Gas Laws

1
Gas Laws
2
Factors That Affect Gas Behavior

• 1. Temperature (T) ? a measure of the average
  kinetic energy (movement) of particles in a
  sample of matter
• If the kinetic energy of particles increases,
  the temperature of the substance increases.
• KE ½ mv2
• m mass of the particles
• v speed of particles
• http//youtube.com/watch?vEH5v54dmb5U

3

• Think about a balloon in hot versus cold weather.
  What is happening with the movement of the gas
  particles? Kinetic energy?

4

• Units of temperature can be measured in
• 1. Celsius
• 2. Fahrenheit
• 3. Kelvin
• Who uses these temperature scales?
• U.S.A. uses Fahrenheit
• The rest of the world uses Celsius
• Scientists use Kelvin

5

• Important equations needed to do temperature
  conversions
• F 1.8 (C) 32
• K C 273

6
(No Transcript)
7

• 2. Volume (V) ? the amount of space an object
  takes up
• Gases have an indefinite shape and size
  depending on pressure and temperature
• Gases are compressible and expandable
• Units of volume can be measured in
• 1. mL (for irregular shaped objects using H2O
  displacement)
• 2. cm3 (for regular shaped objects using the
  equation l x w x h)

8

• 3. Amount (n) ? how much of a substance is
  present
• Units of amount can be measured in
• 1. Moles (the unit of measurement we use for
  ALL gas laws)
• 2. Grams
• 3. Number of molecules

9

• 4. Pressure (P) ? the force per unit area
• P force/area

10

• Ex. 2 female students are going to prom. One
  is wearing Stilettos and the other is wearing a
  chunky heeled shoe. They decide to take pictures
  on the grass at Erickson Park. Assuming both
  women have the same mass, which one is going to
  have a harder time walking due to the amount of
  pressure she is exerting on the ground?

11

• The pressure exerted by the girl wearing the
  Stilettos will be greater than the girl wearing
  the chunky heeled shoe.

12

• Units of pressure can be measured in
• 1. Pascals
• 2. Millimeters of mercury (mm Hg)
• 3. Torr
• 4. Newton per meter squared (N/m2)
• 5. Atmospheres (atm)

13

• At standard temperature and pressure (STP) O
  C and 1 atm, the following pressure conversions
  hold true
• 1 atm 760 mm Hg 760 torr 101.3 kPa

14
Unique Properties of Gases According to Kinetic
Molecular Theory

• 1. Expansion
• Gas particles move rapidly and spread out in all
  directions without significant attraction or
  repulsion between them.
• Ex. Perfume diffusing throughout the room

15

• When gas particles collide, they exhibit elastic
  collisions where no kinetic energy is gained or
  lost, just transferred from one particle to
  another.
• Ex. super ball (elastic) versus hacky sack
  (inelastic)
• Expansion allows gases to take the shape and
  volume of the container they are in.

16

• 2. Compressibility
• Gas particles that are initially apart can
  become crowded closer together.
• Compression is possible because gases consist of
  mostly empty space.

17

• 3. Low Density (mass/volume ratio)
• Gas particles are much farther apart that in the
  liquid or solid state.
• The density of gases is about 1/1000 the density
  of the same substance in the liquid or solid
  state.
• http//www.youtube.com/watch?vd-XbjFn3aqE
• http//www.youtube.com/watch?v1PJTq2xQiQ0

18

• 4. Fluidity
• Gas particles can glide past each other without
  being significantly attracted to one another.
• This behavior is similar to liquids because you
  are able to pour both states of matter.
• Ex. Pouring CO2 gas on a lighted candle

19
Looking at the Relationships Between Variables
Graphically Mathematically

• Dependent versus Independent Variable
• A dependent variable will change based on an
  independent variable.
• Dependent variables are contingent on other
  variables. They depend on the other factors
• Ex. Speed (miles per hour)
• Miles are dependent on the amount of hours
  traveled
• The dependent variable will always be found on
  the y-axis when graphing

20

• Independent variables do not depend on any other
  variables to change.
• Independent variables will change in their normal
  conditions regardless of what happens
• Ex. Speed (miles per hour)
• The hours are independent and will continue to
  change, regardless of the miles traveled
• The independent variable will always be found
  on the x-axis

21

• Direct Versus Inverse Relationships
• Direct relationships represent two variables
  acting in the same way.
• kX/Y
• If X increases, Y increases to keep k constant
• If X decreases, Y decreases to keep k constant

