What affects the behavior of a gas? The number of particles present Volume (the size of the container) Temperature

2

Behavior of gas?? Usually refers to pressure But what is pressure? Collisions between molecules &

container More collisions = higher pressure

3

Number of particles Assume same volume &

temperature… Increasing the number of particles

will increase the number of collisions

Increased collisions means increased pressure

4

1 atm

If you double the number of molecules

If you double the number of molecules

You double the pressure.

2 atm

Number of particles Decreasing the number of

particles will decrease the number of collisions

Decreased collisions means decreased pressure

7

As you remove molecules from a container

4 atm

As you remove molecules from a container the pressure decreases

2 atm

As you remove molecules from a container the pressure decreases

Until the pressure inside equals the pressure outside

1 atm

UNDERSTANDING CHECK

11

Volume (the size of the container) Assume constant number of

particles & temperature If the volume decreases, molecules

have less room to move More collisions = increased pressure

1 atm

4 Liters

As the volume of a gas decreases,

2 atm

2 Liters

As the volume of a gas decreases, the pressure increases

Volume (size of the container) If the volume increases, there is

more room for the molecules to move

Fewer collisions = decreased pressure

SO… pressure and volume are INVERSELY related

15

UNDERSTANDING CHECK

16

Temperature Assume volume and number of

particles are constant Raising the temperature of a gas

makes the particles move faster Faster movement = more collisions =

increased pressure Decreasing temp = slower movement =

less collisions = decreased pressure DIRECT relationship

Start with 1 liter of gas at 1 atm pressure and 300 K

Heat it to 600 K

300 K

300 K 600 K

•Pressure will increase to 2 atm.

If volume not held constant, the volume will increase to 2 liters at 1 atm

300 K (Start)

600 K

What does that mean? Assume pressure is constant Increasing the temperature will lead

to an increase in volume And thus decreasing the temperature

will lead to a decrease in volume Temperature & volume have a

DIRECT relationship

21

UNDERSTANDING CHECK

22

Dalton’s Law of Partial Pressures The total pressure inside a container

is equal to the sum of the partial pressure of each gas.

The partial pressure of a gas is the pressure of that individual gas hitting the wall.

PTotal = P1 + P2 + P3 + … For example

We can find out the pressure in the fourth container

By adding up the pressure in the first 3

2 atm

1 atm

3 atm

6 atm

25

Dalton’s Law This means that we can treat gases

in the same container as if they don’t affect each other.

We can figure out their pressures separately

And add them to get total pressure

Pressure measurements Can use 3 different units

• Kilopascals (kPa)

• Atmospheres (atm)

• Millimeters of mercury (mm Hg) Remember…

• 1 atm = 101.3 kPa = 760 mm Hg

26

Examples What is the total pressure in a balloon

filled with nitrogen & oxygen if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg?

ExamplesIn a second balloon the total pressure

is 1.3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mm Hg?

Gas Laws To make things easier, we are going

to assume the gases behave ideally Assume particles have no volume Assume no attractive forces between

molecules Situation does not really exist but it...

• makes the math easier

• close approximation to reality

Boyle’s Law At a constant temperature, pressure

and volume are inversely related As one goes up, the other goes down

P1V1 = P2V2

P

V

A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm, what is the new volume?

Example

A balloon is filled with 73 L of air at 1.3 atm pressure. What pressure is needed to change to a volume of 43 L?

Example

34

A sample of oxygen occupies 47.2 liters under a pressure of 1240 mm Hg at 25oC. What volume would it occupy at 25oC if the pressure were decreased to 730 mm Hg?

(a) 27.8 L

(b) 29.3 L

(c) 32.3 L

(d) 47.8 L

(e) 80.2 L

Charles’ Law The volume of a gas is directly

proportional to the Kelvin temperature if the pressure is held constant.

K = degrees Celsius + 273 V1 = V2

T1 T2

V

T

Example What is the temperature of a gas that

is expanded from 2.5 L at 25ºC to 4.1L at constant pressure?

Example What is the final volume of a gas that

starts at 8.3 L and 17ºC and is heated to 96ºC?

39

A sample of nitrogen occupies 5.50 liters under a pressure of 900 mm Hg at 25oC. At what temperature will it occupy 10.0 liters at the same pressure?

(a) 32oC

(b) -109oC

(c) 154oC

(d) 269oC

(e) 370oC

Gay Lussac’s Law The temperature and the pressure of a

gas are directly related at constant volume.

P1 = P2

T1 T2

P

T

42

A rigid container at 25C has a pressure of 430 kPa. What would the pressure be at 125 C?

A. 574 kPa

B. 320 kPa

C. 86 kPa

D. 2200 kPa

E. 620 kPa

Examples What is the pressure inside a 0.250 L

can of deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC?

Combined Gas Law The Combined Gas Law deals with

the situation where only the number of molecules stays constant.

Everything else varies P1 V1 = P2 V2

T1 T2

Lets us figure out one thing when two of the others change.

The combined gas law contains all the other gas laws!

If the temperature remains constant.

P1 V1

T1

x=

P2 V2

T2

x

Boyle’s Law

The combined gas law contains all the other gas laws!

If the pressure remains constant.

P1 V1

T1

x=

P2 V2

T2

x

Charles’ Law

The combined gas law contains all the other gas laws!

If the volume remains constant.

P1 V1

T1

x=

P2 V2

T2

x

Gay-Lussac’s Law

Examples A 15 L cylinder of gas at 4.8 atm

pressure at 25ºC is heated to 75ºC and compressed to 17 atm. What is the new volume?

Examples If 6.2 L of gas at 723 mm Hg at 21ºC is

compressed to 2.2 L at 4117 mm Hg, what is the temperature of the gas?

Adding another variable Avogadro’s Hypothesis – If T & P

constant, 2 equal volumes of gas contain the same # of molecules

22.4 L = 1 mole = 6.022 x 1023 molecules Volume has a DIRECT relationship to

number of moles present More volume = more moles Add this to the combined gas law

The Ideal Gas Law PV = nRT

Pressure (P) times Volume (V) equals the number of moles (n) times the Ideal Gas Constant (R) times the temperature in Kelvin (T).

Doesn’t compare 2 situations like other gas laws

If pressure is in atm, R = 0.0821 If pressure is in mm Hg, R = 62.4 If pressure is in kPa, R = 8.31

The Ideal Gas Constant

Example

How many moles of air are there in a 2.0 L bottle at 19ºC and 747 mm Hg?

Example What is the pressure exerted by 1.8 g of

H2 gas in a 4.3 L balloon at 27ºC?