1

D. Partial Pressures and Mole Fractions

All gases have the same Volume and same T

PO2V = nO2RT PO2

nO2=

RT

V

PArV = nArRT PAr

nAr=

RT

V

PN2V = nN2RT PN2

nN2=

RT

V

PtotV = ntotRT Ptot

ntot=

RT

V

Individual Gas (O2)

2

IV. Kinetic Molecular Theory

Statements of the Kinetic Molecular Theory

1. Gas particles are infinitesimally small particles.

2. Gases consist of lots of particles in continuous

random motion.

3. Gas particles move in straight lines until they

collide. These collisions are brief and elastic.

4. Gas particles do not influence each other except

during collisions.

5. The kinetic energy of gas particles is directly

proportional to temperature. At constant

temperature, the total energy of all gas particles

is constant.

3

QUALITATIVE and Quantitative Relationship

between Speed, Temperature, and Identity of a Gas

Mathematical Gymnastics

P ∝ impulse per collison ∙ collision frequency

- impulse ∝ m ∙ u̅

- collision frequency ∝ NA

V∙ u̅

- P ∝ m u̅ ∙ NA

Vu̅ - P ∝ m u̅2 NA

V

- P = 1

3m u̅2 NA

V

- PV = 1

3m u̅2NA

4

Mathematical Gymnastics Cont’d

PV = 1

3m u̅2NA PV = nRT

PV = RT

- RT = 1

3m u̅2NA - RT =

1

3u̅2NAm

- RT = 1

3u̅2M

Relationship Between Speed, Temp, and Identity of Gas

√�̅�2 = √3𝑅𝑇

M √u̅2= urms=root mean square speed

urms = √3𝑅𝑇

M R = 8.314

J

mol K= 8.314

𝑘𝑔 𝑚2

𝑠2

𝑚𝑜𝑙 𝐾

𝑀 = molar mass = kg

mol

5

Terms Used to Describe the Speed of a Gas

urms = root mean square speed

uaverage = average speed

umost probable = most likely speed

Why do we use urms?

6

Qualitative Conclusions of K.M.T.

urms = √3𝑅𝑇

M K.E.̅̅ ̅̅ ̅ =

1

2 m urms

2

Comparing speed and K.E. of the same gas at different T

Speed of O2 at 273 K Speed of O2 at 1000K

K.E.̅̅ ̅̅ ̅ of O2 at 273 K K.E.̅̅ ̅̅ ̅ of O2 at 1000 K

Comparing speed and K.E. of different gases at the same T

T = 273 K

Speed of H2 Speed of O2

K.E.̅̅ ̅̅ ̅ of H2 K.E.̅̅ ̅̅ ̅ of O2

7

A. Effusion and Diffusion of Gases

Effusion - movement of gases through a pinhole

into an evacuated region

Diffusion - movement of a substance through

space as a result of random molecular

motion

Rate = how long it takes for something to happen

(mol/s, g/min, etc)

Qualitative

urms = √3𝑅𝑇

M

http://images.businessweek.com/mz/06/39/0639_106environ.gif

8

Quantitative

Diffusion - no simple quantitative relationship

Effusion - simple quantitative relationship

Graham’s Law - relates rate of effusion to molar

mass at constant T and P

limitations -

9

Example Problem:

If Nike used N2(g) instead of SF6(g) as a filler in its

“air” cushions, would you expect the shoes to “deflate”

faster or slower than with SF6(g)? What is a rough

approximation for how much faster or slower the shoes

would deflate? Assume Graham’s law is the only

important consideration.

10

A. Real Gases vs. Ideal Gases

When does the ideal gas law not work?

Ideal gas law assumptions

1. Molecules/gas particles are assumed

to occupy an infinitesimally small

volume relative to the size of the container

Conditions Assumption 1 valid or not valid?

a.) small # of gas

particles in a

large volume

container

b.) large # of gas

particles in a

small volume

container

11

Ideal gas law assumptions cont’d

2. Gas particles are assumed not

to interact with each other

Conditions Assumption 2 valid or not valid?

a.) K.E. of gas particles

much larger than the

energy of attraction

b.) K.E. of gas particles

is close to the energy

of attraction

12

Corrections to the Ideal Gas Law

1. A better value for volume of free space

2. Account for Molecular Attraction