1. Gas Laws and KMT
Chapter 5

2. Pressure Barometer – first pressure measuring device Torricelli, 1643
A glass tube filled with mercury, inverted into a dish of mercury.
At sea level, height of mercury in the tube is 760 mm
Why does the Hg stay in the tube, defying gravity?

3. Air Pressure
Why does a barometer measure lower air pressure when a storm is approaching?
Lower air pressure means the weight of air being pulled toward the earth is lower
Air is being pulled UP, so air is rushing into a low (wind)
Air pressure is also lower at higher elevation
At 9600 ft, air pressure is only 560 mm
Less air pushing down on earth’s surface

4. Manometer
The principle of a manometer measurement depends on the fact that given the same fluid, pressure is the same at equal heights.
Pgas= Patm – h OR Pgas= Patm + h
Manometer is a substitute for a Barometer and both measure mm Hg
Mm Hg =Torr

5. Pressure Standard Atmosphere = 760 torr = 760 mm Hg
Pressure = Force/area
SI units of measure
Force = Newtons
Area = m2
SI unit of measure for pressure is Pascal (Pa)
1 Standard atmosphere – 101,325 Pa

6. Gas Laws Boyles Law Charles Law Guy-Lussac’s Law (Not used much)
Avogadro’s Law
Ideal Gas Law
All Lead To:
Gas Stoichiometry

7. Boyles Law Boyle studied pressure and volume PV = k Variation:
Temperature constant
Amount of gas constant
Variation:
V=k/P
P=k/V
Boyles Law is also frequently written and used as:
P1V1 = P2V2

8. Charles Law Studied relationship between pressure and temperature
Determined that plots of volume vs. temperature are linear
V = bT
Constant pressure
Constant amount of gas
NOTE: gas cannot have a negative volume, so temperature cannot be negative. Thus we MUST use Kelvin scale for temperature at all times.
More on this later
Variations:
V/T=b

9. Charles Law Charles Law is also frequently written and used as:
V1/T1 = V2/T2

10. Avogadro’s Law
Postulated that equal volumes of gases at the same temperature and pressure contain the same number of ‘particles’.
Avogadro’s Law
V = an
a = proportionality constant
N = number of moles of gas
Variations:
V/n = a (constant)

11. Combined Gas Law Assumes constant amount of gas PV/T = k Or
P1V1/T1 = P2V2/T2

12. Ideal Gas Law Boyles Law: V = k/P (constant T & n)
Charles Law: V = bT (constant P & n)
Avogadro’s Law: V=an (constant P & T)
Combined: V = R(Tn/P)
Or PV=nRT
R is universal gas constant ( L*Atm/mole*K)
MAKE SURE ALL TEMPS ARE IN KELVIN
This is the IDEAL GAS LAW
Real gasses behave somewhat differently

13. Gas Stoichiometry
Molar volume of a gas = L at standard temperature and pressure
STP (standard temperature and pressure)
0ºC (273K)
1 atm (760 torr or 760 mm Hg
Using gas density:
Density = mass/volume
PV=nRT  P = nRT/V

14. Gas Stoichiometry Using Density
Density = mass/volume
PV=nRT  P = nRT/V
n = mass/molar mass =m/molar mass
P = (m/molar mass)RT/V
P = mRT/V(molar mass)
m/V = density (d)
P = dRT/molar mass
Molar mass = dRT/P

15. Dalton’s Law of Partial Pressures
Applies to Gasses
For a mixture of gasses in a container, the total pressure is the sum of the pressures that each gas will exert if it were alone
PTOTAL = P1 + P2 + P3+…..
PTOTAL = n1RT/V + n2RT/V + n3RT/V….
Equals (n1 + n2 + n3 + …)RT/V
Equals NtotalRT/V

16. Collecting Gas Over Water
Whenever you collect gas over water, water vapor is present:
Water molecules escape from surface of water
Pressure due to water, depends on temperature, and is the vapor pressure of water.
Total pressure of gas collected is Pressure of gas + pressure of water vapor

