1

Gases

What are the four variables

needed to describe a gas?

2

Gases

The simplest state of matter

•K.E. >> molecular attraction

•Random motion

•Predictable behavior

3

Gases at STP

Few Elements:

H2 N2 O2

O3

F2 Cl2Noble Gases

Few Molecules:

HF HCl HBr

HI CO CO2

NH3 NO NO2

N2O SO2 H2S

No ionic compounds; WHY?

4

KMT of Gases

Hard spheres

Insignificant volume

Far apart

1. Gas “particles”

(atoms or molecules):

5

Straight paths until collision

Random motion

Fill container

KMT of Gases

2. Particles motion:

6

KMT of Gases

3.Gas particles have no

attractions between them.

7

4. Collisions are perfectly “elastic”.

no energy lost

during collision

KMT of Gases

8

Pressure

What is pressure?

Collisions of gas particles

with the walls of the container

impart a force (f)

P =force

area

9

Atmospheric Pressure

10

11

Gas VariablesFour “macroscopic” variables

are needed to describe a gas.

P = pressure

V = volume

T = temperature

n = number of moles

Inter-

related

12

You Predict

How to increase P ?

n

V

T

add gas

smaller V

higher T

(and Why?)

P =f

A

13

Gas Laws

Charles’ Law V & T

Avogadro’s Law V & n

Boyle’s Law P & V

The other two variables are constant.

14

Boyle’s Law (T,n constant)

Relationship of P & V

15

Boyle’s Law (T,n constant)

P = k 1

Vor PV = k

P then V

P

1/V

16

Boyle’s Law (T,n constant)

P1V1 = P2V2

before after

same

Condition #1: = kP1V1

Condition #2: = kP2V2

17

P1V1 = P2V2

A balloon is filled with 30. L of He

at 1.0 atm. What is the new

volume of the balloon if it rises to

where P = 0.25 atm?

18

P1V1 = P2V2

Boyle’s law is how

your lungs work !!

19

Charles Law

What happens to the

volume of a balloon if

temperature is increased?

20

Charles Law (P,n constant)

(T in Kelvin)

V = k’ T

V/T = k’

V1

T1

=V2

T2

before after

T then V

21

V

T (oC)

-200 0 200 4000

Charles Law

-273.15oC

V/T = k’

22

Charles Law

A sample of CO occupies

3.20 L at 125oC. Calculate

the temperature at which it

will occupy 1.54 L.

V1 /T1 = V2/T2

23

Avogadro’s Law:

Thus any two gas samples with

the same P, V, & T will have the

same number of particles!

At constant P & T,

V a n

independent of gas type!

24

Kinetic Molecular Theory

Explain:

Boyle’s Law

Charles’ Law

Avogadro’s Law

In terms of KMT

(what are the particles doing?)

25

Help !!!

How are you suppose to

remember all these equations?

26

Ideal Gas Law:

V a 1/P

V a T

V a n

V = RnTP

PV = nRT

R = universal gas constant

constant

Independent of type of gas !!

“pivnert”

27

PV = nRT

Knowing 1 mole of “ideal” gas

occupies 22.4 L at STP, what is

the value of R? (units?)

R = 0.0821L atm

mol K

28

PV = nRT

•How many moles of N2

are in a 2.00 L tank at

25oC and 20. atm?

•How many grams?

29

PV = nRT

Units must be consistent with ‘R’

P in atm.

V in liters

n in moles

T in K

First convert from

kPa, mmHg

mL, cm3

g, kg, #particles

oC

R = 0.0821L atm

mol K

30

PV = nRTWhat is the P in a 4.0 L fire

extinguisher that contains

260 g CO2 at T = 30oC?

31

What if conditions of a

gas change?

R =P1V1

n1T1

before change after change

R =P2V2

n2T2

=P2V2

n2T2

P1V1

n1T1

32

=P2V2

n2T2

P1V1

n1T1

This can replace Boyle’s,

Charles, etc. laws.

33

=P2V2

T2

P1V1

T1

Show that the combined gas

law reduces to Boyle’s law if

T and n are constant.

= P2V2P1V1

34

=P2V2

T2

P1V1

T1

The volume of a balloon is 30. L

at 40 oC and 150 kPa.

What is its volume at STP ?

Let’s step through a problem.

