1. Gases

2. Measuring Pressure The first device for measuring atmospheric
pressure was developed by Evangelista Torricelli
during the 17th century.
The device was called a “barometer”
  Baro = weight
  Meter = measure

3. An Early Barometer
The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high.

4. Pressure
Is caused by the collisions of molecules with the walls of a container ( or your head )
is equal to force/unit area
SI units = Newton/meter2 = 1 Pascal (Pa)

5. Einstein, Newton and Pascal are playing hide and go seek
Einstein, Newton and Pascal are playing hide and go seek. It’s Einstein’s turn to be it. Einstein covers his eyes and counts to ten. Pascal runs and hides. Newton draws a 1 meter square line on the ground with chalk and stands in the middle of it. Einstein reaches ten and uncovers his eyes. He sees Newton and exclaims “Newton! I found you! You’re it. “ Newton smiles and says, “You didn’t find me, you found a Newton over a square meter. You found a Pascal!!”

6. 760.0 mm Hg = torr
760.0 torr = atm
1.000 atm = kPa
1.000 atm = psi
760.0 mm Hg = 1 atm
760.0 mm Hg = 101,325 Pa
760.0 mm Hg = psi

7. Examples = 97.2 kPa = 14.2 psi 729 mm 760. mm Hg 729 mm 14.69 psi
The mercury has risen to a height of 729 mm. What is this pressure in kPa & psi?
729 mm
kPa
= 97.2 kPa
760. mm Hg
729 mm
14.69 psi
= 14.2 psi
760. mm Hg

8. Standard Temperature and Pressure “STP”
P = 1 atmosphere, 760 torr
T = 0°C, 273 Kelvins
The molar volume of an ideal gas is liters at STP

9. Converting Celsius to Kelvin
Gas law problems involving temperature require
that the temperature be in KELVINS!
Kelvins = C + 273
°C = Kelvins - 273

10. Boyle’s Law Pressure is inversely proportional to volume
when temperature is held constant.

11. P1V1 = P2V2 P1 = P2V2/V1 P1 = 3.00 cm Hg x 0.240 cm3/200 cm3
A sample of helium gas at 25°C is compressed from 200 cm3 to cm3. Its pressure is now 3.00 cm Hg. What was the original pressure of the helium?
P1 = ?
V1 = 200 cm3
P2 = 3.00 cm
V2 = cm3 Hg
P1V1 = P2V2
P1 = P2V2/V1
P1 = 3.00 cm Hg x cm3/200 cm3
P1 = 3.60 x 10-3 cm Hg

12. Charles’s Law
 The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.
(P = constant)

13. Gay Lussac’s Law The pressure and temperature of a gas are
directly related, provided that the volume
remains constant.

14. A sample of oxygen gas has a volume of 2. 73 dm3 at 21. 0 oC
A sample of oxygen gas has a volume of 2.73 dm3 at 21.0 oC.  At what temperature would the gas have a volume of 4.00 dm3?
V1 = V2
T T2
T1 = 294 K V1 = 2.73 dm3 T2 = ? V2 = 4.00 dm3
2.73 dm3 = dm3
294 K T2
T2 = 294 K x 4.00 dm3                      2.73 dm3
T2  = K

15. The Combined Gas Law
The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.
Boyle’s law, Gay-Lussac’s law, and Charles’ law are all derived from this by holding a variable constant.

16. A 350 cm3 sample of helium gas is collected at 22. 0 oC and 99. 3 kPa
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 ?
V1 = 350 cm3 P1 = 99.3 kPa T1 = 295 K V2 = ? P2 = kPa (standard press) T2 = 273 K (standard temp))
P1 V1 = P2 V2
T T2
(99.3 kPa )(350 cm3 ) = (101.3 kPa) V2
___________________
( 295 K) (273 K)
V2 = 320 cm3

17. ------------------------------------
Avogadro’s Law
For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas.
V = an
a = proportionality constant
V = volume of the gas
n = number of moles of gas
31. D
32. D
33. D
34. C
35. C
36. B
37. B

18. Ideal Gases Ideal gases are imaginary gases that perfectly
fit all of the assumptions of the kinetic molecular
theory.
Gases consist of tiny particles that are far apart
relative to their size.
Collisions between gas particles and between
particles and the walls of the container are
elastic collisions
No kinetic energy is lost in elastic collisions

19. Ideal Gases (continued)
Gas particles are in constant, rapid motion. They
therefore possess kinetic energy, the energy of
motion
There are no forces of attraction between gas
particles
The average kinetic energy of gas particles
depends on temperature, not on the identity
of the particle.

