Ideal gas equation example 3 | Chemistry | Khan Academy

Khan Academy
28 Aug 200905:46
EducationalLearning
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TLDRThis educational video script delves into the ideal gas equation, clarifying the role of the ideal gas constant 'R' as a unit converter and proportionality constant. It demonstrates the calculation of moles of O2 in a specific volume and pressure, converting the result to grams using the molar mass of oxygen. The script aims to demystify the concept of 'R' and provides a step-by-step problem-solving approach, culminating in determining the mass of oxygen in a 300-milliliter container at 12 atmospheres and 10 degrees Celsius, concluding with approximately 5 grams of O2.

Takeaways
  • 📚 The ideal gas equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.
  • 🔍 The ideal gas constant (R) is a proportionality constant that ensures the units are correct and translates between the world of moles and Kelvins to the world of pressure and volume.
  • 🌡️ Temperature in the ideal gas equation must be in Kelvin, not Celsius.
  • 🔄 The ideal gas constant converts mole Kelvins to joules, matching the units of pressure times volume.
  • 🧪 The script discusses the conversion of units from atmospheres and liters to joules using the ideal gas constant.
  • 📉 The script addresses a common misconception about the ideal gas constant being mysterious, explaining its role in unit conversion and proportionality.
  • 📝 The script provides a step-by-step example problem involving a 300-milliliter container of oxygen at 12 atmospheres pressure and 10 degrees Celsius.
  • 🔢 The example problem involves calculating the number of moles of O2 in the container using the ideal gas equation.
  • 📏 Conversion from milliliters to liters is necessary for the volume in the ideal gas equation.
  • 🌡️ The temperature must be converted from Celsius to Kelvin for use in the ideal gas equation.
  • 🧪 The molar mass of O2 is 32 grams per mole, which is used to calculate the mass of oxygen in grams from the number of moles.
  • 📊 The final calculation in the example results in approximately 5 grams of molecular oxygen in the container.
Q & A

  • What is the ideal gas equation?

    -The ideal gas equation is PV = nRT, where P is the pressure, V is the volume, n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature in Kelvin.

  • Why is the ideal gas constant R considered mysterious by some?

    -The ideal gas constant R might seem mysterious because it sets the exact constant of proportionality and ensures the units are correct when converting between different units of pressure, volume, and temperature.

  • What does the ideal gas constant R represent in the equation PV = nRT?

    -In the equation PV = nRT, R represents the ideal gas constant that converts the product of moles and Kelvin into a unit of energy (joules), ensuring that the units on both sides of the equation are consistent.

  • How is the pressure times volume (PV) related to energy in the context of the ideal gas equation?

    -Pressure times volume (PV) is proportional to the total energy in the system. Temperature represents the average energy per molecule, and when multiplied by the total number of molecules (n), it gives the total energy in the system.

  • What is the unit of the ideal gas constant R when using liters and atmospheres?

    -The unit of the ideal gas constant R when using liters and atmospheres is liter-atmosphere per mole-Kelvin (L·atm/mol·K).

  • How do you convert 300 milliliters to liters?

    -To convert 300 milliliters to liters, you divide by 1000, which gives you 0.3 liters (300 mL = 0.3 L).

  • What is the value of the ideal gas constant R in the context of the problem with liters and atmospheres?

    -The value of the ideal gas constant R in the context of the problem with liters and atmospheres is 0.082 L·atm/mol·K.

  • Why is it necessary to convert the temperature to Kelvin when using the ideal gas equation?

    -It is necessary to convert the temperature to Kelvin when using the ideal gas equation because the equation requires the temperature to be in absolute units, which is Kelvin, to accurately represent the average kinetic energy of the gas molecules.

  • How many degrees Celsius correspond to 283 Kelvin?

    -To convert 283 Kelvin to Celsius, you subtract 273.15, which gives you 10 degrees Celsius (283 K - 273.15 = 10°C).

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

    -The molar mass of O2 (oxygen gas) is 32 grams per mole, since each molecule of O2 consists of two oxygen atoms, each with an atomic mass of approximately 16 u.

  • How do you calculate the mass of O2 in grams given the number of moles?

    -To calculate the mass of O2 in grams, you multiply the number of moles by the molar mass of O2. For example, if you have 0.155 moles of O2, you would multiply 0.155 by 32 grams/mole to get the mass in grams.

Outlines
00:00
🧪 Ideal Gas Law and the Mysterious Constant R

This paragraph delves into the ideal gas equation, PV = nRT, and addresses a common confusion about the ideal gas constant, R. It clarifies that R is a proportionality constant that ensures the correct units of energy (joules) when converting between moles, Kelvin, and pressure-volume units. The paragraph also demonstrates how to use the ideal gas equation to solve for the number of moles of a gas given specific conditions, using the example of oxygen gas in a 300-milliliter container at 12 atmospheres pressure and 10 degrees Celsius. The process involves converting the temperature to Kelvin, using the appropriate value of R for the units involved, and solving for the number of moles (n).

