1. Gases

2. Characteristics of Gases
A Gas has neither a definite shape nor definite volume:
-adopts the volume and shape of the vessel containing it.
-is highly compressible.
-has extremely low density.

3. Substances exist as gases
Elements that exist as gases at 250C and 1 atmosphere

4. Some substances that exist as gases at 250C and 1 atmosphere

5. Pressure Pressure is the amount of force applied to an area.
Units of pressure:
1 pascal (Pa) = 1 N/m2
1 bar = 105 Pa = 100 kPa

6. Atmospheric pressure is the weight of air per unit of area.
mm Hg or torr
These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury.
Atmosphere pressure:
1 atm = 760 mmHg = 760 torr
1 atm = 101,325 Pa (~105)
A mercury barometer

7. Publishing or establishing entity
Standard Pressure
Normal atmospheric pressure at sea level is referred to as standard pressure.
Temperature
Absolute pressure
Relative humidity
Publishing or establishing entity °C
kPa %
IUPAC (STP)
NIST, ISO, formerly IUPAC 15
ICAO's ISA, ISO, EEA, EGIA 20
EPA, NIST 22
20-80
American Association of Physicists in Medicine 25
EPA
Standard pressure= 1.00 atm = kPa

8. Boyle’s Experiment

9. Boyle’s Law
The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.
P a 1/V
P x V = constant
P1 x V1 = P2 x V2
At: Constant temperature
Constant amount of gas

10. Relationship between P and V
PV = k : a plot of P versus V will be a curve.
V = k (1/P) : a plot of V versus 1/P will be a straight line.

11. A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?
P1 x V1 = P2 x V2
P1 = 726 mmHg
P2 = ?
V1 = 946 mL
V2 = 154 mL
P1 x V1 V2 =
P2 = =

12. Charles’s Law
The volume of a gas at constant pressure increases linearly with the absolute temperature of the gas.
V a T
V = constant x T
V1/T1 = V2/T2
Temperature must be in Kelvin
T (K) = t (0C)
A plot of V versus T will be a straight line.

13. Plot V vs. T (K)

14. A sample of carbon monoxide gas occupies 3. 20 L at 125 0C
A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?
V1/T1 = V2/T2
V1 = 3.20 L
V2 = 1.54 L
T1 = K
T2 = ?
V2 x T1 V1 =
T2 = =

15. Avogadro’s Law
A gas at constant temperature and pressure the volume is directly proportional to the number of moles of gas.
V a number of moles (n)
V = constant x n
V1/n1 = V2/n2

16. Ammonia burns in oxygen to form nitric oxide (NO) and water vapor
Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure?
4NH3 + 5O NO + 6H2O
__ mole NH __ mole NO
At constant T and P
__ volume NH __ volume NO

17. Ideal-Gas Equation 1 Boyle’s law: V a (at constant n and T) P
Charles’ law: V a T (at constant n and P)
Avogadro’s law: V a n (at constant P and T)
V a nT P
V = constant x = R nT P
Or PV = nRT
R is the gas constant

18. The conditions: 0 0C and 1 atm are called standard temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal gas occupies 22.4 L.
PV = nRT
R = PV nT =
(1 atm)(22.414L)
(1 mol)( K)
R = L.atm / (mol.K)

19. The constant of proportionality is known as R, the gas constant.

20. What is the volume (in liters) occupied by 49.8 g of HCl at STP?
T = 0 0C = K
P = 1 atm
n = 49.8 g x
1 mol HCl
36.45 g HCl
= 1.37 mol
V =
nRT P
PV = nRT
V =

21. Examples
48.7 K
3.05 x 10-3 mol
11.2 L
10.3 atm

22. Relating the Ideal-Gas Equation and the Gas Laws
When the quantity of gas and the temperature are held constant, n & T have fixed values.
PV = nRT = constant
P1V 1= P2V2

23. A metal cylinder holds 50 L of O2 gas at 18
A metal cylinder holds 50 L of O2 gas at 18.5 atm and 21oC, what volume will the gas occupy if the temperature is maintained at 21 oC while the pressure is reduced to 1.00 atm?
18.5 atm x 50 L = 1.00 atm x V2
V2 = 925 L
P1V 1= P2V2

24. When the quantity of gas and the volume are held constant, n & V have fixed values.P T nR V =
= constant P1 T1 P2 T2 =

25. The gas pressure in an aerosol can is 1. 5 atm at 25 oC
The gas pressure in an aerosol can is 1.5 atm at 25 oC. Assuming that the gas inside obeys the ideal-gas equation, what would the pressure be if the can were heated to 450 oC?
P2 = 3.6 atm P1 T1 P2 T2 =
1.5 atm
298 K P2
723 K =

26. = When the quantity of gas is held constant, n has fixed values.
= nR = constant PV T
P1V1 T1
P2V2 T2 =

27. A scuba diver’s tank contains 0
A scuba diver’s tank contains 0.29 kg of O2 compressed into a volume of 2.3 L. (a) Calculate the gas pressure inside the tank at 9 oC. (b) What volume would this oxygen occupy at 26 oC and 0.95 atm?
PV = nRT
P x 2.3 L = ( 290 g/32 gmol-1) x x 282 K
P = 91 atm
V2 = 233 L
P1V1 T1
P2V2 T2 =

