Ideal Gas

Lesson 9.3: Ideal Gases

What is an Ideal Gas?

• Ideal Gas: A hypothetical Gas that exactly obeys the kinetic model of gases

  • Particles have insignificant size and no intermolecular attractive forces

  • An ideal gas always obeys the Gas laws we described

  • Not really possible outside of a controlled lab setting

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Experience Chemistry | Lesson 9.3

The Ideal Gas Law

• Pressure, Volume, Temperature, and moles all are used to describe a gas sample

• Using all the laws we know, we can combine them to make the Ideal gas law

  • tells you the state of a gas under the most ideal circumstances

  • PV=nRT

    • P= Pressure

    • V=Volume

    • n=number​ of moles

    • R= a constant

    • T=Temperature in Kelvin

Experience Chemistry | Lesson 9.3

The Ideal Gas Constant

• R= The ideal Gas constant

  • Value depends on what units you are using in ideal gas problem

    • ​Units for T and n will never change

    • V should be in Liters

Experience Chemistry | Lesson 9.3

Ideal Gas Law Sample Problem 1

• A deep underground cavern contains 2.24 x 10⁶ L of Methane Gas (CH₄) at a pressure of 1.50 x 10³ kPa and a temperature of 315 K. How many kilograms of CH₄ does the cavern contain?

  • Step 1: Identify the known and unknown variables

    • P=

    • T=

    • V=

    • R=

    • n=​

Experience Chemistry | Lesson 9.3

Ideal Gas Law Sample Problem 1

• A deep underground cavern contains 2.24 x 10⁶ L of Methane Gas (CH₄) at a pressure of 1.50 x 10³ kPa and a temperature of 315 K. How many kilograms of CH₄ does the cavern contain?

  • Step 1: Identify the known and unknown variables

    • P= 1.50 x 10³ kPa

    • T= 315 K

    • V=2.24 x 10⁶ L

    • R= 8.31

    • n=​?

  • Step 2: Rearrange the Ideal Gas Law equation to solve for n

    • PV=nrT --> n= (PV)/(rT)

Experience Chemistry | Lesson 9.3

Ideal Gas Law Sample Problem 1

Experience Chemistry | Lesson 9.3

Ideal Gas Law Sample Problem 1

• A deep underground cavern contains 2.24 x 10⁶ L of Methane Gas (CH₄) at a pressure of 1.50 x 10³ kPa and a temperature of 315 K. How many kilograms of CH₄ does the cavern contain?

  • Step 4: Convert your moles to kilograms using the molar mass

    • Molar mass of Methane

      • 1 C=12

      • 4 H= 4 *1=4

      • 12+4=16 

Experience Chemistry | Lesson 9.3

Ideal Gas Law Sample Problem 2

• A Child's lungs can hold 2.20 L of air. How many grams of air do her lungs hold at a pressure of 102 kPa and body temperature of 37°C? (Use a molar mass of 29 g/mol for air)

  • Step 1: Identify the known and unknown variables

    • P=

    • T=

    • V=

    • R=

    • n=​

Experience Chemistry | Lesson 9.3

Ideal Gas Law Sample Problem 2

• A Child's lungs can hold 2.20 L of air. How many grams of air do her lungs hold at a pressure of 102 kPa and body temperature of 37°C? (Use a molar mass of 29 g/mol for air)

  • Step 1: Identify the known and unknown variables

    • P= 102

    • T= 37+ 273= 310

    • V=2.20 L

    • R= 8.31

    • n=​

  • Step 2: Rearrange the Ideal Gas Law equation to solve for n

    • PV=nrT --> n= (PV)/(rT)

Experience Chemistry | Lesson 9.3

Ideal Gas Law Sample Problem 2

• A Child's lungs can hold 2.20 L of air. How many grams of air do her lungs hold at a pressure of 102 kPa and body temperature of 37°C? (Use a molar mass of 29 g/mol for air)

  • Step 3: Convert your moles to kilograms using the molar mass

Experience Chemistry | Lesson 9.3

Applications of the Ideal Gas Law

• The Ideal Gas Law can be used to find the molar volume and density of a gas if certain properties are known

  • Makes it easier to work with large amounts of gas like the atmosphere because those amounts are so large

  • Rewriting the ideal gas law in terms of molar volume

    • V_m​= (RT)/P

  • Rewriting the ideal gas law in terms of density (ρ)

    • ρ= (PM)/(RT)

      • M= molar mass

Experience Chemistry | Lesson 9.3

Applications of the Ideal Gas Law Sample 1

• The CO₂ gas inside a rigid container of a fire extinguisher is held at high pressure (5,700 kPa). Determine the molar volume and the density of the contained CO₂ gas if the fire extinguisher has been sitting at room temperature (298 K)?

  • Step 1: Identify you variables

    • V_m=

    • R=

    • T=

    • P=

    • M=

Experience Chemistry | Lesson 9.3

Applications of the Ideal Gas Law Sample 1

• The CO₂ gas inside a rigid container of a fire extinguisher is held at high pressure (5,700 kPa). Determine the molar volume and the density of the contained CO₂ gas if the fire extinguisher has been sitting at room temperature (298 K)?

  • Step 1: Identify you variables

    • V_m= ?

    • R= 8.31

    • T=298

    • P= 5, 700 KPa​

    • M= 12 + (2 x 16)=44

Experience Chemistry | Lesson 9.3

Applications of the Ideal Gas Law Sample 1

• The CO₂ gas inside a rigid container of a fire extinguisher is held at high pressure (5,700 kPa). Determine the molar volume and the density of the contained CO₂ gas if the fire extinguisher has been sitting at room temperature (298 K)?

  • Step 2: Plug your values into your equation

Experience Chemistry | Lesson 9.3

Isobaric, Isovolumetric, & Isothermal Processes

Experience Chemistry | Lesson 9.3