Gas Laws

1
Unit 14

• Gas Laws

2
Properties of Gases

• Gas properties can be modeled using math. Model
  depends on
• V volume of the gas (L)
• T temperature (Kelvin, K)
• n amount (moles, mol)
• P pressure (atmospheres, atm)

3
STP

• STP standard temperature and pressure
• Standard temperature 0C 273 K
• Standard pressure 1 atm

4
Pressure of a Gas

• SI unit of pressure pascal (Pa)
• Other common pressure units
• Millimeters of mercury (mm Hg)
• Atmospheres (atm)
• 1 atm 760 mmHg 101.3 kPa 760 torr

5
Practice Converting Units

• 1 atm 760 mmHg 101.3 kPa

A tire pressure gauge records a pressure of 450
kPa. What is the pressure in atmospheres? In mm
Hg?
6
Boyles Law

• Relationship between pressure and volume

7
Boyles Law in Real Life

• Popping a balloon
• As you squeeze the balloon, what happens to the
  pressure and volume inside the balloon?
• Are pressure and volume directly proportional or
  inversely proportional?

P V
8
Boyles Law in Real Life

• Operating a water gun/syringe
• As you pull back on the plunger, are you
  increasing or decreasing the volume? How does the
  pressure change?
• Are P and V directly or inversely proportional?

P V
9
Boyles Law in Real Life

• Marshmallow/balloon in a vacuum
• As we evacuate the chamber, what do you think
  will happen to the pressure? What do you think
  will happen to the volume of the marshmallow?
• Are P and V directly or inversely proportional?
• 400 Marshmallows in a Vacuum

P V
10
Boyles Law

• When temperature is held constant, pressure and
  volume increase and decrease as opposites
• Pressure volume are inversely or indirectly
  related
• If pressure increases, volume decreases
• If pressure decreases, volume increases

P1V1 P2V2
11
Practice with Boyles Law

• 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 held
  constant)

P1V1 P2V2 P1 V1 P2 V2
12
Practice with Boyles Law

• At room temperature, 10.01 L of a gas is found to
  exert 97.0 kPa. What pressure (in atm) would be
  required to change the volume to 5.00 L?

P1V1 P2V2 P1 V1 P2 V2
1 atm 101.3 kPa
13
Practice with Boyles Law

• Nitrous oxide (N2O) is used as an anesthetic. The
  pressure on 2.50 L of N2O changes from 105 kPa to
  40.5 kPa. If the temperature does not change,
  what will the new volume be?

P1V1 P2V2 P1 V1 P2 V2
14
Charles law

• Relating Volume and Temperature

15
Charles Law in Real Life

• Balloons popping when kept outdoors
• As the balloons sits outside, what happens to the
  temperature of the gas inside the balloon? What
  happens to the volume of the balloon?
• Are volume and temperature directly proportional
  or inversely proportional?

V T
16
Charles Law in Real Life

• A ball outside on a cold day
• You pump the ball up indoors. After going
  outside where its colder, what happens to the
  volume of the ball?
• Are volume and temperature directly or inversely
  proportional?

V T
17
Charles Law in Real Life

• Liquid Nitrogen demo video
• When the balloon is placed in the liquid
  nitrogen, what happened to the temperature of the
  gas inside the balloon? What happened to the
  volume?
• Are volume and temperature directly or inversely
  proportional?

V T
18
Charles Law

• If pressure is held constant (doesnt change),
  volume and temperature increase or decrease
  together
• If volume increases, so does the temperature
• If temperature decreases, so does the volume

T must be in Kelvin!!!
19
Practice with Charles Law

• A balloon inflated in a room at 24 ºC has a
  volume of 4.00 L. The balloon is then heated to
  a temperature of 58 ºC. What is the new volume
  if the pressure remains constant?
• V1
• T1
• V2
• T2

20
Practice with Charles Law

• Exactly 5.00 L of air at -50 ºC is warmed to some
  temperature so that the volume was 8.36 L. What
  temperature was the system warmed to?
• V1
• T1
• V2
• T2

21
Practice with Charles Law

• A 50.0 mL sample of a gas is cooled from 119 ºC
  to 353 K. If the pressure remains constant, what
  is the final volume of the gas?
• V1
• T1
• V2
• T2

22
Gay-Lusaacs Law

• The Relationship Between Pressure and Temperature

23
Gay-Lusaacs Law in Real Life

• Warnings on aerosol cans
• What do the warnings say regarding putting them
  near flames?
• As the temperature of the can increases, what
  happens to the pressure in the can?
• Are pressure and temperature directly or
  inversely proportional?

