Boyle’s Charles’ and Gay-Lussac’s Laws Combined Gas Laws Chapter 12 Notes, part I Boyle’s Charles’ and Gay-Lussac’s Laws Combined Gas Laws

From Last Episode... In chapter 10 gases were said to be mostly empty space. This gives rise to a property called compressibility. The particles in a gas can be forced closer together.

3 Relationships... There are three relationships between the conditions a gas is in that will be affected by this property. Pressure and volume Volume and temperature Pressure and temperature

Pressure vs. volume (Boyle’s Law) As the volume of a certain amount of gas is decreased, the amount of pressure is increased at constant temperature. (P#V$ or P#V$) Mathematically, P1V1=P2V2

Why? With less volume, there is greater frequency of the same amount of particles hitting the surface of the container.

Temperature and Volume (Charles’ Law) As the temperature of an amount of gas is increased, the volume is increased at constant pressure. (V#T# or V$T$) Mathematically: V1 V2 T1 T2 =

Why? As the temperature increases, the average kinetic energy of the particles increases. This increases the amount of volume needed to maintain the same frequency of collision with the surface of the container.

Meanwhile... Jaques Charles also noticed that no matter what gas he experimented with, when he extrapolated the volume down on a graph, the temperature was the same: -273oC!

Kelvin William Thomson (a.k.a. Lord Kelvin) recognized this as the theoretical point at which the average kinetic energy of all substances would be zero. Thus, the concept of absolute zero and the Kelvin scale were born!

K=oC+273

When comparing temperatures during this chapter, they must be in Kelvin, because Celsius is a degreed scale and Kelvin is an absolute scale!

Pressure and Temperature (Gay-Lussac’s Law) As you increase temperature of an amount of gas, its pressure will increase if at a constant volume. (P#T# or P$T$) Mathematically: P1 P2 T1 T2 =

Why? As the temperature increases, the average kinetic energy of the particles increases, thus they move faster. This increases the frequency of collisions, as well as the amount of force in each collision.

But wait a minute... Are you saying that I have to keep ALL these equations straight in my head? NO! There’s a handy, dandy equation that will show you ALL these equations in one!

Combined Gas Laws P1V1 P2V2 T1 T2 =

When one variable is constant, you can just cross it out, and the equation works for all three laws, as well as for combined problems!

Practice Problem #1 The pressure on 2.5L of anesthetic gas changes from 105 kPa to 40.5 kPa. What will the new volume be if the temperature is constant? ANS: 6.5L

Practice Problem #2 A balloon has a volume of 6.7L at 20oC. What will its volume be at 350oC? ANS: 14.2L

Practice Problem #3 The pressure in an automobile tire is 198 kPa at 27oC. On a hot sunny day the pressure has risen to 225 kPa. What is the temperature? ANS: 341K or 68oC

Practice Problem #4 A gas at 155 kPa and 25oC occupies a container with an initial volume of 1.00L. By changing the volume the pressure of the gas increases to 605 kPa as the temperature is raised to 125oC. What is the new volume? ANS: 0.34L