20. The Nature of Gases Gases expand to fill their containers
Gases are fluid – they flow
Gases have low density
1/1000 the density of the equivalent liquid or solid
Gases are compressible
Gases effuse and diffuse
Effusion, molecules moving at a high rate of speed will eventually “collide” with a hole and escape.
Effusion is gas escaping through a hole,
Example: air escaping through a hole in your tire
Diffusion, again because the molecules are moving at a high rate of speed, they will spread out
Example: perfume diffusing through air
Example: Liquids also diffuse: food coloring in water

21. PV = nRT Ideal Gas Law P = pressure in atm V = volume in liters
n = moles
R = proportionality constant
= L atm/ mol·K
T = temperature in Kelvins
Holds closely at P < 1 atm

22. What volume is occupied by 5. 03 g of O2 at 28°C and a pressure of 0
What volume is occupied by 5.03 g of O2 at 28°C and a pressure of atm?
P = atm
V= ?
Mass = 5.03 g O2 / 1 mol O2 / =
/ 32 g O2 /
n= moles
R = L atm
mol K
T = 28°C = 301 K
PV = nRT
(0.998 atm) V = (0.157 mol) ( L atm ) ( 301 K)
mol K
=3.9 L

23. Standard Molar Volume
Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.
- Amedeo Avogadro

24. Density and the Ideal Gas Law
Combining the formula for density with the Ideal
Gas law, substituting and rearranging algebraically:
M = Molar Mass
P = Pressure
R = Gas Constant
T = Temperature in Kelvins
dRT = molar
P mass

25. Gas Stoichiometry #1
If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios.
3 H2(g) N2(g)  NH3(g)
3 moles H mole N  moles NH3
3 liters H liter N  liters NH3

26. Gas Stoichiometry #2
How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen?
3 H2(g) N2(g)  NH3(g)
12 L H2 2
L NH3
= L NH3
8.0 3
L H2

27. Gas Stoichiometry #3
How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s)  2 KCl(s) + 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
22.4 L O2
g KClO3
2 mol KClO3
1 mol O2
= L O2
13.7

28. Gas Stoichiometry #4
How many liters of oxygen gas, at 37.0C and atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s)  2 KCl(s) + 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
= “n” mol O2
g KClO3
2 mol KClO3
0.612
mol O2
= 16.7 L

29. Dalton’s Law of Partial Pressures
For a mixture of gases in a container,
PTotal = P1 + P2 + P
This is particularly useful in calculating the pressure of gases collected over water.
nTotal = n1 + n2 + n

30. Dalton’s law of partial pressures collecting gases over water
Mixture of gas and water vapor.
PT = pgas + pvap(H2O)

31. Ptotal = Pgas + P water vapor
Hydrogen gas is collected over water at
a total pressure of 95.0 kPa and a temperature of 25 C. What is the partial pressure of hydrogen gas?
According to a water vapor pressure table, the vapor pressure of water at 25C is 3.17 kPa.
Ptotal = Pgas + P water vapor
95.0 kPa = X kPa
X = 91.8 kPa

32. e. g. , If 6. 00 g of O2 and 9. 00 g of CH4 are placed in a 15
e.g., If 6.00 g of O2 and 9.00 g of CH4 are placed in a 15.0-L container
at 0ºC, what is the partial pressure of each gas and the total pressure in
the container.

33. Kinetic Energy of Gas Particles
At the same conditions of temperature, all gases
have the same average kinetic energy.

34. The Meaning of Temperature
Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

35. Kinetic Molecular Theory
Particles of matter are ALWAYS in motion
Volume of individual particles is  zero.
Collisions of particles with container walls cause pressure exerted by gas.
Particles exert no forces on each other.
Average kinetic energy µ Kelvin temperature of a gas.

36. Diffusion
Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

37. Effusion
Effusion: describes the passage of gas into an evacuated chamber.

38. Kinetic Molecular Theory
Gases have certain properties that can be explained by the KMT.
Low Density, because the molecules are moving at a high rate of speed and are not held back by electrostatic attractions, they, spread out. And because gases have small volume as well as being spread out, they have low density
Compressibility, because the molecules have space between them, they can be forced to compress unlike liquids and solids where there is little space between the molecules
Expansion, because the molecules are moving at a high rate of speed, they will spread out if given the opportunity
Diffusion, again because the molecules are moving at a high rate of speed, they will spread out
Example: perfume diffusing through air
Example: Liquids also diffuse: food coloring in water
Effusion, molecules moving at a high rate of speed will eventually “collide” with a hole and escape.
Effusion is gas escaping through a hole,
Example: air escaping through a hole in your tire

39. Graham’s Law Rates of Effusion and Diffusion

40. Real Gases ­ ­ corrected pressure corrected volume Videal Pideal
Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).
corrected pressure
corrected volume
Videal
Pideal