05:02
📚 Calculating the Mass of Oxygen Gas Using Ideal Gas Law

Building on the previous explanation of the ideal gas equation, this paragraph focuses on calculating the mass of oxygen gas (O2) in a specific volume under given conditions. It provides a step-by-step calculation starting from the ideal gas equation, using the known values of pressure, volume, and temperature converted to Kelvin. The calculation results in the determination of the number of moles of O2 present. The paragraph then explains how to convert moles to grams by using the molar mass of oxygen, which is 32 grams per mole, given that an oxygen molecule consists of two oxygen atoms. The final step is to multiply the number of moles by the molar mass to obtain the mass in grams, concluding that approximately 5 grams of O2 are present in the container.

Mindmap
Keywords
💡Ideal Gas Equation
The Ideal Gas Equation is a fundamental principle in physical chemistry that describes the behavior of an ideal gas. It is represented as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. In the video, the equation is used to solve problems involving the amount of gas in a container, demonstrating its central role in understanding gas behavior.
💡Pressure
Pressure in the context of the video refers to the force exerted per unit area on the walls of a container by the gas molecules inside. It is a key variable in the Ideal Gas Equation and is crucial in calculating the amount of gas present in a given volume. The script mentions pressure in atmospheres, which is a common unit for measuring pressure in chemistry.
💡Volume
Volume is the amount of space occupied by a substance, typically measured in liters or cubic meters. In the Ideal Gas Equation, volume is directly proportional to the number of moles of gas at a constant pressure and temperature. The video uses the volume of a container to determine the amount of oxygen gas present.
💡Moles
Moles are a unit of measurement used in chemistry to express amounts of a chemical substance, numerically equivalent to Avogadro's number (approximately 6.022 × 10^23). The video explains that the number of moles is essential in calculating the mass of a gas, as it relates directly to the amount of substance present.
💡Ideal Gas Constant (R)
The Ideal Gas Constant, denoted as R, is a physical constant that relates the pressure, volume, and temperature of an ideal gas. It has the unit of energy per mole per Kelvin (J/mol·K). The video script clarifies that R is crucial in converting units and ensuring the equation's balance, as it connects moles and Kelvins to the energy in joules.
💡Temperature in Kelvin
Temperature in Kelvin is an absolute temperature scale that starts at absolute zero, the lowest possible temperature. The video emphasizes the importance of using Kelvin instead of Celsius for scientific calculations, as it is necessary for the Ideal Gas Equation to maintain unit consistency and accuracy.
💡Energy per Molecule
Energy per molecule, or temperature, is a measure of the average kinetic energy of the molecules in a gas. The video script explains that temperature is proportional to the total energy in the system, which is crucial for understanding how gases behave under different conditions.
💡Oxygen (O2)
Oxygen, specifically molecular oxygen (O2), is a diatomic molecule consisting of two oxygen atoms. In the video, the mass of oxygen gas in a container is calculated using the Ideal Gas Equation, highlighting the application of chemical principles in real-world scenarios.
💡Molar Mass
Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). The video uses the molar mass of oxygen (32 g/mol) to convert the number of moles of O2 to grams, demonstrating the practical use of molar mass in chemical calculations.
💡Atmospheres
Atmospheres are a unit of pressure measurement commonly used in chemistry and physics. The video script uses atmospheres to express the pressure of the gas in the container, showing how different units of pressure can be used in the Ideal Gas Equation.
💡Joules
Joules are a unit of energy in the International System of Units (SI). The video script explains that pressure times volume (PV) results in a unit of energy (joules), which is essential for understanding the relationship between the physical properties of a gas and its energy content.
Highlights

Introduction to the ideal gas equation and its components.

Explanation of the ideal gas constant (R) and its role in the equation.

Clarification that R converts units and sets the exact constant of proportionality.

Description of how temperature in Kelvin relates to average energy per molecule.

Equation rearrangement to emphasize the proportionality between pressure times volume and energy.

Conversion of pressure times volume to joules to maintain unit consistency.

Introduction of a problem involving calculating grams of O2 in a container.

Use of the ideal gas equation to solve for the number of moles of O2.

Conversion of volume from milliliters to liters for the calculation.

Selection of the appropriate value for R based on the units used in the problem.

Conversion of temperature from Celsius to Kelvin for the equation.

Solving the equation for the number of moles of O2.

Calculation of the molar mass of O2 and its relation to grams.

Final calculation of the grams of O2 in the container.

Approximation of the final answer to 5 grams of molecular oxygen.

Transcripts

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Ideal GasEquationChemistryPhysicsMolesTemperaturePressureVolumeOxygenMolar Mass