22

• Inverse(Indirect) relationships represent two
  variables acting oppositely.
• k XY
• If X increases, Y must decrease to keep k
  constant
• If X decreases, Y must increase to keep k
  constant

23
Gas Laws

• Boyles Law ? As pressure of a gas increases,
  the volume decreases at the same rate
• Temperature and amount of gas must remain
  constant
• Inverse relationship
• PV k
• Ex. Station 2 from gas laws lab (adding books to
  create pressure to the block apparatus)

24

• This law can be used to predict the result of
  introducing a change, in volume or pressure only,
  to a fixed amount of gas, by using the following
  equation
• If P1V1 k and P2V2 k for a fixed amount of
  gas, then
• http//www.chem.iastate.edu/group/Greenbowe/secti
  ons/projectfolder/flashfiles/gaslaw/boyles_law_gra
  ph.html
• P1V1 P2V2
• 1 initial situation
• 2 final situation

25

• Sample problem
• If I have 5.6 liters of gas in a piston at a
  pressure of 1.5 atm and compress the gas until
  its volume is 4.8 L, what will the new pressure
  inside the piston be?

26

• Charless Law ? As the temperature (in Kelvins)
  of a gas increases, the volume increases at the
  same rate
• Pressure and amount of gas must remain constant
• Direct relationship
• V/T k or T/V k
• Ex. Station 3 from gas law lab (placing plungers
  with a specific amount of gas into different
  temperature water baths)

27

• This law can be used to predict the result of
  introducing a change, in volume or temperature
  only, to a fixed amount of gas, by using the
  following equation
• If V1/T1 k and V2/T2 k for a fixed amount of
  gas, then
• http//www.chem.iastate.edu/group/Greenbowe/sectio
  ns/projectfolder/flashfiles/gaslaw/charles_law.htm
  l
• V1/T1 V2/T2
• 1 initial situation
• 2 final situation

28

• Sample Problem
• If I have 45 liters of helium in a balloon at
  250 C and increase the
• temperature of the balloon to 550 C, what will
  the new volume of the balloon be?

29

• Gay-Lussiacs Law ? As the temperature (in
  Kelvins) of a gas increases, the pressure
  increases at the same rate
• Volume and amount of gas must remain constant
• Direct relationship
• P/T k or T/P k
• Ex. Station 1 from gas law lab (pop can
  crushing)

30

• This law can be used to predict the result of
  introducing a change, in pressure or temperature
  only, to a fixed amount of gas, by using the
  following equation
• If P1/T1 k and P2/T2 k for a fixed amount of
  gas, then
• P1/T1 P2/T2
• 1 initial situation
• 2 final situation

31

• Sample Problem
• A gas cylinder containing explosive hydrogen gas
  has a pressure of 50 atm at a temperature of 300
  K. The cylinder can withstand a pressure of 500
  atm before it bursts, causing a
  building-flattening explosion. What is the
  maximum temperature the cylinder can withstand
  before bursting?

32

• Review
• Boyles Law PV k
• Charless Law V/T k
• Gay-Lussiacs Law P/T k
• How can we mathematically represent all 3 of
  these gas laws?

33

• Combined Gas Law ? When 2 variables of a gas
  sample change, the third variable will adjust to
  keep k a constant
• This law incorporates Boyles, Charless, and
  Gay-Lussiacs Law
• The amount of the gas must remain constant
• PV/T k
• If P1V1/T1 k and P2V2/T2 k, then
• P1V1/T1 P2V2/T2

34

• Sample Problem
• A 350 cm3 sample of helium gas is collected at
  22.0 oC and 99.3 kPa.  What volume would this gas
  occupy at STP?

35

• Dalton Law of Partial Pressures
• The total pressure of a mixture of gases is equal
  to the sum of the partial pressures of the
  component gases
• Ptotal P1 P2 P3
• Atmospheric pressure, temperature and volume of
  the gas mixture must remain constant

36

• Sample problem 1
• If you have three 400 L tanks, each filled with a
  different gas,
• Tank 1 contains N2 and has a pressure valve
  reading of 320 kPa
• Tank 2 contains CO2 and has a pressure valve
  reading of 2.0 atm
• Tank 3 contains O2 and has a pressure valve
  reading of 380 torr
• What would be the total pressure in kPa if all
  the gases were contained in the same 400 L tank?

