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### Chapter 14The Behavior of Gases

Did you hear about the chemist who was reading a book about Helium?

He just couldn't put it down.

14.1 Properties of Gases

- OBJECTIVES:
- Explain why gases are easier to compress than solids or liquids are
- Describe the three factors that affect gas pressure

Compressibility

- Gases can ______to fill its container, unlike solids or liquids
- The reverse is also true:
- They are easily compressed, or squeezed into a smaller volume
- Compressibility is a measure of how much the ______of matter decreases under _________

Compressibility

- This is the idea behind placing air bags in automobiles
- In an accident, the air compresses more than the steering wheel or dash when you strike it
- The impact forces gas particles closer together, which is possible because there is a ___________between them

Compressibility

- At __oC, the distance between particles is about 10x the diameter of the particle
- Fig. 14.2

Shows spacing between

O2 and N2 molecules

in air

- This empty space makes gases good _________
- down & fur keep animals warm because the air ________in them prevents heat from escaping the animal’s body)
- How does the volume of the particles in a gas compare to the overall volume of the gas (kinetic theory)?

Variables that describe a Gas

- The four variables and their common units:

1. ________(P) in kilopascals

2. volume (V) in Liters

3. temperature (T) in Kelvin

4. ______(n) in moles

- The amount of gas, volume, andtemperature are factors that affect gas pressure.

1. Amount of Gas

- When we inflate a balloon, we are adding gas molecules.
- Increasing the number of gas particles increases the number of _______
- thus, pressure increases
- If temperature is constant, then doubling the number of particles doubles the ________

Pressure and the number of molecules aredirectly related

- More molecules means more _______, and…
- Fewer molecules means ______collisions.
- Gases naturally move from areas of high pressure to _____pressure, because there is empty space to move into

Using Gas Pressure

- A practical application is aerosol (spray) cans
- gas moves from higher pressure to lower pressure
- a _______forces the product out
- whipped cream, hair spray, paint
- Fig. 14.5, page 416
- Is the can really ever “empty”?

2. Volume of Gas

- In a smaller container, the molecules have _____room to move.
- The particles hit the _____of the ________more often.
- As volume decreases, pressure increases. (syringe example)
- Thus, volume and pressure are ________related to each other

3. Temperature of Gas

- Raising the temperature of a gas increases the pressure, if the volume is held _________. (T and P are directly related)
- The faster moving molecules hit the walls harder, and more frequently!
- Should you throw an aerosol can into a fire?
- When should your automobile tire pressure be checked?

14.2 The Gas Laws

- OBJECTIVES:
- Describe the relationships among the temperature, pressure, and volume of a gas
- Use the combined gas law to solve problems

The Gas Laws are mathematical

- The gas laws will describe HOW gases behave.
- Gas behavior can be predicted by the _______.
- The ______________can be calculated with mathematical equations.
- You need to know both of these: the theory, and the math

Robert Boyle(1627-1691)

- Boyle was born into an aristocratic _____family
- Became interested in ______ and the new science of Galileo and studied chemistry.
- A founder and an influential fellow of the Royal Society of London
- Wrote extensively on science, philosophy, and theology.

Don’t you love my swell scarf??

#1. Boyle’s Law - 1662

Gas pressure is ________proportional to volume, at a constant _________(Check out this cool animation)

Pressure x Volume = a constant

Equation: P1V1 = P2V2 (at a constant T)

As volume increases, pressure decreases

An inverse relationship!

Jacques Charles (1746-1823)

- French Physicist
- Part of a scientific balloon flight in 1783 – one of three passengers in the second balloon ascension that carried humans
- This is how his interest in gases started
- It was a _________filled balloon – good thing they were careful!

#2. Charles’ Law - 1787

- For a fixed ____(moles), gas volume is directly proportional to the _____temperature, when pressure is _______.
- This extrapolates to zero volume at a temperature of zero Kelvin.

Charles’ Law Animation

Converting Celsius to Kelvin

- Gas law problems involving temperature always require Kelvin temperature.

