1. Gases
Chapter 5

2. The Gaseous State Ideal Gas Concept
Ideal gas - a model of the way that particles of a gas behave at the microscopic level.
We can measure the following of a gas:
temperature,
volume,
pressure and
quantity (mass)
We can systematically change one of the properties and see the effect on each of the others.

3. The most important gas laws involve the relationship between
Measurement of Gases
The most important gas laws involve the relationship between
number of moles (n) of gas
volume (V)
temperature (T)
pressure (P)
Pressure - force per unit area.
Gas pressure is a result of force exerted by the collision of particles with the walls of the container.

4. Pressure P = Force/unit area
Force exerted per unit area of surface by molecules in motion.
P = Force/unit area
1 atmosphere = 14.7 psi
1 atmosphere = 760 mm Hg
1 atmosphere = 101,325 Pascals
1 Pascal = 1 kg/m.s2
SI unit for force is Newton (N)
Force = mass x acceleration
N = 1 kg m/s2
1 Pa = 1 N/m2 , 1 kg m/s2 / m2 = 1 kg/m.s2 2

5. Barometer - measures atmospheric pressure.
Invented by Evangelista Torricelli
A commonly used unit of pressure is the atmosphere (atm).
1 atm is equal to:
760 mmHg
760 torr
76 cmHg

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

8. Boyle’s Law
Boyle’s Law - volume of a gas is inversely proportional to pressure if the temperature and number of moles is held constant.
PV = k1 or
PiVi = PfVf

10. Charles’ Law
Charles’ Law - volume of a gas varies directly with the absolute temperature (K) if pressure and number of moles of gas are constant. or

12. The Empirical Gas Laws
Gay-Lussac’s Law: The pressure exerted by a gas at constant volume is directly proportional to its absolute temperature.
P a Tabs (constant moles and V) or 3

13. Combined Gas Law 1
This law is used when a sample of gas undergoes change involving volume, pressure, and temperature simultaneously.

14. Avogadro’s Law V a number of moles (n) V = constant x n
Constant temperature
Constant pressure
V a number of moles (n)
V = constant x n
V1 / n1 = V2 / n2

15. Ideal Gas Equation 1 Boyle’s law: P a (at constant n and T) V
Charles’s 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
R is the gas constant
(universal gas constant)
PV = nRT

16. PV = nRT PV (1 atm)(22.414L) R = = nT (1 mol)(273.15 K)
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 L.
PV = nRT
R = PV nT =
(1 atm)(22.414L)
(1 mol)( K)
R = L • atm / (mol • K)

17. Ch-5 Review of concept, greatest volume at STP? (a) 0.82 mole of He
V=(0.82 mol x L/1mol)=18.38 L
(b) 24 g N2
V=24g N2x (1mol N2/28.02g) x (22. 4 L/mol)
= L
©5.0 x 1023 molecules of Cl2
V= 5.0 x 1023 moleculesx (1mole/6.022 x 1023 molecules) x 22.4 L/mole =18.60 L

18. Ch-5, Highest density? At STP, 1mole of He, N2, or Cl2?
Mass of 1 mole of He = 4.003g
V at STP = 22.4 L, D= M/V, = 4.003g/22.4 L = g/L
Mass of 1 mole of N2 = 28.02g
D = g/22.4L = g/L
Mass of 1 mole of Cl2 = g
D = g/22.4 L = 3.17 g/L
at 1 atm the density of water vapor at 100degree Celsius is g/l and the density of liquid water at that temperature is 0.958g/cm3. also at 1 atm the density of ice at 0 degree Celsius is g/cm3, the density of liquid water at 0 degree Celsius is g/cm3

19. Density (d) Calculations
m is the mass of the gas in g
d = m V = PM RT
M is the molar mass of the gas
PV = nRT, PV = m/M RT, P/RT = m/MV, d= m/V, and P/RT = d/M , d = PM/RT
Molar Mass (M ) of a Gaseous Substance
dRT P
M =
d is the density of the gas in g/L

20. Gas Stoichiometry

21. Dalton’s Law of Partial Pressures
V and T are constant P2
Ptotal = P1 + P2 P1

22. PA = nART V PB = nBRT V XA = nA nA + nB XB = nB nA + nB PT = PA + PB
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
XA = nA
nA + nB
XB = nB
nA + nB
PT = PA + PB
Pi = Xi PT
mole fraction (Xi ) = ni nT

23. PT = PA + PB
= nART/V + nBRT/V
= (nA+nB)RT/V
n = nA + nB
=nRT/V
PA/PT = = nART/V/ (nA+nB)RT/V
=nA/nA+nB
=XA
XA is called the mole fraction of A.
PA/PT = XA
PA = XAPT
PB = = XBPT
Pi = Xi PT
mole fraction (Xi ) = ni nT

24. Kinetic Molecular Theory of Gases
A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume.
Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic.
Gas molecules exert neither attractive nor repulsive forces on one another.
The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy
KE = ½ mu2

25. Kinetic theory of gases and …
Compressibility of Gases
Boyle’s Law
P a collision rate with wall
Collision rate a number density (number of molecules/V)
Number density a 1/V
P a 1/V
Charles’s Law
Collision rate a average kinetic energy of gas molecules
Average kinetic energy a T
P a T

26. Kinetic theory of gases and …
Avogadro’s Law
P a collision rate with wall
Collision rate a number density
Number density a n
P a n
Dalton’s Law of Partial Pressures
Molecules do not attract or repel one another
P exerted by one type of molecule is unaffected by the presence of another gas
Ptotal = SPi

27. Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. r1 r2 M2 M1  =
NH3 (17 g/mol)
NH4Cl
HCl
36 g/mol

28. Gas effusion is the process by which gas under pressure escapes from one compartment of a container to another under vacuum by passing through a small opening. (Fig.5.21) = r1 r2 t2 t1 M2 M1 

29. ( ) } } Deviation from Ideal Behavior Van der Waals equation
nonideal gas (
an2 V2 )
P (V – nb) = nRT }
corrected
pressure }
corrected
volume
Occurs at high pressure and low temp.
P>5 atm and low temp.

30. Deviation from Ideal Behavior (cont.)
a is a constant, n and V are the number of moles and volume of the container, respectively (applies for P)
V-nb, V = vol.of container
b, a constant and n is the number of moles of gas, nb is the number of moles of the gas.

31. Copyright © Cengage Learning. All rights reserved
CONCEPT CHECK! He H2
You are holding two balloons of the same volume. One contains helium, and one contains hydrogen. Complete each of the following statements with “different” or “the same” and be prepared to justify your answer.
Copyright © Cengage Learning. All rights reserved

32. Copyright © Cengage Learning. All rights reserved
CONCEPT CHECK! He H2
The pressures of the gas in the two balloons are __________.
the same
Copyright © Cengage Learning. All rights reserved

33. Copyright © Cengage Learning. All rights reserved
CONCEPT CHECK! He H2
The temperatures of the gas in the two balloons are __________.
the same
Copyright © Cengage Learning. All rights reserved

34. Copyright © Cengage Learning. All rights reserved
CONCEPT CHECK! He H2
The numbers of moles of the gas in the two balloons are __________.
the same
Copyright © Cengage Learning. All rights reserved

35. Copyright © Cengage Learning. All rights reserved
CONCEPT CHECK! He H2
The densities of the gas in the two balloons are __________.
different
Copyright © Cengage Learning. All rights reserved