P T
24
Gay-Lusaacs Law in Real Life

• Warm soda fizzing vs. cold soda fizzing
• When opened, which one fizzes more, cold soda or
  warm soda?
• Does more fizzing mean there was higher pressure
  inside or lower pressure?
• Are pressure and temperature directly or
  inversely proportional?

P T
25
Gay-Lusaacs Law in Real Life

• Egg and flask demo
• When the boiling water gets dumped goes out,
  what happens to the temperature of the gases
  inside the flask?
• Do the gas particles have more kinetic energy or
  less? Are they creating more pressure or less?
• Are pressure and temperature directly or
  inversely proportional?

P T
26
Gay-Lusaacs Law

• If volume is held constant, pressure and
  temperature increase and decrease together
• If pressure increases, so does the temperature
• If temperature decreases, so does the pressure

27
Practice with Gay-Lusaacs Law

• The gas in a used aerosol can is at a pressure of
  103 kPa at 25 ºC. If the can is thrown onto a
  fire, what will the pressure be when the
  temperature reaches 928 ºC?
• P1
• T1
• P2
• T2

28
Practice with Gay-Lusaacs Law

• A sample of nitrogen has a pressure of 6.58 kPa
  at 539 K. If the volume does not change, what
  will the pressure be at 211 K?
• P1
• T1
• P2
• T2

29
Practice with Gay-Lusaacs Law

• A 10.01 L sample of a gas is found to exert 97.0
  kPa at 25 ºC. What temperature (in celsius)
  would be required to change the pressure to 1.00
  atm?
• P1
• T1
• P2
• T2

30
The Combined Gas Law

• Taking Into Account Pressure, Volume, AND
  Temperature

31
In Review

• Boyles Law looked at which 2 factors?
• Charles Law?
• Gay Lusaacs?

32
Imploding Can Demo

• What happened to the volume of the can?
• What happened to the temperature of the gas
  inside the can?
• How did pressure play a role in the can imploding?

33
The Combined Gas Law

• The combined gas law considers the effect of all
  3 factors at the same time
• All 3 of the gas laws can be derived from the
  combined gas law

34
Example Boyles Law from Combined Gas Law

• If temperature is constant, T1 T2
• Rearrange the equation to get both temperatures
  together

35
Examples with Combined Gas Law

• A 200 mL sample of gas is collected at 50 kPa and
  a temperature of 271oC. What volume would this
  gas occupy at 100 kPa and a temperature of -14oC?

36
Examples with Combined Gas Law

• Helium in a 100 mL container at a pressure of
  66.6 kPa is transferred to a container with a
  volume of 250 mL. What is the new pressure if the
  temperature changes from 20oC to 15oC?

37
Examples with Combined Gas Law

• A certain sample of gas has a volume of 0.452 L
  measured at 87oC and 0.620 atm. What is its
  volume at 1 atm and 0oC?

38
The Ideal Gas Law

• P, V, T, and n

39
The Combined Gas Law

• Takes into account P, T, and V but not the amount
  of gas present
• Amount of gas moles of gas present (n)

40
The Ideal Gas Law

• Takes into account all 4 variables pressure
  (P), volume (V), temperature (T), AND the amount
  of moles (n)
• R 0.0821 8.314

Ideal Gas Constant
41
Sample Problem Ideal Gas Law

• How many moles are in a sample of gas occupying
  12 L at a temperature of 15C and a pressure of
  2.4 atm?

PV nRT
42
The Ideal Gas Law

• Once you calculate the moles of gas you can
  convert this to a mass (in grams, kilograms,
  etc.) using what?
• You may also be given the amount of gas in grams
  and have to convert it to moles in order to plug
  into the ideal gas law

43
Sample Problem Ideal Gas Law

• What is the volume occupied by 36.0 grams of
  water vapor at 125?C and 102 kPa?

PV nRT
44
Sample Problem Ideal Gas Law

• What mass of carbon dioxide will occupy 5.5 L at
  5?C and 0.74 atm?

PV nRT
45
Sample Problem Ideal Gas Law

• A deep underground cavern contains 2.24 x 106 L
  of methane gas (CH4) at a pressure of 1500 kPa
  and a temperature of 315 K.
• (a) How many moles of CH4 does the cavern
  contain?
• (b) How many kilograms does the cavern contain?

PV nRT
46
Ideal Gases vs. Real Gases

• Ideal Gas a gas which behaves according to the
  gas laws and KMT at all pressures and
  temperatures
• Gas particles have no volume and no attraction to
  one another
• No such thing as an ideal gas just real gases
  which behave like ideal gases under certain
  conditions

47
Ideal Gases vs. Real Gases

• Real gases behave like ideal gases under the
  following conditions
• At high temperature
• At low pressure
• When the gas itself has small, non-polar
  molecules
• Why??