Kelvin = C + 273

°C = Kelvin - 273

and

Practice Problems 9-10

- If a sample of gas occupies 6.80 L at 325oC, what will its volume be at 25oC if the pressure does not change?
- Exactly 5.00 L of air at –50.0oC is warmed to 100.0oC. What is the new volume if the pressure remains constant?

Joseph Louis Gay-Lussac (1778 – 1850)

- ____chemist and physicist
- Known for his studies on the _________properties of gases.
- In 1804 he made balloon ascensions to study magnetic forces and to observe the composition and temperature of the air at different altitudes.

#3. Gay-Lussac’s Law - 1802

- The pressure and Kelvin temperature of a gas are directly proportional, provided that the ________remains constant.

- How does a pressure cooker affect the time needed to cook food? (Note page 422)

Practice Problems 11-12

- A sample of nitrogen gas has a pressure of 6.58 kPa at 539 K. If the volume does not change, what will the pressure be at 211 K?
- The pressure in a car tire is 198 kPa at 27oC. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire (assume the volume is constant).

#4. The Combined Gas Law

The combined gas law expresses the relationship between ______, volume and _________of a fixed amount of gas.

Practice Problems 13-14

See Sample Problem 14.4, page 424 if needed

- A gas at 155 kPa and 25oC has an initial volume of 1.00 L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125oC. What is the new volume?
- A 5.00 L air sample has a pressure of 107 kPa at – 50oC. If the temperature is raised to 102oC and the volume expands to 7.00 L, what will the new pressure be?

The combined gas law contains all the other gas laws!

- If the temperature remains constant...

P1

V1

P2

x

V2

x

=

T1

T2

______Law

The combined gas law contains all the other gas laws!

- If the pressure remains constant...

P1

V1

P2

x

V2

x

=

T1

T2

________Law

The combined gas law contains all the other gas laws!

- If the volume remains constant...

P1

V1

P2

x

V2

x

=

T1

T2

_________Law

14.3 Ideal Gases

- OBJECTIVES:
- Compute the value of an unknown using the ____gas law
- Compare and contrast real an ideal gases

5. The Ideal Gas Law #1

- Equation: P x V = n x R x T
- Pressure times Volume equals the number of moles (n) times the _________________(R) times the Temperature in Kelvin.
- R = ______(L x kPa) / (mol x K)
- The other units must match the value of the constant, in order to cancel out.
- The value of R could change, if other units of measurement are used for the other values (namely pressure changes)

Units and the Ideal Gas Law

- R = 8.31L·kPa/K·mol (when P in kPa)
- R = ______L·atm/K·mol (when P in atm)
- R = 62.4L·mmHg/K·mol (when P in mmHg)
- Temperature always in _______!!

The Ideal Gas Law

- We now have a new way to count _____(the amount of matter), by measuring T, P, and V. We aren’t restricted to only STP conditions:

P x V

R x T

n =

Practice Problems

- A rigid container holds 685 L of He(g). At a temperature of 621 K, the pressure of the gas is 1.89 x 103 kPa. How many grams of gas does the container hold?
- A child’s lungs hold 2.20 L. How many moles of air (mostly N2 and O2) do the lungs hold at 37oC and a pressure of 102 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 do not really exist, but it makes the math easier and is a very close approximation.
- Particles have no volume? ______!
- No attractive forces __________!

Ideal Gases

- There are no gases that are absolutely “ideal” however…
- Real gases do behave “ideally” at
- high temperature, and low pressure
- Because under these conditions, the gas particles themselves are so far apart they take up a very small proportion of the gas’s volume and the IM forces are so weak that they can be ignored

Ideal Gas Law: Useful Variations

- PV = nRT
- Replace n with _________mass
- P x V = m x R x T M
- m = mass, in grams
- M = molar mass, in g/mol
- Rearrange equation 1
- Molar mass = M = m R T P V

n (moles) = mass (g)

molar mass (g/mol)

Using Density in Gas Calculations

- ______is mass divided by volume

m

V

- so, we can use a density value to give us two values needed in PV = nRT
- Volume (usually 1 L) and…
- -, if we know the _________, because we can calculate it
- grams (from D) x 1 mole

grams

D =

Using Density in Gas Calculations

- What is the pressure of a sample of CO2 at 25oC, with a density of 2.0 g/L?

