of moles over mass in these calculations.

Takeaways
  • 🎈 The scenario involves a four-meter cubed container filled with a mixture of oxygen, hydrogen, and nitrogen gases.
  • 📊 The total mass of the gas mixture is 2.1 kilograms, with oxygen constituting 30.48%, hydrogen 2.86%, and nitrogen 66.67% of the total mass.
  • 🌡 The gases are at standard temperature, which is 0 degrees Celsius or 273 Kelvin.
  • 🧪 The task is to calculate the total pressure in the container and the partial pressures of each gas.
  • 📚 The concept of partial pressure is introduced, which is the pressure exerted by an individual gas in a mixture.
  • 🔍 The process begins by determining the total moles of gas present in the container.
  • ⚖️ The molar mass of each gas (O2, H2, N2) is used to calculate the moles of each gas from their mass percentages.
  • 🔢 It is found that there are 50 moles of N2, 20 moles of O2, and 30 moles of H2, summing up to 100 moles of gas in total.
  • 📐 The ideal gas law PV = nRT is applied to calculate the total pressure, where n is the number of moles, R is the gas constant, T is the temperature in Kelvin, and P is the pressure.
  • 📉 The calculated total pressure is 56,746 pascals, which is equivalent to 0.56 atmospheres.
  • 🔄 The partial pressures are determined by the proportion of moles each gas contributes to the total, resulting in 0.112 atmospheres for oxygen, 0.28 atmospheres for nitrogen, and 0.168 atmospheres for hydrogen.
  • 🔍 The final takeaway is that each gas contributes to the total pressure according to its mole fraction, regardless of its mass fraction.
Q & A

  • What is the total mass of gas in the container?

    -The total mass of gas in the container is 2.1 kilograms.

  • What are the percentages of oxygen, hydrogen, and nitrogen in the container by mass?

    -The percentages of oxygen, hydrogen, and nitrogen in the container by mass are 30.48%, 2.86%, and 66.67% respectively.

  • How many moles of nitrogen are in the container?

    -There are 50 moles of nitrogen (N2) in the container.

  • What is the molar mass of a nitrogen molecule (N2)?

    -The molar mass of a nitrogen molecule (N2) is 28 grams per mole.

  • How many moles of oxygen are in the container?

    -There are 20 moles of oxygen (O2) in the container.

  • What is the molar mass of an oxygen molecule (O2)?

    -The molar mass of an oxygen molecule (O2) is 32 grams per mole.

  • How many moles of hydrogen are in the container?

    -There are 30 moles of hydrogen (H2) in the container.

  • What is the molar mass of a hydrogen molecule (H2)?

    -The molar mass of a hydrogen molecule (H2) is 2 grams per mole.

  • What is the total pressure in the container in pascals?

    -The total pressure in the container is 56,746 pascals.

  • How many atmospheres is the total pressure in the container?

    -The total pressure in the container is equivalent to 0.56 atmospheres.

  • What is the partial pressure of oxygen in the container?

    -The partial pressure of oxygen in the container is 0.112 atmospheres.

  • What is the partial pressure of nitrogen in the container?

    -The partial pressure of nitrogen in the container is approximately 0.28 atmospheres.

  • What is the partial pressure of hydrogen in the container?

    -The partial pressure of hydrogen in the container is 0.168 atmospheres.

  • How does the total pressure relate to the partial pressures of the individual gases?

    -The total pressure in the container is the sum of the partial pressures of oxygen, hydrogen, and nitrogen.

Outlines
00:00
🟠 Understanding the Problem: Gas Mixture in a Container

We are given a scenario involving a 4-cubic-meter container (like a balloon) with a mixture of oxygen, hydrogen, and nitrogen gases. The total gas mass is 2.1 kilograms, with 30.48% oxygen, 2.86% hydrogen, and 66.67% nitrogen. The goal is to determine the total pressure and partial pressures of each gas at standard temperature (0°C or 273 Kelvin). The process involves calculating the total number of moles of each gas type by using their respective masses and molar masses, then using the ideal gas law (PV=nRT) to find the pressures.

05:03
🔵 Calculating Moles of Each Gas

To find the total number of moles of each gas: 66.67% of the total mass is nitrogen (1400 grams), which has a molar mass of 28 grams/mole, resulting in 50 moles of nitrogen. For oxygen, 30.48% of the total mass is 640 grams, with a molar mass of 32 grams/mole, giving 20 moles of oxygen. Lastly, 2.86% of the total mass is hydrogen (60 grams), with a molar mass of 2 grams/mole, resulting in 30 moles of hydrogen. Summing these, we get 100 moles of gas in the container.

10:06
🟢 Total Pressure Calculation Using Ideal Gas Law

Using the ideal gas law (PV=nRT) and the values calculated: total moles (100 moles), volume (4 cubic meters), temperature (273 Kelvin), and gas constant (8.3145 meters cubed pascals per mole Kelvin), we solve for the total pressure (P). This gives P = 56,746 pascals (56.746 kilopascals or 0.56 atmospheres). Dimensional analysis confirms the correctness of units, resulting in pressure units in pascals.

🟡 Determining Partial Pressures

Partial pressures are found by multiplying the total pressure by the mole fraction of each gas. For oxygen (20% of total moles), the partial pressure is 0.112 atmospheres (20% of 0.56). For nitrogen (50% of total moles), the partial pressure is 0.28 atmospheres. For hydrogen (30% of total moles), the partial pressure is 0.168 atmospheres. Summing these partial pressures confirms the total pressure of 0.56 atmospheres, demonstrating that each gas's contribution is proportional to its mole fraction.

