Gas Volumes and the Ideal Gas Law

Gas Volumes and the Ideal Gas Law

By Abby Fancsali

Avogadro's Law and standard volume of a gas

• When studying gases early on, there was confusion as to how​ certain reactions between gases yielded different volumes than expected

  • Example: 2 Liter of hydrogen gas + 1 liter of oxygen gas = 2 liters of water vapor​

• Avo​gadro found that these reactions occurred based not on the volumes, but on the number of moles involved in the reaction

  • Recall: hydrogen gas= H₂ and Oxygen gas= O_2,

• Avogadro's Law: volumes of gases at the same temperature and pressure contain the same number of moles

  • V=kn​

    • k is a constant, n=number of molecules​

• Recall: at STP 22.4 of gas L in one mole

Avogadro's Law and standard volume of a gas Sample Problem 1

• What Volume does 0.0685 mol of gas occupy at STP?

  • Step one: convert moles of gas to liters​

Avogadro's Law and standard volume of a gas Sample Problem 2

• What Quantity of gas, in moles, is contained in 2.21 L at STP?

  • Step one: convert liters of gas to moles

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

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

Ideal Gas Law Sample Problem 1

• What is the pressure in the atmosphere exerted by a 0.500 mol sample of nitrogen gas in a 10 L container at 298 K?

  • Step 1: Identify what we know

    • P=

    • n=

    • V=

    • T​

    • R=

Ideal Gas Law Sample Problem 1

• What is the pressure in the atmospheres exerted by a 0.500 mol sample of nitrogen gas in a 10 L container at 298 K?

  • Step 1: Identify what we know

    • P= ?

    • n=0.500 mol

    • V= 10.0 L

    • T​= 298

    • R=

  • Step 2: Figure out our R Value by looking at the unit for Pressure

Multiple Choice

Which R value do we want to use to solve this problem?

• $$62.4\ \frac{L\cdot mm\ Hg}{mol\cdot K}$$  

• $$0.0821\ \frac{L\cdot atm}{mol\cdot K}$$  

• $$8.314\ \frac{L\cdot kPa}{mol\cdot K}$$  

Ideal Gas Law Sample Problem 1

• What is the pressure in the atmospheres exerted by a 0.500 mol sample of nitrogen gas in a 10 L container at 298 K?

  • What we know

    • P= ?

    • n=0.500 mol

    • V= 10.0 L

    • T​= 298

    • R=0.0821

  • Step 3: Plug our values into the ideal gas equation and solve

Ideal Gas Law Sample Problem 2

• What Pressure in atmospheres is exerted by 0.325 mol of hydrogen gas in a 4.08 L container at 35 °C?

  • Step 1: Identify what we know

    • P=

    • n=

    • V=

    • T​=

    • R=

Ideal Gas Law Sample Problem 2

• What Pressure in atmospheres is exerted by 0.325 mol of hydrogen gas in a 4.08 L container at 35 °C?

  • Step 1: Identify what we know

    • P= ?

    • n=0.325

    • V= 4.08 L

    • T​= 35+273= 308

    • R=

  • Step 2: Figure out our R Value by looking at the unit for Pressure

Multiple Choice

Which R value do we want to use to solve this problem?

• $$62.4\ \frac{L\cdot mm\ Hg}{mol\cdot K}$$  

• $$0.0821\ \frac{L\cdot atm}{mol\cdot K}$$  

• $$8.314\ \frac{L\cdot kPa}{mol\cdot K}$$  

Ideal Gas Law Sample Problem 2

• What Pressure in atmospheres is exerted by 0.325 mol of hydrogen gas in a 4.08 L container at 35 °C?

  • What we know

    • P= ?

    • n=0.325

    • V= 4.08 L

    • T​= 35+273= 308

    • R= 0.0821

  • Step 3: Plug in information and Solve