Gases

1
Gases

• Chapter 10 in Brown LeMay

2
General characteristics

• Atmosphere is 78 nitrogen and 21 oxygen
• Gas vs. vapor oxygen is a gas, water can be
  vapor
• Volume of gas volume of container
• Highly compressible
• Form homogeneous mixtures spontaneously

3
Pressure

• Force/unit area
• High heels example
• What is the pressure inside a balloon
• Atmospheric pressure in Denver?
• 14 lbs/square inch, 101.3 kPa, 760 mm Hg called
  torr), 1 atmosphere

4
Illustration
5
Open manaometer problem

• Gas pushes down on mercury
• Either add or subtract mm Hg difference
• Animation
• Try one

6
Gas Laws

• Consider P,V,T, and n
• Simple laws look at two when the other two are
  held constant
• Boyles, Charles, and Gay-Lussacs

7
Boyles Law

• At constant temperature, the pressure of an
  enclosed amount of gas will increase if the
  volume is decreased (syringe)
• V k(1/P) or PV k
• P1V1 P2V2
• What would this graph look like?
• Animation

8
Charles Law

• 1787 hot air balloon rides
• When pressure is held constant for a volume of
  gas, temperature and volume increase linearly.
• Absolute temperature only!
• At a certain temperature, a volume of gas would
  have 0 volume. This is absolute zero.
• V kT or V/T k, V1/T1 V2/T2
• Graph?

9
Gay-Lussacs Law

• At a given pressure and temperature, the volume
  of gases that react are in simple whole number
  ratios.
• One interpretation is that if a confined gas is
  at constant volume, pressure and temperature will
  vary directly.
• Avogadro Equal volumes of gases at the same
  pressure and temperature contain equal numbers of
  molecules.

10
STP

• At 0 C and 1 atmosphere of pressure, the volume
  of 1 mole is gas is 22.4 liters.

11
Ideal Gas Equation

• We now know how volume is affected by pressure
  and temperature.
• V 1/P
• V T
• V n
• V nT/P or V knT/P
• k is the proportionality constant, called R
• Solve for R for I mole at STP
• PV nRT

12
Values for R

• Determined by units used for pressure and volume
• Use the first one for this chapter, the second
  whenever J is involved.

13
Further Applications

• PV nRT
• What is n?
• N m/M (mass you have over molar mass
• PV mRT/M
• What is density?
• Rearrange with density on the left
• m/V d PM/RT
• Molar mass from density equation?
• Look at equation sheets

14
Gas Stoichiometry

• Equation determines number of moles and/or grams.
  This is at STP.
• Change initial amounts to STP first, then do
  stoichiometry, or vice versa, depending upon the
  question.
• Airbags is a good example of gas stoichiometry.
  (animation)
• Try one.

15
Daltons Law of Partial Pressure

• Ptot p1 p2 p3 .
• What does this mean?
• http//www2.wwnorton.com/college/chemistry/gilbert
  /tutorials/ch8.htm
• Finding n or mole fraction for each will give
  you the partial pressure if you know Ptot.
• Used most often when gas is collected over water.
  Why? See next slide
• Try a few.

16
Ptot pgas pwater
17
Kinetic Molecular Theory

• Large number of particles in constant, random,
  motion
• Volume of particle is negligible
• Forces between particles are negligible
• Collisions are perfectly elastic
• Average kinetic energy is proportional to average
  Kelvin temperature

18
KE Distribution
19
Speed of Different Gases, same temperature
20
Equations

• Average KE 1/2mu2
• u is the root mean square speed which is almost
  the velocity or speed that we are used to.
• Explain the three gas laws with this

21
Effusion and Diffusion

• Average speed equation, no derivation
• The smaller the M, the faster the average speed
• Effusion escape of a gas from a tiny hole into
  an evacuated space
• Diffusion spread of a gas into a space or
  another substance (we usually mean this!)

22
Comparing two gases

• Derive ratio of speeds of gas a and gas b
• This is diffusion
• Same for effusion, use r for rate

23
Practice

• Calculate the ratio of the rates of effusion for
  N2 and O2 gases at the same temperatures.

24
Derivations from Ideal BehaviorIncreased Pressure

• PV/RT n For 1 mole, this ratio should be equal
  to 1
• Pressure less than 10 atmospheres, ideal behavior
  is seen.
• After that, what happens?
• Particles take up space within the volume of the
  gas.

25
Actually lowers pressure
26
Also causes attractive forces, again lowering
pressure
27
Decreased Temperature

• Lower temperature, what happens?
• Particles begin to attract each other.
• Constants to correct for this available for each
  gas.