28. An inflated balloon has a volume of 6. 0 L at sea level (1
An inflated balloon has a volume of 6.0 L at sea level (1.0 atm) and is allowed to ascend in altitude until the pressure is 0.45 atm. During ascent the temperature of the gas falls from 22 oC to -21 oC. Calculate the volume of the balloon at its final altitude.
V2 = 11 L
P1V1 T1
P2V2 T2 =
1.0 atm x 6.0 L
295 K
0.45 atm x V2
252 K =

29. Gas Density Density (d) = mass (m)  volume (V) moles (n)= mass(m)
molecular mass ()
PV = nRT n V P RT =
n = m  m V PM RT = m V
d = PM RT m V =
d =

30. What is the density of carbon tetrachloride (CCl4) vapor at 714 torr and 125 oC?PM RT
d =
714 torr x 154 g mol -1
62.36 L torr mol -1K-1 x 398 K
d =
d = 4.43 g L-1

31. Which gas is most dense at 1.00 atm and 298 K? CO2, N2O, or Cl2.PM RT
d =
1 x 44
0.082 x 298
d =
= 1.8 g L-1
CO2
d = 1.8 g L-1
N2O
d = 2.91 g L-1 Cl

32. Molecular Mass
We can manipulate the density equation to enable us to find the molecular mass of a gas: P RT
d =
dRT P
 =

33. Calculate the density of NO2 gas at 0. 970 atm and 35 oC
Calculate the density of NO2 gas at atm and 35 oC. (b) Calculate the molar mass of a gas if 2.50 g occupies L at 685 torr and 35 oC. PM RT
d =
0.97 x 46
0.082 x 308
d =
d = g L-1

34. dRT P
 =
mass
volume
d =
2.5 g
0.875 L
d = = g L-1
2.86 x x 308
685
 =
 = g mol-1

35. Dalton’s Law of Partial Pressures
The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.
V and T are constant P1 P2
Ptotal = P1 + P2

36. Consider a case in which two gases, A and B, are in a container of volume V.
PA =
nART V
nA is the number of moles of A
PB =
nBRT V
nB is the number of moles of B
X is the mole fraction
XA = nA
nA + nB
XB = nB
nA + nB
PT = PA + PB
PA = XA PT
PB = XB PT
Pi = Xi PT

37. A sample of natural gas contains 8. 24 moles of CH4, 0
A sample of natural gas contains 8.24 moles of CH4, moles of C2H6, and moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)?
Pi = Xi PT
PT = 1.37 atm
0.116
Xpropane = =
Ppropane = x 1.37 atm
= atm

38. Kinetic-Molecular Theory
This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

39. Main Tenets of Kinetic-Molecular Theory
Gases consist of large numbers of molecules that are in continuous, random motion.
The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.
Attractive and repulsive forces between gas molecules are negligible.
Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

40. The average kinetic energy (u) of the molecules is proportional to the absolute temperature.
The distribution of speeds for nitrogen gas molecules at three different temperatures

41.  Root-Mean-Square Speed (rms) 3RT urms = M
Calculate the rms speed, u, of an N2 molecule at 25 °C.

42. Effusion
Suppose there is a tiny hole of area A in the wall and that outside the container is a vacuum.
Escape of a gas through a tiny hole is called effusion

43. Graham's Law

44. Diffusion
Diffusion is the spread of one substance throughout a space or throughout a second substance.
Relative diffusion rates of NH3 and HCl molecules

45. An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only times that of O2 at the same temperature. Calculate the molar mass of the unknown gas.

46. Real Gases
The behavior of real gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

47. Even the same gas will show wildly different behavior under high pressure at different temperatures.

48. Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular model (no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

49. The van der Waals Equation
The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.
The corrected ideal-gas equation is known as the van der Waals equation.
) (V − nb) = nRT
n2a V2
(P +
a : the effect of intermolecular attractive forces on the gas pressure
b : nonzero volume of molecules and volume exclusive by intermolecular repulsive force.

50. Analysis of the van der Waals Constants a constant
The a constant corrects for the force of attraction between gas particles.
attraction between particles↑ a ↑
As the force of attraction between gas particles becomes stronger, we have to go to higher temperatures for the molecules in the liquid to form a gas.
Gases with very small values of a, such as H2 and He, must be cooled to almost absolute zero before they condense to form a liquid.

51. Analysis of the van der Waals Constants b constant
a rough measure of the size of a gas particle
the volume of a mole of Ar atoms is L

52. Values of van der Waals constants for some common gases

53. Calculate pressure for 1 mole of CO2 at 0oC in containers with 22.4 L
Use idea gas equation
Use van der Waals equation
P = atm

54. Calculate pressure for 1 mole of CO2 at 0oC in containers with 0.2 L
Use idea gas equation
Use van der Waals equation
P = 52.6 atm

55. Calculate pressure for 1 mole of CO2 at 0oC in containers with 0.05 L
Use idea gas equation
Use van der Waals equation
P = 1620 atm

56. If 1. 000 mol of an ideal gas were confined to 22. 41 L at 0
If mol of an ideal gas were confined to L at 0.0 °C, it would exert a pressure of atm. Use the van der Waals equation and the constants (a=6.49 L2–atm/mol2, b= L/mol) to estimate the pressure exerted by mol of Cl2(g) in L at 0.0 °C.