Kinetic Molecular Theory of Gases 1. A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be

points

; that is, they possess mass but have negligible volume.

2. Gas molecules are in constant motion in random directions. Collisions among molecules are perfectly elastic.

3. Gas molecules exert neither attractive nor repulsive forces on one another.

4. The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy

Pressure = Force Area Units of Pressure 1 pascal (Pa) = 1 N/m 2 1 atm = 760 mmHg = 760 torr 1 atm = 101,325 Pa Barometer

10 miles 0.2 atm 4 miles 0.5 atm Sea level 1 atm

Boyle’s Law

P

a 1/

V P

x

V

= constant

P

1 x

V

1 =

P

2 x

V

2 Constant temperature Constant amount of gas Boyle's Law ( scuba style! ) ACSBR physics mini project – YouTube http://www.youtube.com/watch?v=cIVMkV SIAbw

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?

P

1 x

V

1 =

P

2 x

V

2

P

1 = 726 mmHg

P

2 = ?

V

1 = 946 mL

V

2 = 154 mL

P

2 =

P

1 x

V

1

V

2 = 726 mmHg x 946 mL 154 mL = 4460 mmHg

As

T

increases

V

increases

Variation of gas volume with temperature at constant pressure.

V

a

T V

= constant x

T V

1 /

T

1 =

V

2 /

T

2 Charles’ & Gay Lussac’s Law Temperature

must

in Kelvin be

T

(K) =

t

( 0 C) + 273.15

A sample of carbon monoxide gas occupies 3.20 L at 125 0 C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?

V

1 /

T

1 =

V

2 /

T

2

V

1 = 3.20 L

T

1 = 398.15 K

V T

2 2 = 1.54 L = ?

T

2 =

V

2 x

T

1 =

V

1 1.54 L x 398.15 K 3.20 L charles law demonstration - Google Videos Giant Koosh Ball in Liquid Nitrogen! - YouTube = 192 K

V

a number of moles (

n

)

Law

V

= constant x

n V

1 /

n

1 =

V

2 /

n

2

Avogadro’s

Constant temperature Constant pressure

Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure?

4NH 3 + 5O 2 4NO + 6H 2 O 1 mole NH 3 1 mole NO At constant

T

and

P

1 volume NH 3 1 volume NO

Ideal Gas Law

Boyle’s law: V a (at constant

n P

Charles’ law:

V

a

T

(at constant

n

and

T

and

P

) ) Avogadro’s law: V a

n

(at constant

P

and

T

)

V V

a

nT P nT

= constant x =

R P nT P R

is the

gas constant

PV

=

nRT

The conditions 0 0 C and 1 atm are called

standard temperature and pressure (STP).

Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.

PV = nRT R = PV nT

(1 atm)(22.414L) = (1 mol)(273.15 K)

R

= 0.082057 L • atm / (mol • K)

What is the volume (in liters) occupied by 49.8 g of HCl at STP?

T

= 0 0 C = 273.15 K

PV = nRT V = nRT P P = 1 atm n

= 49.8 g x 1 mol HCl 36.45 g HCl = 1.37 mol

V

= 1.37 mol x 0.0821 x 273.15 K mol •K 1 atm

V

= 30.6 L

Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0 C is heated to 85 0 C at constant volume. What is the final pressure of argon in the lightbulb (in atm)?

PV

=

nRT n, V

and R are constant

nR V

=

P T

= constant

P 1

= 1.20 atm

T 1 =

291 K

P 2

= ?

T 2 =

358 K

P T 1 1 P 2

= =

P 2 T 2 P 1 x T 2 T 1

= 1.20 atm x 358 K 291 K = 1.48 atm Egg in a Bottle.wmv - YouTube

Density (

d

) Calculations

d = m V

=

P M RT m

is the mass of the gas in g

M

is the molar mass of the gas Molar Mass (

M

) of a Gaseous Substance

M

=

dRT P d

is the density of the gas in g/L

Deviations from Ideal Behavior of Gases

• Deviation from ideal behavior is large at

high pressure and low temperature

• At lower pressures and high temperatures, the deviation from ideal behavior is typically small, and the ideal gas law can be used to predict behavior with little error.

Deviation from ideal behavior as a function of temperature • As temperature is decreased below a critical value, the deviation from ideal gas behavior becomes severe, because the gas CONDENSES to become a LIQUID.

(a) In an ideal gas, molecules would travel in straight lines. (b) In a real gas, the paths would curve due to the attractions between molecules.

• J. D. van der Waals corrected the ideal gas equation in a simple, but useful, way

Mixtures of Gases

• Dalton's law of partial pressure states: – the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.

Dalton's Law of Partial Pressure

P

T

= P

1

+ P

2

+ P

3

+ …….

Partial Pressure in terms of mole fraction OR

X A P total = P A (

X A = mole fraction of A and P A = partial pressure of gas A)

Mole fraction

•

What is the mole Fraction of Gas A in mixture I?

•

What is the mole fraction of Gas B in mixture II?

Example: If there are 3 moles of gas A, 4 moles of gas B and 5 moles of gas C in a mixture of gases and the pressure of A is found to be 2.5 atm, what is the total pressure of the sample of gases?

X A = 3 3+4+5 = 0.2

P A = 2.5 atm P T = P A / X A = 2.5/0.2 = 12.5 atm

2KClO 3 (

s

) 2KCl (

s

) + 3O 2 (

g

)

P

T =

P

O +

P

H O 2 2

Bottle full of oxygen gas and water vapor

Graham’s Law of Effusion

 Graham’s law states that the rates of effusion of two gases are inversely proportional to the square roots of their molar masses at the same temperature and pressure:  Graham’s Law of Effusion  diffusion of a gas - YouTube

Graham’s Law of Effusion

 The velocity of effusion is also inversely proportional to the molar masses:

Graham’s Law of Effusion

 But the time required for effusion to take is directly proportional to the molar masses:  The density of the gas is also directly proportional to the molar masses:

Graham’s Law of Effusion

 Compare the rate of effusion for hydrogen and oxygen gases.