Gases Part 2: Boyle's Law and Charles's Law

Introduction​

• The Gas Laws are a set of mathematical relationships between

  • volume

  • temperature

  • pressure

  • amount of gas​

Section 1: Boyle's Law​

• Robert Boyle found that doubling the pressure on a sample reduced the volume of a gas by half

  • A smaller area means gas molecules have less room and are more likely to bump into one another

• Mathematically shown:

  • P ×​ V = k

    • k is a constant

  • P₁ × V₁ = P₂ × V₂

    • The units do not matter as long as they are the same on both sides of the equation!

Section 1: Boyle's Law​ Sample Problem 1

• A Sample of Oxygen Gas has a Volume of 150.0 mL when its Pressure is 0.947 atm. What will the volume of the gas be at 0.987 atm if the volume of the gas remains constant?

  • Identify what we have

    • V₁= 150

    • P₁=0.947

    • V₂ = ?

    • P₂ =0.987

  • Plug our Values into Boyle's Law

    • 150 x 0.947 = V₂ x 0.987 ​

Section 1: Boyle's Law​ Sample Problem 2

• A helium ballon contains 125 mL of gas at a pressure of 0.974 atm. What Volume will the gas occupy at STP (1 atm)?

  • Identify what we have

    • V₁= 125

    • P₁=0.974

    • V₂ = ?

    • P₂ =1

  • Plug our Values into Boyle's Law

    • 125 x 0.974 = V₂ x 1 ​

Section 1: Boyle's Law​ Sample Problem 3

• Use Boyle's Law to solve for the missing value

  • V₁= 2 x 10⁵ L

  • P₁=?

  • V₂ = 1.8 x 10³

  • P₂ = 180 mm Hg

• Plug our Values into Boyle's Law

  • (2 x 10⁵) x P₁ = (1.8 x 10³) x 180 ​

The Kelvin Temperature Scale

• The Kelvin Temperature scale is used in Charles's Law

  • Convert from Celsius by adding 273 to your temperature

    • 0 ° C = 273 K

    • 100 ° C = 373 K

Section 2: Charles's Law

• Charles's Law looks at how Temperature affects a gas

  • When the pressure is constant, an increase in temperature also increases the volume

    • All Gases expand to the same extent when heated by the same temperature interval​

  • Mathematically: V/T = k

    • For changes:

Section 2: Charles's Law Sample Problem 1

• A Sample of neon Gas occupies a volume of 752 mL at 25° C. What will the Volume be at 50° C if the pressure remains constant?

  • Step 1: Identify what we know

    • V₁= 752 mL

    • T₁= 25°​C

    • V₂=?

    • T₂= 50°C

  • Step 2 Change Temperatures to Kelvin

    • T₁= 25 + 273

    • T₂= 50 + 273

Section 2: Charles's Law Sample Problem 1

• A Sample of neon Gas occupies a volume of 752 mL at 25° C. What will the Volume be at 50° C if the pressure remains constant?

  • what we know

    • V₁= 752 mL

    • T₁= 298°​C

    • V₂=?

    • T₂= 323°C

  • Step 3: Plug Values into our Equation and solve for our unknown

Section 2: Charles's Law Sample Problem 2

• A balloon filled with Oxygen gas occupies a volume of 5.5 L at 25°C. What Volume will the balloon be at 100°C?

  • what we know°

    • V₁= 5.5 L

    • T₁= 25°​C + 273 = 298

    • V₂=?

    • T₂= 100°C+273 =373 K

  • Step 3: Plug Values into our Equation and solve for our unknown