Gas Law and Gas Behavior

Meyer 2014

Ch. 12 and 13

2

Characteristics of Gases

Gases are highly compressible and occupy the full volume of their containers.

Gases exert pressure, P = F/A (force/area).

Gases always form homogeneous mixtures with other gases.

Actual gas atoms and molecules only occupy about 0.1 % of the volume of their containers.

The Composition of the Atmosphere

Dry Atmosphere at Sea Level (% by Volume)Nitrogen 78.084Oxygen 20.948Argon 0.934Carbon dioxide 0.033 Neon 0.00182Hydrogen 0.0010Helium0.0052Methane 0.0002*Krypton 0.0001Xenon 0.000008Carbon monoxide, ozone, ammonia, nitrogen dioxide, sulfur dioxide <0.00001* * = variable depending upon pollution

Water content in the atmosphere isvariable in actualcontexts, rangingto over 5% in hotsteamy climates to <<1% in dryarid environments.

A Mercury Barometer

The pressure exerted by the column of mercury …

… must be the same as that exerted by the atmosphere.

5

PressureAtmospheric Pressure and the Barometer

. Standard atmospheric pressure is the pressure required to support 760 mm of Hg in a column.

Units: 1 atm = 760 mmHg 760 torr 1.013 105 Pa 101.3 kPa

1000 Pa = 1kPa

6

Practice

.456 Torr = ___?___ Atm

1689 mmHg= ___?___ Torr

156kPa = __?__ Atm

Boyle’s Law:Pressure-Volume RelationshipFor a fixed amount of a gas at constant

temperature, the volume of the gas varies inversely with its pressure.

For a fixed amount of a gas at constant temperature, the product of pressure and volume is a constant.

If you squeeze (increase pressure) a balloon gets smaller (volume decreases)

P V or V P

P1V1=P2V2

PinitialVinitial = PfinalVfinal

Example

A helium-filled party balloon has a volume of 4.50 L at sea level, where the atmospheric pressure is 782 Torr. Assuming that the temperature remains constant, what will be the volume of the balloon when it is taken to a mountain resort at an altitude of 2500 m, where the atmospheric pressure is .89 Atm?

Charles’s Law:Temperature-Volume RelationshipThe volume of a fixed amount of a gas at

constant pressure is directly proportional to its Kelvin (absolute) temperature.

Absolute zero is the temperature obtained by extrapolation to zero volume.

Absolute zero on the Kelvin scale = –273.15 °C

Absolute ZeroAbsolute temperature is

measured in Kelvin Never be a negative KelvinAbsolute zero is zero (0) Kelvin or

-273.15 degrees CMolecular motion stopsDegree C + 273.15 =

Degree K

Charles’s Law:Temperature-Volume Relationship

If the temperature goes up a balloon expands

If the temperature goes down a balloon contracts

T must be in Kelvin2

2

1

1

T

V

T

V

Example

A weather balloon has a volume of 900 liters at 25 degrees C. What would the volume be if the same balloon was -45 degrees C?

Gay Lussac’s Law:Temperature-Pressure Relationship

If the temperature goes up the pressure goes up

If the temperature goes down the pressure goes down

T must be in Kelvin

2

2

1

1

T

P

T

P

Example

A coke can has a pressure of 1.1 atm at 25 degrees C what would the pressure be if you left the coke can in your car and it warmed to 125 degree C?

Standard Temperature and Pressure:STP

We define STP (Standard Temperature and Pressure)

= 0C (273.15 K) = 1 atm.

STP is used often and represents a standard condition which gases can be compared to each other

The Combined Gas Law:Temperature-Pressure Relationship

Puts the first three gas laws together in one law

Allows for all three variables to be changed at once

T must be in Kelvin2

22

1

11

T

PV

T

PV

Example

A pump is attempting to compress propane gas. The propane has an initial volume of 2500 liters, temperature of 30 degree C, and a pressure of one atm. If the pump manages to compress the propane to 1000 liters at 2.5 atm what is the temperature of the propane gas?

Example (opener)

If a balloon contains 50 liters of gas at 25 degrees C and 1200 mmHg what would the volume of the gas be at STP?

Mixtures of Gases: Dalton’s Law of Partial Pressures

Dalton’s law of partial pressures is used in dealing with mixtures of gases.

The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by the separate gases:

Ptotal = P1 + P2 + P3 + …

Partial pressure: the pressure a gas would exert if it were alone in the container.

Example

The gases in a light bulb are at STP. If a light bulb contains three gases, xenon at a pressure of 450 mmHg, argon at a pressure of 50 mmHg, and neon gas. What is the pressure of the neon gas in atm?

21

Gas Mixtures and Partial PressuresCollecting Gases over Water

Water Vapor-Water vapor is a

problem-The pressure of the

water vapor changes with temperature

-Must look up vapor pressure of water on a chart (refer to handout)

Temperature (˚C)

Vapor Pressure (mmHg)

19 16.520 17.5421 18.722 19.823 21.124 22.425 23.826 25.2

ExampleSuppose that 120 ml of argon is collected over water at 22 degree C and the total pressure is 780 torr. Calculate the pressure of the dry argon gas?

The Ideal Gas Law:Adding Moles to the Gas Laws

V must be in LitersP must be in AtmT must be in Kelvin

Ideal gas equation: PV = nRTR = gas constant = 0.08206 L•atm/mol-

K

ExampleIf Emily had 1.4 moles of propane in a one liter bottle at 30 degrees C what is the pressure?

ExampleA helium balloon has a volume of 12 liters at a temperature of 20 degrees C and 749 mmHg. How many grams of helium are in the balloon?

ExampleAmy the adventurous astronaut needed an oxygen tank that contained 40 moles of oxygen at STP. What is the volume of the tank? (liters)