17. Kinetic Molecular Theory
A theory summarizes observed behavior
A model allows you to use theories to predict behavior
Also can be viewed as a way of understanding, a way of thinking, a mental construct
KMT is a model based on gas laws

18. Kinetic Molecular Theory
Particles are so small compared to distances between the particles that the volume of the particles can be assumed to be negligible (zero).
The particles are in constant motion. Collisions of the particles with the walls of the container are the cause of pressure exerted by the gas.
The particles are assumed to exert no forces on each other; they are assumed to neither attract nor repel each other.
The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

19. Boyles Law If volume decreases, pressure increases.
KMT says a decrease in volume means the particles will hit the wall more often

20. Pressure and Temperature
Ideal Gas Law: Pressure is directly proportional to temperature
KMT: as temperature increases;
Speeds of particles increases
Particles hit wall with greater force
Particles hit walls with greater frequency
Result: increased pressure

21. Charles Law
Ideal Gas Law: at constant pressure, volume of gas is directly proportional to temperature Kelvin
KMT: When heated;
Speed of molecules increases
Hit walls with greater force
Hit walls with greater frequency
Only way to keep pressure constant is to increase volume

22. Avogadro’s Law
Ideal Gas Law: Volume is directly proportional to number of particles present
Constant temperature & pressure
KMT: If you add more particles to a container;
Pressure would increase
Only way to maintain pressure is to increase volume

23. Dalton’s Law
Dalton: Total pressure is the sum of the partial pressures
KMT: Assumes;
all gas particles are independent of each other
Volumes of individual particles are unimportant
Identities of particles do not matter

24. Deriving Ideal Gas Law Apply particle physics to assumptions of KMT:
Use definitions of velocity, momentum, force, pressure
See Appendix 2 for details
KE = 1/2 mv2 where v is root mean squared speed.
Total kinetic energy is KE = NA(1/2 mv2) where N is Avogadro's number
Final derivation is: P = 2/3 (n NA(1/2 mv2) / V)

25. What is Temperature? KMT bases temperature on Kelvin
Because it is based on average kinetic energy of the particles
Requires an absolute energy scale
Hence: Kelvin

26. Problem:
Calculate the average kinetic energy of the CH4 particles in a sample of CH4 gas at 273K and at 546K

27. Thursday Effusion and Graham’s Law Diffusion
Real Gases and van der Waal’s equation.

28. Effusion & Diffusion Diffusion – the mixing of gases without agitation
Effusion – passage of a gas through a tiny orifice (hole)

29. Effusion Graham’s Law of Effusion √M2 Rate of Effusion for gas 1 √M1 =
M1 and M2 are molar masses for the gases.

30. Diffusion Diffusion takes a long time
Even though molecules are travleing 450 and 660 m/s
Why?
Tube is filled with air
Lots of collisions with air that don’t lead to a reaction
Difficult to describe theoretically

31. Next
Real Gases
Corrections for pressure
Corrections for volume

32. Real Gases
Ideal gas behavior is best thought of as the behavior approached by real gases under certain conditions.
Ideal gas behavior fails at:
Low temperatures
High pressures
Real gases behave most like ideal gases at:
High temperature
Low pressure

33. Real Gases Ideal gas assumption of volume is incorrect:
Molecules always take up some space.
Correct for volume by subtracting volume for the molecules
VREAL = VIDEAL-nb
n is number of moles
b is an empirical correction constant
So:
P’ = nRT/(V-nb)

34. Real Gases
But we still have to correct for the fact that real gases DO have attraction forces.
Effect is to make observed pressure POBS smaller than it normally would if there were no attractions:
POBS = (P’ – correction factor)(nRT/(V-nb) – correction factor
Size of correction factor depends on concentration of the gas molecules in particles per liter (n/V)
Higher concentration, more likely particles are close enough to attract. Depends on square of number of particles because 2 particles have to get close enough.

35. Real Gases
So:
POBS = P’ – s(n/V)2
Inserting correction factors for both volume and attractions gives the equation:
POBS = (nRT/(V-nb)) – a(v/V)2
Pressure correction factor
Volume of container
Volume correction factor

36. Van Der Waals Equation
POBS + a(n/V)2 x (V-nB) = nRT