PV = nRT P =

- V = 1 L, R = 8.31 L·kPa/mol·K
- n = 2.0 g x 1 mole/44.0 g = 0.045 mole
- P = _____________________= 113 kPa

1 L

nRT

V

Ideal Gases don’t exist, because:

- Molecules __ take up space
- There ____ ________ forces between particles

- otherwise there would be no liquids

Real Gases behave like Ideal Gases...

- When the molecules are far apart.
- The molecules take up a very small percentage of the space
- We can ignore the particle volume.
- True at low pressures and/or high temperatures

Real Gases behave like Ideal Gases…

- When molecules are moving fast
- = _____________
- Collisions are harder and ____.
- Molecules are not next to each other very long.
- __________forces can’t play a role.

Real Gases do NOT Behave Ideally…

- When temperature is very low
- Because the low KE means particles may ________with one another for longer periods of time, _______weaker IM forces to have an effect
- When the pressure are _____
- Because the particles are _______together more closely and thus occupy a much ________percentage of the volume

14.4 Gas Mixtures & Movements

- OBJECTIVES:
- Relate the total pressure of a mixture of gases to the partial pressures of its component gases
- Explain how the molar mass of a gas affects the rate at which it 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 “___________”,or the contribution by that gas.
- Dalton’s Law is useful in calculating the pressure of gases ________over water – a common lab technique

Collecting a Gas over Water

Gas being

produced

- A common lab technique for collecting and measuring a gas produced by a chemical reaction
- The bottle is filled with water and inverted in a pan of water
- As the gas is produced in a separate container, tubing is used to carry it to the bottle where it displaces the water in the bottle
- When the level of the gas in the bottle is even with the water in the pan, the pressure in the bottle = atmospheric pressure
- A graduated cylinder is often used to collect the gas (for ease of measuring the gas volume)

Atmospheric

pressure

Dalton’s Law of Partial Pressures

- If the gas in containers 1, 2 & 3 are all put into the fourth, the pressure in container 4 = the ____of the pressures in the first 3

2 atm

+ 1 atm

= _ atm

+ 3 atm

4

3

2

1

Practice Problems

- Determine the total pressure of a gas mixture containing oxygen, nitrogen and helium: PO2= 20.0 kPa, PN2= 46.7 kPa, PHe= 20.0 kPa.
- A gas mixture containing oxygen, nitrogen and carbon dioxide has a total pressure of 32.9 kPa. If PO2= 6.6 kPa and PN2= 23.0 kPa, what is the PCO2?

Diffusion and Effusion

- Diffusion = molecules moving from areas of ____to areas of ____concentration
- Is mathematical phenomenon caused by random movements of gas particles

- Effusion = gas particles escaping through a tiny hole in a container
- Both diffusion and effusion depend on the molar mass of the particle, which determines the _______at a given ________(= average KE)

- describes the mixing of gases
- Molecules move from areas of high concentration to low concentration
- A function of probability
- Fig. 14.18, p. 435

Two gases mix after the wall separating them is removed.

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

- balloons slowly lose air over time

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

8. Graham’s Law

RateAMB

RateBMA

- The rate of effusion and diffusion is inversely proportional to the square root of the molar masses (M) of the gases.
- Relationship based on: KE = ½ mv2
- At a given temperature (avg KE) larger molecules will have lower velocities

=

Graham’s Law Explained

- Temperature is a measure of the average KE of the particles in a sample of matter
- At a given temperature (say 25oC), the molecules of a lighter gas will be moving faster than molecules of a heavier one, so…
- Faster-moving particles spread out faster!

Graham’s Law

- Sample: compare rates of effusion of Helium (He) with Nitrogen (N2) – p. 436
- 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 2.7 times faster than nitrogen – thus, helium escapes from a balloon quicker than air, which is ~79% N2!

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