Mindmap
Keywords
💡Container
In the context of the video, a 'container' refers to a four-meter cubed space, which is likened to a balloon. It is the physical space that holds the different gases being discussed. The container is crucial as it is the volume in which the gases exert pressure, and its size directly impacts the calculations of moles and pressures.
💡Molecules of Gas
The term 'molecules of gas' is used to describe the different types of gases present in the container, namely oxygen, hydrogen, and nitrogen molecules. These molecules are the fundamental units that make up the gases and are essential for understanding the behavior of gases in the container, including their contribution to the total pressure.
💡Total Pressure
The 'total pressure' is the combined force exerted by all the gas molecules inside the container on the walls of the container. It is a key concept in the video, as the calculation of total pressure is the main objective. The script explains how to determine this by using the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
💡Partial Pressure
'Partial pressure' refers to the pressure exerted by a specific type of gas molecule within a mixture of gases. The video script explains how to calculate the partial pressures of oxygen, hydrogen, and nitrogen by considering their respective moles as a percentage of the total moles of gas in the container. This concept is crucial for understanding how each gas contributes to the total pressure.
💡Moles
In the video, 'moles' is used to quantify the amount of a substance, specifically the gas molecules in the container. The number of moles is calculated based on the mass of the gas and its molar mass. Moles are essential for calculating both the total pressure and the partial pressures of the gases, as they directly relate to the number of particles exerting pressure.
💡Molar Mass
'Molar mass' is the mass of one mole of a substance, expressed in grams per mole (g/mol). The script uses the molar masses of nitrogen (N2), oxygen (O2), and hydrogen (H2) to convert the mass of each gas into moles. Understanding molar mass is critical for determining the number of moles of each gas, which is necessary for calculating pressures.
💡Ideal Gas Law
The 'ideal gas law' is a fundamental principle in the study of gases, represented by the equation PV = nRT. It is used in the video to calculate the total pressure exerted by the gases in the container. The law assumes that the gas behaves ideally, meaning that the molecules do not interact with each other except during collisions.
💡Temperature
The 'temperature' in the video is specified as 0 degrees Celsius, which is equivalent to 273 Kelvin. Temperature is a critical variable in the ideal gas law, as it affects the kinetic energy of the gas molecules and, consequently, the pressure they exert. The video uses the temperature to calculate the total pressure in the container.
💡Gas Constant
'Gas constant' (R) is a fundamental constant in the ideal gas law, used to relate the pressure, volume, and temperature of a gas. The video script specifies the value of R as 8.3145 meters cubed pascals per mole Kelvin (m^3 Pa/mol K). This constant is crucial for converting the number of moles and temperature into pressure.
💡Percentage Composition
'Percentage composition' refers to the proportion of each type of gas in the mixture by mass. The script provides the percentages of oxygen, hydrogen, and nitrogen in the total mass of the gas mixture. These percentages are used to calculate the moles of each gas, which in turn are used to determine the partial pressures.
Highlights

A four-meter cubed container filled with a mixture of oxygen, hydrogen, and nitrogen gases is considered.

The total mass of the gas mixture is 2.1 kilograms, with specific percentages for each gas type.

The calculation of moles of nitrogen is demonstrated using its percentage in the mixture and molar mass.

50 moles of nitrogen (N2) are determined, highlighting the relationship between mass and moles.

The process for calculating moles of oxygen involves using its percentage of the total mass and molar mass.

20 moles of oxygen (O2) are calculated, emphasizing the atomic mass of oxygen in the calculation.

Hydrogen's moles are determined by its percentage in the mixture and its atomic mass, resulting in 30 moles of hydrogen (H2).

The concept of partial pressure and its relation to the number of gas particles is introduced.

The total number of moles of gas particles in the container is summed up to be 100 moles.

The application of the ideal gas law (PV=nRT) to calculate the total pressure in the container is explained.

The total pressure is calculated to be 56,746 pascals, demonstrating the use of R and temperature in the formula.

Conversion of the total pressure to atmospheres and kilopascals for different unit perspectives.

The method to find the partial pressure of each gas based on their moles percentage in the total mixture is detailed.

The partial pressures of oxygen, nitrogen, and hydrogen are calculated, showing their individual contributions to the total pressure.

The importance of understanding that each molecule contributes to the total pressure proportional to its moles is emphasized.

A verification that the sum of partial pressures equals the total pressure, reinforcing the concept of ideal gas behavior.

The conclusion highlights the significance of mole count over mass in determining partial pressures in an ideal gas mixture.

Transcripts

Browse More Related Video

Introduction to partial pressure | Gases and kinetic molecular theory | Chemistry | Khan Academy

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

9.3 Additional Gas Laws | Dalton's Law and Graham's Law | High School Chemistry

Daltons Law | Partial Pressures

Gas Law Problems Combined & Ideal - Density, Molar Mass, Mole Fraction, Partial Pressure, Effusion

Gas Stoichiometry Problems

Rate This

5.0 / 5 (0 votes)

Thanks for rating:

Related Tags
Gas DynamicsPressure CalculationMolecular MolesIdeal GasesPartial PressuresChemical MixturesPhysics LessonEducational ContentMolecular MassStandard TemperatureKinetic Theory