P1 = 150 kPa

V1 = 30. L

T1 = 40oC = 313 K

P2 = 101.3 kPa

V2 = ?

T2 = 273 K

35

=P2V2

T2

P1V1

T1

1. Cancel n1 & n2 because

n doesn’t change.

2. Substitute values. Use same

units for all pairs; T in K.

(150 kPa)(30.L) (101.3 kPa)V2

313 K 273 K=

V2 = 39 L

36

Before a long road trip, a car tire

has P = 3.1 atm at T = -12oC. After

driving the tire T rises to 45oC.

What is the new P in the tire ?

Try a Problem!!!

37

A 2.1 mL bubble rises from the

bottom of a lake where

T = 8oC and P = 6.4 atm to the

lake surface where

T = 25oC and P = 1.0 atm.

What is new V

of the bubble?

Try another.

38

Which Equation to Use ?Use: PV = nRT

If conditions don’t change.

Not on Regents Chart.

R = 0.0821 L atm/mol K

Units

=P2V2

T2

P1V1

T1

If conditions do change. Table ‘T’

Units: T

must be K

39

What is an “Ideal” Gas ?

Ideal gases obey all the

assumptions of KMT.

Most gases under “normal” T & P

behave like ideal gases.

Ideal gases obey PV = nRT

40

“Real” GasesParticles have volume

Have molecular attractions

Under what conditions of

T & P is a real gas most like

an ideal gas? Why ??

(high T & low P)

41

Dalton’s Law

of Partial Pressures

Every gas in a mixture of

gases (for example, air)

contributes to the total

pressure as if it were the

only gas in the container!

42

Dalton’s Law

PA =nART

V

Mixture of gases A, B, C…

confined in a volume V.

and Ptotal = PA + PB + PC…

Partial pressure of gas ‘A’

43

Air: a Mixture of GasesWhat is partial pressure of O2 if

PTotal = 101.3 kPa

PN2 = 79.1 kPa

Pothers = 0.9 kPa

PTotal = PO2 + PN2 + Pothers

101.3 = PO2 + 79.1 + 0.9

PO2 = 21.3 kPa

44

Graham’s Law of Diffusion

Perfume spreads throughout a

room by diffusion, a mixing

process controlled molecular

collisions.

(start demo)

How fast a gas diffuses

is related to its velocity.

45

Graham’s Law of Diffusion

Compare the kinetic energy (KE)

of 2 gases at the same T.

KEA = mAvA21

2KEB = mBvB

21

2

Since T’s are the same:

mAvA21

2 mBvB21

2=

mass velocity

46

Graham’s Law of Diffusion

mAvA21

2mBvB

21

2=

vA2

vB2

mB

mA=

vA

vB

mB

mA=

=molar massB

molar massA

Diff.RateA

Diff.RateB

47

Graham’s Law of Diffusion

NH3

HCl

NH3(g) + HCl(g)

What is equation for this

combination reaction ?

Which gas diffuses faster ?

By how much?

Carry answer to 3 sig figs.

NH4Cl(s)

48

Graham’s Law of Diffusion

Which gas “effuses” out of a balloon

faster, N2 or He? By how much?

(Hint: let gas ‘A’ have the

smaller molar mass.)

=molar massB

molar massA

Diff.RateA

Diff.RateB

49

Warm-up

50

What are the four

“macroscopic” variables

that describe a gas?

Warm-up

51

A gas at 3.3 atm in a 2.7 L

container is transferred to an

empty 8.6 L container.

What is the new pressure?

Warm-up

52

•What is Charles’ law?

•What assumptions does Charles’

law make?

•Explain, on the molecular level.

•If a gas has a volume of 4.7 L at

120oC, what volume does it

have at 450oC?

Warm-up

53

Explain using KMT why the gas

pressure in a container increases

if the temperature is raised.

Warm-up

54

How many grams of O2 gas

are in a 42 L container at

370kPa at 58oC?

Warm-up

55

Show that the combined gas law

on Table T reduces to Charles’ law.

=P2V2

T2

P1V1

T1

Warm-up

56

How many grams of

dintrogen pentoxide are in

a 3.7 L balloon at STP?

Warm-up

57

How many grams of CO2 are in a

3700 mL flask at 25oC and 670 kPa?

A 2.7 L balloon on the ground at STP

rises to the upper atmosphere where

T = -12oC and P = 18 kPa.

How big is the balloon?