Kinetic Molecular Theory

1) Gas particles do not attract or repel.2) Gas particles are smaller than space between

them.(almost all the volume of a gas is empty space)

3) Gas particles (atoms or molecules) are in constant random motion.

4) No Kinetic Energy is lost when gas particles collide.

5) All gasses have the same average K.E. at a given temperature.

GAS LAWSGAS LAWS Basis of Gas Laws is the

Interdependence of Gas Variables: Volume Pressure Temperature Number of Moles

STP (standard temperature STP (standard temperature and pressure)and pressure)

• Standard temperature is either:

• 0° Celsius or 273 Kelvin (no ° sign)• For these formulas, Temperature MUST BE IN KELVIN (remember 0 deg. K is the absence of all heat energy!)

Standard pressure in several units:

• 1 atm = 101.3 KPa =760 mm of Hg = 760 torr

The volume for one mole of a gas at STP is 22.4 L

Boyles LawBoyles LawWhen the temperature and the # of

moles of a sample of a gas is held constant, its volume is inversely proportional to its pressure.

In other words, as volume increases, pressure decreases, or as volume decreases, pressure increases.

P1V1=P2V2

(inverse relationship graph)

P

V

Practice ProblemsPractice Problems

• If a gas has a volume of 100 mL when the pressure is 1.50 atm, what is the volume in mL when the pressure is increased to 4.5atm, and the temperature is held constant?

• Think first: If my pressure increases, what should the volume do?____________________

• V1= P1= V2 = P2=

Practice ProblemsPractice Problems

• If a gas has a volume of 100 mL when the pressure is 1.50 atm, what is the volume in mL when the pressure is increased to 4.5atm, and the temperature is held constant?

• Think first: If my pressure increases, what should the volume do? (Decrease)

V1= 100 mL; P1=1.5 atm; V2 =? P2= 4.5 atm

1.5 atm x 100 mL = 4.5 atm x ? mL

1.5 atm x 100 mL = ? mL = 33mL(decrease) 4.5 atm

Charles’ LawCharles’ Law• If pressure is held constant, when

temperature increases, volume will increase. When the temperature decreases, volume will decrease. (directly proportional)

• To convert degrees Celsius to Kelvin add 273… because 0 K is the same as -273 °C

Charles’ LawCharles’ LawRemember, standard temperature is 273 K

• V1 = V2 at constant pressure

T1 T2

Direct relationship graphV

T

Charles’ LawCharles’ Law

• So if you are solving for a variable

• V1T2 = V2T1 or V1 T2 = V2

T1

Gay-Lussac’s LawGay-Lussac’s Law• If volume is held constant, when

temperature increases, pressure will increase. When the temperature decreases, pressure will decrease. (directly proportional)

• Temperatures must be in Kelvin.

Gay-Lussac’s LawGay-Lussac’s Law• Remember, standard pressure is 1 atm or 101.3 kPa

• P1 = P2 at constant volume

T1 T2

Direct proportional graphP

T

Boyle’s LawBoyle’s Law

Robert Boyle Robert Boyle (1627-1691). Son (1627-1691). Son of Earl of Cork, of Earl of Cork, IrelandIreland

Boyle’s LawBoyle’s Law

Jacques Charles (1746-Jacques Charles (1746-1823). Isolated boron 1823). Isolated boron and studied gases. and studied gases. Balloonist.Balloonist.

Joseph Louis Gay-Lussac Joseph Louis Gay-Lussac (1778-1850)(1778-1850)

Which heel exerts more pressure on a surface

http://genchem.chem.wisc.edu/demonstrations/Gen_Chem_Pages/05gasespage/collapsing_aluminum_can.htmhttp://www.delta.edu/slime/cancrush.html

http://http://www.kentchemistry.com/www.kentchemistry.com/

links/GasLaws/manBar.htm links/GasLaws/manBar.htm

Combined Gas LawCombined Gas Law• We can use one big equation for all the

laws except Dalton’s. This is called the Combined Gas Law.

• That means there are only 2 equations to remember

• P1V1 = P2V2 or rewritten…

T1 T2

• P1V1T2=P2V2T1

WEB SITEWEB SITE

• PhET Simulations.lnk

http://phet.colorado.edu/simulations/sims.php?sim=Gas_Properties

Tricks Tricks • Use P1V1T2=P2V2T1

• Ignore the constants(they cancel out)

• Box the numbers AND units given!!!

• List out P1=V1= T1= P2= V2= T2=

• Temperatures in KELVIN!!!

• Remember, STP is 273 K and 1.0 atm (101.3 kPa, 760 torr, 760 mmHg)

• Plug and chug…

Example Problem #2Example Problem #2

Calculate the moles that are in 19.7 L of gas at STP.

19.7 L X 1 mole = ? Moles

22.4 L

19.7 L X 1 mole = 0.881 moles

22.4 L

Ideal Gas LawIdeal Gas Law•The physical behavior of a single gas sample in terms of the pressure,volume, temperature, number of moles of gas present or PV =nRTP= Pressure V= Volume n= moles of gas R= ideal gas constantT= Temperature

Ideal Gas LawIdeal Gas Law

• Assumes that Particles:

– take up no space

– have no intermolecular attractive forces

– follows the gas laws under all conditions of T and P

Ideal Gas Constant Ideal Gas Constant (R)(R)

• An experimentally determined constant whose value in the ideal gas equation depends on the units used for pressure

0.0821 if in Latm/molK8.314 if in LkPa/molK62.4 if in LmmHg/molK

To Be Ideal GasesTo Be Ideal Gases

• Must completely follow the gas laws

• Cannot liquify

• Must be at:– low pressures– high temperatures

Real vs Ideal GasesReal vs Ideal Gases

• Most gases will behave like ideal gases except when:

– At extremely high pressures– At low temperatures– A polar gas

– A large gas molecule (C4H10)

Example ProblemExample Problem• Calculate the number of moles of gas contained in a 3.0 L vessel at 3.00 x 102 K with a pressure of 1.50 atm

PV = nRT

V = 3.0 L T = 3.00 x 102 K = 300KP = 1.50 atm R = .0821 Latm/molKn = ?

Answer:Answer:V = 3.0 L T = 3.00 x 102 K = 300KP = 1.50 atm R = .0821 Latm/molKn = ?

PV = nRT

P V n R T

(1.5atm)(3.0L) =n(.0821 Latm/molK)(300 K)

n = (1.5 atm)(3.0 L) .

(.0821 Latm/molK)(300 K)

n = .18 mol