chapter 14 the behavior of gases. section 14.3 ideal gases l\

Chapter 14

The

Behavior of Gases

Section 14.3Section 14.3Ideal GasesIdeal Gases

l\l\

STPSTP Standard Standard

temperature and temperature and pressurepressure

1atmosphere1atmosphere

0 degrees Celsius0 degrees Celsius

STP is also a motor STP is also a motor oil. That’s cool, if oil. That’s cool, if irrelevantirrelevant..

The Gas Laws are mathematical.

The gas laws will describe HOW gases behave.

Four Variables Describe a Gas

1.pressure (P) in atm

2. volume (V) in Liters

3. temperature (T) in Kelvin

4. amount (n) in moles

•

Four Variables Describe a Gas

1.pressure (P) in atm

2. volume (V) in Liters

3. temperature (T) in Kelvin

4. amount (n) in moles

•

Not Held constant in Section 14.3

Ideal Gas Law

5. The Ideal Gas Law #1 Equation: P x V = n x R x T

R = 0.08206 L x atm) / (mol x K)

The other units must match the value of the constant, in order to cancel out.

Sample ProblemSample Problem

What is the pressure in What is the pressure in atmospheres exerted by a 0.500 atmospheres exerted by a 0.500 mol sample of nitrogen gas in a mol sample of nitrogen gas in a 10.0 L container at 298 K?10.0 L container at 298 K?

P = P = 1.22 atm1.22 atm

A 1.50 mole sample of Helium is A 1.50 mole sample of Helium is placed in a 15.0 L container at 400K. placed in a 15.0 L container at 400K. What is the pressure in the What is the pressure in the container?container?

Answer: 3.28 atmAnswer: 3.28 atm

Evan has 23.7 grams of nitrogen gas Evan has 23.7 grams of nitrogen gas in a 30.8 L container with a pressure in a 30.8 L container with a pressure of 1.5 atm. What is the temperature of 1.5 atm. What is the temperature of the gas?of the gas?

Answer: 670 K Answer: 670 K

Susan has 2.03 moles of Helium in a Susan has 2.03 moles of Helium in a 400.1 mL container at 282 degrees 400.1 mL container at 282 degrees Celsius. What is the pressure of this Celsius. What is the pressure of this gas in kPa?gas in kPa?

Answer: 23400 kPaAnswer: 23400 kPa

Ideal Gases We are going to assume the gases

behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure

Ideal Gases An ideal gas does not really exist, but it

makes the math easier and is a close approximation.

Particles have no volume? Wrong!

No attractive forces? Wrong!

Ideal GasesThere are no gases which are

truly “ideal”; however,

Real gases behave this way at a) high temperature, and b) low pressure.

#6. Ideal Gas Law 2

Equation: P x V = m x R x T M

Allows LOTS of calculations, and some new items are:

m = mass, in grams M = molar mass, in g/mol

Molar mass = m R T P V

Sample ProblemSample Problem

At 28°C and 0.974 atm, 1.00 L of At 28°C and 0.974 atm, 1.00 L of gas has a mass of 5.16 g. What is gas has a mass of 5.16 g. What is the molar mass of this gas?the molar mass of this gas?

Molar Mass = Molar Mass = 131 g/mol 131 g/mol

Density Density is mass divided by volume

m

V

so,

m M P

V R T

D =

D = =

Practice ProblemsPractice Problems

What is the molar mass of a gas if What is the molar mass of a gas if 0.427 g of the gas occupies a volume 0.427 g of the gas occupies a volume of 125 mL at 20.0°C and 0.980 atm?of 125 mL at 20.0°C and 0.980 atm?

83.8 g/mol83.8 g/mol What is the density of a sample of What is the density of a sample of

ammonia gas, NHammonia gas, NH33, if the pressure is , if the pressure is 0.928 atm and the temperature is 0.928 atm and the temperature is 63.0°C?63.0°C?

0.572 g/L NH0.572 g/L NH33

The density of a gas was found to The density of a gas was found to be 2.0 g/L at 1.50 atm and 27°C. be 2.0 g/L at 1.50 atm and 27°C. What is the molar mass of the What is the molar mass of the gas?gas?

33 g/mol33 g/mol What is the density of argon What is the density of argon

gas,Ar, at a pressure of 551 torr gas,Ar, at a pressure of 551 torr and a temperature of 25°C?and a temperature of 25°C?

1.18 g/L Ar1.18 g/L Ar

Ideal Gases don’t exist, because:

1. Molecules do take up space

2. There are attractive forces between particles

- otherwise there would be no liquids formed

Real Gases behave like Ideal Gases...

When the molecules are far apart.

The molecules do not take up as big a percentage of the space We can ignore the particle

volume. This is at low pressure

Real Gases behave like Ideal Gases…

When molecules are moving fastThis is at high temperature

Collisions are harder and faster.Molecules are not next to each

other very long.Attractive forces can’t play a role.

Section 14.4Gases: Mixtures and Movements

OBJECTIVES:

Relate the total pressure of a mixture of gases to the partial pressures of the component gases.

Section 14.4Gases: Mixtures and Movements

OBJECTIVES:

Explain how the molar mass of a gas affects the rate at which the gas diffuses and effuses.

#7 Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

•P1 represents the “partial pressure”, or the contribution by that gas.•Dalton’s Law is particularly useful in calculating the pressure of gases collected over water.

Collecting a gas over water

Connected to gas generator

If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3:

2 atm + 1 atm + 3 atm = 6 atm

1 2 3 4

Diffusion is:

Effusion: Gas escaping through a tiny hole in a container.

Both of these depend on the molar mass of the particle, which determines the speed.

Molecules moving from areas of high concentration to low concentration.Example: perfume molecules spreading across the room.

•Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

•Molecules move from areas of high concentration to low concentration.

Effusion: a gas escapes through a tiny hole in its container

-Think of a nail in your car tire…

Diffusion and effusion are explained by the next gas law: Graham’s

8. Graham’s Law

The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules.

Derived from: Kinetic energy = 1/2 mv2

m = the molar mass, and v = the velocity.

RateA MassB

RateB MassA

=

With effusion and diffusion, the type of particle is important: Gases of lower molar mass diffuse and

effuse faster than gases of higher molar mass.

Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases

Graham’s Law