KINETIC MOLECULAR THEORY Kinetic Molecular Theory A theory that explains the physical properties of...

KINETICMOLECULAR

THEORY

Kinetic Molecular Theory

A theory that explains the physical properties of gases by describing

the behavior of subatomic particles

Physical Properties of Gases:

• Gases have mass• Gases are easily compressed• Gases completely fill their containers•Gases diffuse rapidly•Gases exert pressure

KMT has 5postulates:

#1A gas consists of very small particles that

have mass. (molecules or atoms)

#2Gas particles are

very far apart from each other.

(therefore gases are easily compressed)

#3Gas particles are in continuous, rapid, random motion.

#4Collisions of gas

particles (with each other and with container) are perfectly elastic(no energy lost)

#5The average energy of the gas particles

depends on the temperature of the

gas.

We can measure gases in 4 ways:

Measurement UnitAmount of gas Moles

Volume (V) Liters (L)

Temperature (T) °C, °F, or K

Pressure (P) atm, kPa, Torr, mm Hg, or lb/in2

Temperature (T)

A measurement of the average

kinetic energy of a substance

Higher temperatures

cause gas particles to move

faster

K = C + 273

14C = ? K14C + 273 = 287K

To solve gas problems, the temp must always be

in Kelvin (K) !!!

Pressure (P)

The force per unit area on a

surface

Pressure is caused by gas particles

slamming into the container’s walls.

Units of Pressure:1) atmosphere (atm) 2) kilopascal (kPa)

3) millimeters of Mercury (mm Hg)4) Torr

5) Pounds per square inch (lb/in2)

1 atm = 101.3 kPa = 760 mm Hg = 760 torr = 14.7 lb/in2

STOP…collaborate and listen

Boyle’s Law

MUST BE AT CONSTANT TEMPERATURE!!

P1V1 = P2V21 = before2 = after

A gas occupies a volume of 0.458 L at a pressure of 1.01 kPa and temperature of 295 Kelvin. Although the temperature stays

the same, the volume is increased to 0.477 L. What is the new

pressure?

0.970 kPa

Charles’ Law

MUST BE AT CONSTANT PRESSURE!!

V1T2 = V2T1

1 = before2 = after

What will be the volume of a gas sample at 309 K if its

volume at 215 K is 3.42 L? Assume that pressure is

constant.

4.92 L

Gay-Lussac’s Law

MUST BE AT CONSTANT VOLUME!!

1 = before2 = after

2

2

1

1

T

P

T

P

A balloon with a pressure of 0.900 atm is heated from

105 K to 155 K. If volume is held constant, what is the new

pressure?

1.33 atm

Confused yet???There’s an

easier way…

Combined Gas Law

1 = before 2 = after2

22

1

11

T

VP

T

VP

JUST HOLD ONE QUANTITY CONSTANT!!(take it out of the equation)

The gas in a 0.010 L container has a pressure of 1.39 atmospheres. When the gas is transferred to a

0.017 L container at the same temperature, what is the pressure

of the gas?

0.82 atm

The gas inside a 70.8 mL piston has a temperature of

35.0°C. If the temperature is raised to 100.0°C, what is the

new volume of the gas?

85.7 mL

An elastic container is inflated to a volume of 18.0 liters at a pressure of 1.26 atm. The

container then expands to a new volume at a pressure of 1.05 atm.

What is the new volume?

21.6 liters

Avagadro’s LawEqual volumes of gas

(at same P and T) contain the same

amount of particles

1 mole = 6.02 x 1023 particles

Only works at same P and T

1 mole = 22.4 L

Ideal Gas LawThe mother of all gas

laws. It includes everything!

PV = nRT

P = pressure (atm)V = volume (L)n = moles (mol)

R = Gas ConstantT = Temperature

(Kelvin)

PV = nRT

KmolLatm0821.0R

MUST USE THESE UNITS!!!

PV = nRT

If the pressure exerted by a gas at 0.00°C in a volume of

0.0010 L is 5.00 atm, how many moles of gas are

present?

2.2 x 10-4 moles

Ideal gases don’t really exist…

…real gases do!

Real Gas

All gases are real gases.

DUH!!

Ideal Gas

A gas that is described by the KMT postulates.

Ideal Gas Law works most of the

time.

It does NOT work at very low

temperatures and very high pressures.

Dalton’s Law of Partial Pressures

The sum of the partial pressures

of the gases is equal to the total

pressure

Dalton’s Law of Partial Pressures

Ptotal = P1 + P2 + P3 + …

A balloon contains O2 and N2 gas. If the partial pressure of

the O2 is 0.75 atm and the partial pressure of the N2 is 0.55 atm, what is the total pressure of the balloon?

1.30 atm

The gas inside a 70.8 mL can contains H2O(g) and CO2(g) and has a total pressure of 760 mm Hg. If the partial pressure of the H2O is 350 mm Hg, what is the partial

pressure of the CO2?

410 mm Hg

Graham’s LawGases with smaller

masses move faster than gases with large masses

(like a kid in Walmart)

H2 moves faster than N2. Which of the following gases

moves the fastest?

O2

CO2

NH3

Cl2

I2

H2O

Ar

N2

Br2

STPStandard

Temperature and Pressure:

0C and 1 atm

How many moles of N2 gas are in a 4.5 L balloon at STP?

0.20 moles

A gas at STP is heated to 55°C. What is the new

pressure if volume is held constant?

1.2 atm

A gas tank contains CO2 and O2 gas. What is the total pressure in the tank if the

partial pressure of CO2 is 0.45 atm and the partial pressure

of O2 is 0.55?

1.00 atm