Chapter 14 Notes Chapter 14 Notes Part IPart I

Boyle’s, Charles’ and Boyle’s, Charles’ and Gay-Lussac’s LawsGay-Lussac’s Laws

Combined Gas LawsCombined Gas Laws

GasGasReviewReview

•In chapter 13 gases were In chapter 13 gases were said to be mostly said to be mostly empty empty spacespace..

•This gives rise to a This gives rise to a property called property called compressibilitycompressibility..

•The particles in a gas can The particles in a gas can be forced closer together.be forced closer together.

Kinetic Theory

• Kinetic Energy—Energy that an object has due to motion.

• The Kinetic Theory states that tiny particles form all matter, and they are constantly in motion.

Gases

A gas is composed of particles that are small, hard spheres with almost no volume or particle interaction.

Gases

Particles in a gas are in constant motion—they travel straight paths unless they collide with another particle or their container.

Gases

All collisions are considered elastic—no energy is lost

Temperature When a substance is

heated, the particles speed up, causing faster movement and more collisions.

This is a rise in temperature.

Obj. 1…Ideal vs. real gasesObj. 1…Ideal vs. real gases• behavior of ‘ideal gases’ (from kinetic theory)…behavior of ‘ideal gases’ (from kinetic theory)…

~ ______ relationship b/n P and V.~ ______ relationship b/n P and V. inverseinverse

~ ______ relationship b/n T and V.~ ______ relationship b/n T and V.

~ ______ relationship b/n T and P.~ ______ relationship b/n T and P.

directdirect

directdirect

• however, there are no ‘ideal’ gases in existence.however, there are no ‘ideal’ gases in existence.

• two properties keep ‘real’ gases from being ‘ideal’…two properties keep ‘real’ gases from being ‘ideal’…

~ real gas particles have ~ real gas particles have distinct volumesdistinct volumes

~ real gas particles are ~ real gas particles are slightly attracted to each slightly attracted to each otherother……

……there comes athere comes a

point where V can not get smaller, no matter how much P is appliedpoint where V can not get smaller, no matter how much P is applied

intermolecular attraction of gas molecules causes gases to occupyintermolecular attraction of gas molecules causes gases to occupyless space than assumed by the KT.less space than assumed by the KT.

Obj. 2-3…STPObj. 2-3…STP• STP = standard temperature and pressureSTP = standard temperature and pressure

• standard temp = standard temp =

~ 0°C~ 0°C

~ ~ 273273 K ** K **

• standard pressure = standard pressure =

~ 1 atm~ 1 atm

~ 101.3 kPa~ 101.3 kPa ~ 760 mmHg~ 760 mmHg

•There are three There are three relationships between the relationships between the conditions a gas is in that conditions a gas is in that will be affected by this will be affected by this property.property.

•Pressure and volumePressure and volume•Volume and temperatureVolume and temperature•Pressure and temperaturePressure and temperature

•Boyles LawBoyles Law states that as states that as the volume of a gas is the volume of a gas is decreased, the amount of decreased, the amount of pressure is increased at pressure is increased at constant temperature. constant temperature.

•(P(PVV or P or PVV))• Mathematically, Mathematically,

P1V1=P2V2

Obj. 4-6…Boyle’s LawObj. 4-6…Boyle’s Law• relationship b/n P and V is expressed in the relationship b/n P and V is expressed in the Boyle’s Boyle’s LawLawequation.equation.

~ inverse relationship~ inverse relationship ~ only works if T remains constant!~ only works if T remains constant!

pp11vv11 = p = p22vv22• Ex…Ex…• The pressure on 2.5 L of a gas decreases from 105 kPa The pressure on 2.5 L of a gas decreases from 105 kPa toto40.5 kPa. What is the new volume of the gas?40.5 kPa. What is the new volume of the gas?

VV11 PP11

PP22 VV22

105(2.5) = 105(2.5) = 40.540.5(x)(x)

262.5 = 40.5262.5 = 40.5(x)(x)

40.540.540.540.5 6.5 liters6.5 liters

Why?Why?

