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### The Behavior of Gases

Chapter 14

Chapter 14: Terms to Know

Compressibility

Boyle’s law

Charles’s law

Gay-Lussac’s law

Combined gas

law

Ideal gas constant

Ideal gas law

Diffusion

Effusion

Graham’s law of

effusion

Dalton’s law of

partial pressure

Partial pressure

Introduction

- Gases are a state of matter that are highly compressible.
- There are numerous factors that affect gas pressure.
- There are four gas laws that help to explain gas behavior.
- Ideal gases do not behave like real gases.
- Mixtures of gases exert pressures that are different from individual gases.
- Different gases spread out at different rates.

Gases

A form of matter that takes both the shape and volume of its container.

- Great distances
- between particles
- Easily compressible
- Particles are either
- molecules or atoms
- No attraction between
- particles
- Free flowing

More Gas Properties

- Gas particles are considered to be small, hard spheres with almost no volume.
- Gas particles move in rapid, constant, and random motions.
- When gas particles collide with one another or with other objects the collisions are perfectly elastic.

Properties of GasesSection 14.1

- Compressibility
- Factors Affecting Gas Pressure

I.) Compressibility of Gases

- Gases have a lot of space between each particle.
- Gases have no volume and shape.
- Gases can easily be squeezed together.

Applying the kinetic theory to explain the compressibility of gas particles.

- Particles of gases are far apart relative to particles in solids or liquids.
- The volume of a gas particle is very small compared to the volume occupied by the gas.
- Gas particles do not interact with each other.

II.) Factors Affecting Gas Pressure

- There are four variables that are used to describe a gas: pressure, volume, temperature, and number of moles.
- The amount of gas, volume, and temperature are factors that can affect the pressure of a gas.

Collisions between gas particles are perfectly elastic.

- During an elastic collision, KE is transferred without loss from one particle to another.
- The total KE remains constant

Gas Pressure

- Gas pressure is the force exerted by a gas per unit area of an object.
- Gas particles move and have mass, thus they will exert a force against any object they hit.
- F= m x a

(m=mass; a=acceleration)

What is it that keeps

a balloon inflated?

Gas movement and pressure.

- Moving bodies will exert a force when they collide with another body.
- More collisions = More force
- Force of a single gas particle is small; of many very large.

Therefore, we can say that gas pressure is the result of simultaneous collisions of billions of rapidly moving particles in a gas with an object.

Converting between the three pressure units.

1 atm = 760 mmHg = 101.3 kPa

Gas pressure varies with the amount of a gas.

- In a vacuum there is no gas pressure.
- Increasing the number of gas particles increases the number of collisions.
- Increasing the # of collisions increases pressure.

Practical applications for varying gas pressure.

- Compressed gases can be used for many different purposes.
- As concentration of gas decreases so does the gas pressure.

Gas pressure varies with the volume of the gas.

- Changing the volume of a gas will change the pressure the gas exerts.
- This is due to the change in the number of collisions the gas particles undergo.

Gas pressure varies with the temperature of the gas.

- As a gas is heated the particles of the gas moves faster.
- The average KE of the particles increases.
- The # of collisions and the energy of the collisions also increases.

The Gas Laws(Section 14.2)

- Boyle’s Law: Pressure & Volume
- Charles’s Law: Temperature & Volume
- Gay-Lussac’s Law: Pressure & Temperature
- The Combined Gas Law

Charles

Boyle

Gay-Lussac

I.) Boyle’s Law: Pressure and Volume

- If thetemperature and # particles are constant, then pressure and volume of a gas is inversely proportional.
- Boyle proposed his law in 1662.

Interpreting graphs: Boyles Law

2.) What would the pressure be

if the volume is increased to

3 L?

1.) When the volume is 2L what

is the pressure of the gas?

Mathematical expression of Boyle’s law.

P1 x V1 = P2 x V2

- Temperature and # of particles are constant.
- The product of the pressure and the volume at any two sets of pressure and volume is always constant at a given temperature.
- Thus given three of the variables above we can solve for the fourth.

Sample problem

A balloon contains 30.0 L of helium gas at 103 kPa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa? (Assume temperature is constant.)

What is given?

What are we solving for?

What equation relates these factors?

II.) Charles’s Law: Temperature and Volume

- If the pressure and # particles are constant, then temperature and volume are directly proportional.
- Charles proposed his law in 1787.

Interpreting graphs: Charles’s Law

1.) What is the unit

of temperature?

2.) What happens

to the volume

as the

temperature

rises?

3.) If the temperature is 0 K, what will the volume be?

Mathematical expression of Charles’s law.

V1

T1

V2

T2

- Pressure and # of particles are constant.
- This ratio of volume and temperature is constant at all temperatures and volumes

* The temperature units must always be in Kelvin when working with the gas laws.

=

Sample problem

A balloon in a room at 24o C has a volume of 4.00 L. The balloon is then heated to a temperature of 58oC. What is the new volume if the pressure remains constant?

