Chapter 13

Gases and the Gas LawsMythbuster – cansI

Intro to gas laws

Gas Laws in Action: workers steam cleaned this tanker car and then sealed up the container, they came back the following morning to this disaster. (video)

Kinetic Theory Assumptions for an Ideal Gas

Gas particles are in constant, random motion Gas particles themselves have virtually no

volume Gas particles do not attract nor repel each other No kinetic energy is lost when particles collide If gases are at the same temp. they have the

same KE

NOTE: Real gases (actual gases) do NOT obey all the

assumptions made by the kinetic theory (only ideal gases behave this way- we will get exceptions later)

Factors (variables) that Affect Gases

1. Number of gas particles present

2. Temperature

3. Pressure

4. Volume of the sample

Animation (explanation)

Animation changing each of the variables (graph)

In a tied off balloon the pressure from the outside = pressure from the inside (in this chapter we will look at how changing the factors, changes these values)

=

STP

Standard temperature and standard pressure Standard temperature = 0° C (273 K) Standard pressure = 101.3 kPa (1 atm or

760 mm Hg)

Boyles Law

States that the volume of a gas is inversely proportional to its pressure if the temperature remains constant

As pressure goes up, volume goes down and vice versa if temperature is constant

PV = k

P V P x V

P1= 1 atm V1= 800 ml 800

P2= 2 atm V2= 400 ml 800

P3= 3 atm V3= 267 ml 800

P1V1 = 800

P2V2 = 800

So: P1V1 = P2V2

Boyles Law

If .600 L (V1)of a gas at 100.0 kPa (P1) changes to 62.4 kPa.(P2) What is the new volume if temperature remains constant?

P1V1 = P2V2

(100.0 kPa) (.600L) = (62.4 kPa) (V2)

.96153 L = V2

.962 L = V2

Note: you do not need to convert units as long as they match on both sides of the equation

A 185 ml sample has a pressure of 4.2 atm. What is it’s pressure when the volume is 250 ml if temperature remains constant?

P1V1 = P2V2

(4.2 atm)(185 ml) = P2 (250 ml)

3.1 atm = P2

Charles Law

Jacque Charles investigated the property of changing temperature on the volume of a gas (saw w/ each ° C change the volume changed by 1/273rd)

Charles Law – volume of a fixed mass of gas is directly proportional to its kelvin temperature if the pressure is constant

Ex. Helium balloon deflates when walking outside on a cold day

Charles Law:

V1 = V2

T1 T2

*** “T” must be in Kelvin ( K = C +273)

orV1T2 = V2T1

A balloon inflated in an air conditioned room at 28° C (T1) has a volume of 4.0 L (V1). If it is heated to a temperature of 58 °C ( T2), what is the new volume (V2) of the balloon if pressure remains constant?

V1 = V2

T1 T2

T1 = 28 + 273 = 301K

T2 = 58 + 273 = 331 K

V1T2 = V2

T1

(4.0 L ) (331 K) = V2

(301 K)

4.4 L = V2

Adjust the volume of 609 ml of a gas at 83°C to standard temperature.

Eggs and Gas Laws

Gay-Lussac’s Law

States that the pressure of a gas is directly proportional to the Kelvin temperature if volume is kept constant

Ex. Spray paint can (rigid container) in a bonfire

P1 = P2

T1 T2

orP1T2 = P2T1

“T” must be in Kelvin

As temperature increases, pressure has to increase proportionately to keep same volume

The pressure of a gas in a tank is 3.20 atm (P1) at 22.0 °C (T1). If the temperature is raised to 60.0 °C (T2), what is the new pressure (P2) if volume is held constant?

T1 = 22.0 + 273 = 295 K T2 = 60.0 + 273 = 333 K

P1 = P2

T1 T2

P1T2 = P2

T1

(3.20 atm) (333K) = P2

295 K

3.61 atm = P2

The Combined Gas Law

Many times it is hard to keep a variable constant (and only deal with changing 2 variables at a time), so we have to use all the laws together

Combined Gas Law: all the variables of pressure, temperature and volume change (only thing that is constant is the number of particles)

P1V1 = P2V2

T1 T2

or

P1V1T2 = P2V2T1

Find the volume of a gas at STP if it measures 806 ml at 26.0° C and 103.0 kPa

P1V1 = P2V2

T1 T2

P1 = 103.0 kPa

V1 = 806 ml

T1 = 26.0 + 273 = 299 K

P2 = 101.3 kPa (standard pressure)

V2 = ?

T2 = 273 K (standard temperature)

(103.0 kPa) (806 ml) = (101.3 kPa) (V2)

299 K 273 K

(103.0 kPa) (806ml) (273 K) = V2

(299 K) (101.3 kPa)

748 ml = V2

Gases and the MOLE Rock me Avogadro

Avogadro’s Principle: at equal temperatures and equal pressures, equal volumes of gases contain the same number of molecules

Molar Volume: volume occupied by 1 mole of any gas under STP (0 °C, 101.3 kPa) is 22.4 L (conversion factor= 22.4 L/1 mole)

O2 He

1 mole O2 at STP

6.02 x 10 23 molecules of O2

32.0 g

22.4 L

1 mole He at STP

6.02 x 10 23 atoms He

4.00 g

22.4 L

What is the volume of 8.6 g of Cl2 at STP?

1. Convert g moles (molar mass)

2. Convert moles volume (22.4 L/ mole

1) 8.6 g Cl2

71.0 g Cl2

1 mole Cl2

.12 moles

2) .12 moles

1 mole

22.4 L

2.7 L

Ideal Gas

Combines Avogadro’s principle, Boyles, Charles and Gay-Lussac’s Law into a statement w/ P, V, T and # moles

Changing one variable will affect the other 3 variables

Ideal Gas Equation:

PV = nRT

PV = nRt

n = # of mole R = Ideal Gas Constant ( experimentally

determined constant based on Avogadro’s # and STP dependent on unit used for pressure)

Pressure in: atm use: R= .0821 L· atm/ mole ·K kPa use : R = 8.314 L ·kPa/ mole· K mm Hg use: R = 62.4 L· mm Hg/ mole ·K

Calculate the number of moles of gas contained in a 3.0 L vessel at 30Ō K and a pressure of 1.50 atm.

PV = nRT PV = n R= .0821

RT

(1.50 atm) (3.0 L) = n

(.0821 · 30ŌK)

n = .18 moles

Applying the Ideal Gas Law

Calculate molar mass:n (# of moles) = mass of gas = m

Molar mass M

So: PV = nRT

PV = mRT or

M

M = mRT

PV

Calculate density: D= m/V

M = mRT

PV

(substitute D for m/v in this equation

M = DRT

POr D = MP

RT

Deviations from Ideal Behavior

Ideal Gases: have no attractive forces and do not take up space (volume)

Real Gases: Occupy definite volume (take up space)- but

volume is small Under normal conditions real gases behave like

ideal gases (follow all gas laws)

Under high pressures: particles are forced close together and can’t compress any further, also attractive forces take over

So: real gases will liquefy instead of disappearing like Boyle predicted

Same is true under really low temperatures

Gas Laws Test

Formulas, R values and periodic table will be given to you

> 40 questions 12 multiple choice 13 fill in the blank (need to know who did

what law/PTV card/variables) 7 calculations (1 for each formula, 1 using

22.4 L= 1 mole, 1 PV= nRt)

Know:

Who did each law What each law stands for Scenerios with each law Absolute zero STP Molar Volume /avogadros principle Variables on a gas Real gas vs ideal gas