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

•Charles Law states that as the temperature of a gas is increased, the volume is also increased at constant pressure.

•(VT or VT)•Mathematically:

V1 = V2

T1 T2

Obj. 7-9…Charles’s LawObj. 7-9…Charles’s Law• relationship b/n T and V is expressed in the relationship b/n T and V is expressed in the Charles’ Charles’ LawLawequationequation..

~ direct relationship~ direct relationship ~ only works if P remains constant!~ only works if P remains constant!

vv11 = v = v22

• Ex…Ex…• If a sample of gas occupies If a sample of gas occupies 6.86.8 L at L at 125125°C, what will its °C, what will its

volume be at volume be at 3838°C if pressure remains constant?°C if pressure remains constant?

VV11 TT11

TT22VV22

6.86.8311311398398

5.3 liters5.3 liters

TT11 TT22

~ temp. ~ temp. MUSTMUST be in Kelvin!!! be in Kelvin!!! (°C + (°C + 273273))

= 398 K= 398 K

= 311 K= 311 K

== xxxx ==

6.8 (311)6.8 (311)398398

Why?•As the temperature increases, As the temperature increases,

the average kinetic energy of the average kinetic energy of the particles increases.the particles increases.

•This increases the amount of This increases the amount of volume needed to maintain the volume needed to maintain the same frequency of collision with same frequency of collision with the surface of the container.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=K=ooC+27C+2733

When comparing temperatures during this chapter, they must be in

Kelvin, because Celsius is a degreed scale and Kelvin is

an absolute scale!

•Gay-Lussac’s Law states that as you increase temperature of an amount of gas, its pressure will increase if at a constant volume.

• (PT or PT)• Mathematically:

P1 = P2

T1 T2

Obj. 10-12…Gay-Lussac’s Obj. 10-12…Gay-Lussac’s LawLaw• relationship b/n T and P is expressed in the relationship b/n T and P is expressed in the Gay-Gay-

Lussac’sLussac’sLawLaw equation. equation. ~ direct relationship~ direct relationship ~ only works if V remains constant!~ only works if V remains constant!

PP11 = P = P22

• Ex…Ex…• A sample of gas has a pressure of 6.58 kPa at 339 K. A sample of gas has a pressure of 6.58 kPa at 339 K. What What will the temperature be at 4.21 kPa?will the temperature be at 4.21 kPa?

PP11 TT11

TT22 PP22

6.586.58xx339339 217 217

KK

TT11 TT22

~ temp. ~ temp. MUSTMUST be in Kelvin!!! be in Kelvin!!! (°C + (°C + 273273))

== 4.214.21xx ==

339 339 (4.21)(4.21)6.586.58

Why?• As the temperature increases, As the temperature increases,

the average kinetic energy of the average kinetic energy of the particles increases, thus the particles increases, thus they move faster.they move faster.

• This increases the frequency of This increases the frequency of collisions, as well as the collisions, as well as the amount of force in each amount of force in each collision.collision.

But wait a minute...

NO! There’s a handy, dandy equation that will show you ALL these equations in one!

Are you saying that I have to keep ALL these equations straight in my head?

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?

Practice Problem #2

•A balloon has a volume of 6.7L at 20oC. What will its volume be at 350oC if it is at constant pressure?

Practice Problem #3

•The pressure in an automobile tire that has a constant volume is 198 kPa at 27oC. On a hot sunny day the pressure has risen to 225 kPa. What is the temperature?

Practice Problem #4• A gas at 155 kPa and 25A gas at 155 kPa and 25ooC C

occupies a container with an occupies a container with an initial volume of 1.00L. By initial volume of 1.00L. By changing the volume the changing the volume the pressure of the gas increases pressure of the gas increases to 605 kPa as the temperature to 605 kPa as the temperature is raised to 125is raised to 125ooC. What is the C. What is the new volume?new volume?