What is given?

What are we solving for?

What equation relates these factors?

III.) Gay-Lussac’s Law: Pressure and Temperature

- If the volume and # particles are constant, then temperature and pressure are directly proportional.
- Gay-Lussac proposed his law in 1802.

Mathematical expression for Gay-Lussac’s law.

P1

T1

P2

T2

- Volume and # of particles must be constant.
- This ratio of pressure and temperature is constant for all pressures and temperatures.

* The temperature units must always be in Kelvin when working with the gas laws.

=

Sample problem

The gas used in an aerosol can is at a pressure of 103 kPa at 25oC. If the can is thrown onto a fire, what will the pressure be when the temperature reaches 928oC?

What is given?

What are we solving for?

What equation relates these factors?

IV.) The Combined Gas Law

- This law combines all three of the previous gas laws into one expression.
- Only the # of particles is held constant.

Mathematical expression for the combined gas law.

- Given 5 of the variables we can solve for the 6th.
- Temperature must be in units of Kelvin.

V1P1

T1

V2P2

T2

=

Sample problem

The volume of a gas-filled balloon is 30.0 L at 313 K and 153 kPa. What would the volume be at STP?

Deriving the other gas laws from the combined gas law.

- There is no need to memorize all four of the ideal gas laws.
- We can obtain the three “named” gas laws from the combined gas law.
- Just hold one of the variables in the combined gas law constant .

Ideal Gases(Section 14.3)

- Ideal Gas Law
- Ideal Gases & Real Gases

I.) The Ideal Gas Law

- The combined gas law does not allow you to solve for # of particles of a gas.
- To calculate the # of particles we need to include a new term, n.

Mathematical expression for the ideal gas law.

- This equation holds for ideal gases.
- “R” is the ideal gas constant.
- Temperature must be in Kelvin.
- This law allows us to solve for any of the variables affecting a gas.

PV = nRT

The ideal gas constant

R = 8.31 L kPa/K mol

- Allows us to cancel units that are given.
- Is different depending on the units used to calculate it.
- 0.0821 L atm/ K mol

Sample problem

A deep underground cavern contains 2.24 x 106 L of methane gas (CH4)at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many kilograms of CH4 does the cavern contain?

II.) Ideal & Real Gases

- Real gases do not behave the way ideal gases behave at certain temperatures and pressures.
- Real gases have different properties than ideal gases.

Ideal vs. Real Properties

- Gas particles have no volume of their own.
- There are no intermolecular attractions between gas particles.

- Gas particles have a volume of their own.
- There are intermolecular attractions between the gas particles.

At many conditions of temperature and pressure

real gases behave like ideal gases.

If real gases behaved like ideal gases all the time, gases would never condense or solidify.

Real gases

differ most

from ideal

gases at

low

temperatures

and

pressures.

Gases: Mixtures and Movements(Section 14.4)

- Dalton’s Law
- Graham’s Law

I.) Dalton’s Law

- Dalton’s law deals with the pressures that gases in a sample exert.
- Gas pressure is dependent upon two factors:
- Number of particles
- Average KE of the particles
- Therefore the identity of a gas is not relevant to the pressure it exerts.

What is partial pressure?

- The contribution each gas in a mixture makes to the total pressure of a gas sample.

Dalton’s law relates the partial pressures that the individual gases in a sample make to the total pressure that the sample exerts.

- We can derive a mathematical expression for this.

Ptotal = P1 + P2 + P3 + …

In a mixture of gases, the total pressure is

the sum of the partial pressures of the gases.

Sample problem

Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen (PO2) at 101.30 kPa of total pressure if the partial pressures of nitrogen, carbon dioxide and other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively?

II.) Graham’s Law

- Graham’s law deals with the movement of gas particles.
- Diffusion and effusion are slightly different ways of describing gas movement.

Diffusion defined.

- The tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout.

Effusion defined.

- The movement of a gas through a small hole in a container.
- Graham’s law deals with effusion.

Rates of diffusion and effusion are dependent upon the molar masses of the gas particles.

- Gases of lower molar mass will diffuse and effuse faster than gases of higher molar masses.
- Thomas Graham, a Scottish chemist, discovered the relationship between molar mass and movement in the 1840’s.
- The law he proposed is known as Graham’s law of effusion.

Relationship between rate of effusion/diffusion and molar mass.

- The rate of effusion of a gas is inversely related to the square root of its molar mass.
- In the equation for KE there is an inverse relationship between mass and velocity.

1 ____

√Molar massA

Rate A

=

Using Graham’s Law of Effusion to compare effusion rates.

- We can use this mathematical expression to compare diffusion rates as well.
- Make sure you keep in mind that the rate and molar mass of a gas switches place in the above expression.

√Molar mass B

√Molar mass A

Rate A

RateB

=

Sample problem

About how much faster does helium effuses (or diffuses) than nitrogen at a constant temperature.

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