37

• Sample problem 2
• A container holds 36 g of N2. 28 g of O2 are
  added to the container. The total pressure of
  the container is 40. kPa.
• a. Calculate the mole fraction of each gas
• b. Calculate the partial pressure of the N2 and
  O2

38

• Sample problem 3
• 1.0 mole of oxygen gas and 2.0 moles of ammonia
  are placed in a container and allowed to react at
  850 degrees Celsius according to the equation
• 4NH3(g) 5O2(g) --gt 4NO(g) 6H2O(g)
• If the total pressure in the container is 5.00
  atm, what are the partial pressures for the three
  gases remaining?

39

• Avogadros Law ? the volume of a gas will
  increase as moles of particles increases
• Pressure and temperature of a gas must remain
  constant
• Direct relationship
• V/n k or n/V k
• Ex. Station 4 from gas law lab (balloons)

40

• Ideal Gas Law
• This law incorporates Boyles, Charless,
  Gay-Lussiacs and Avogadros Laws into one.
• P1V1/n1T1 P2V2/n2T2
• The problem with this law is that there are 8
  variables to work with.
• To make it easier, we can compare the gas in
  question to an ideal gas situation (R, which is
  always at STP)

41

• For any gas whose behavior approaches that of an
  ideal gas according to the Kinetic Molecular
  Theory, we can use a constant situation (R, which
  is always at STP) to compare to the gas in
  question. Theoretically, any gas in a normal
  range will behave in the same manner.
• R P2V2/n2T2
• PV nRT
• R P1V1/n1T1 gas situation at STP, where
• P1 1 atm or 760 mm Hg or 101.3 kPa
• V1 22.4 L
• T1 273 K
• n1 1 mol

42

• The Gas Law Constant (R) will change values
  depending on the units of pressure used
• ? see Gas Law Constant reference sheet in packet
• When using the ideal gas law equation,
• V must always be in liters!
• T must always be in Kelvins!
• N must always be in moles!

43

• R P2V2/n2T2
• if atm is used, R .0821 (atm x L)/(mol x K)
• (1 atm x 22.4 L)/(1 mol x 273 K) .0821
• if kPa is used, R 8.314 (kPa x L)/(mol x K)
• (101.3 kPa x 22.4 L)/(1 mol x 273 K) 8.314
• if mm Hg are used, R 62.4 (mm Hg x L)/(mol x
  K)
• (760 mm Hg x 22.4 L) /(1 mol x 273 K)

44

• Exceptions to using the ideal gas law
• Under extreme pressure and temperature
  conditions, a gas might not behave ideally
• For example, gas molecules might become slightly
  attracted to each other at extremely high
  pressures and low temperatures.

45

• Grahams Law of Effusion (Diffusion)
• Diffusion ? the gradual mixing of 2 gases due to
  their spontaneous, random motion
• Ex. Burning incense
• Effusion ? a type of diffusion where gas
  molecules are confined to a tiny container and
  randomly pass through a tiny opening in that
  container
• Ex. Perfume escaping through tiny bottle opening

46

• The rates of effusion of gases are inversely
  proportional to the square roots of their molar
  masses
• Heavier particles effuse at a slower rate
• Lighter molecules travel at a faster rate
• vA/vB ?mB/?mA
• A gas 1
• B gas 2
• v velocity or rate of effusion
• m molar mass

47

• Effusion Demo
• Who will travel faster?
• NH3 or HCl?

48

• Sample problem
• If 10 ml of an unknown gas takes 6.3 seconds to
  pass through small opening while 10 ml of a
  standard gas, Oxygen O2 takes 5.6 seconds to pass
  through the same opening under the same
  conditions of temperature and pressure, what will
  be the molecular mass of the unknown gas?

49

• Barometer
• An instrument that measures atmospheric pressure

50

• Sample problem 1
• How will a barometer be affected on a stormy day?
• How will a barometer be affected on a warm, sunny
  day?
• What will happen to Patm?
• What will happen to the mm Hg inside the tube?

51

• Sample problem 2
• At STP, how much Hg will be in the tube in
  inches?

52

• Sample problem 3
• Using H2O instead of Hg will force the design if
  the barometer to be adjusted. How and why?
  (Hint The density of Hg 13.6 g/mL)

53

• Gas Collection through H2O Displacement
• When collecting a gas through water displacement,
  a small amount of water vapor is produced. This
  water vapor exerts pressure along with the gas
  you are collecting.

54

• To determine the pressure of the gas collected,
  the levels of water both inside and outside of
  the flask must be equal to ensure the following
  mathematical relationship holds true
• PAtmosphere PGas Pwater
• PAtmosphere can be found by reading a barometer
• PWater can be found by measuring the temperature
  of the water used for displacement and by reading
  the Vapor Pressure of H2O chart for this value.
• PGas PAtmosphere - PWater