Gases

1
Gases
Chapter 5 Problems 14, 19, 20, 21, 26, 32, 34,
36, 40, 42, 43, 44, 47, 48, 50, 52, 54, 59, 60,
63, 66, 67, 76, 84, 88, 102,Grahams lawproblems
2
Elements that exist as gases at 250C and 1
atmosphere
5.1
3
5.1
4
Physical Characteristics of Gases

• Gases assume the volume and shape of their
  containers.
• Gases are the most compressible state of matter.
• Gases will mix evenly and completely when
  confined to the same container.
• Gases have much lower densities than liquids and
  solids.

5.1
5
Pressure
(force mass x acceleration)
Units of Pressure
1 pascal (Pa) 1 N/m2 1 atm 760 mm Hg 760
torr 101,325 Pa 14.7 psi 29.92 in. Hg
5.2
6
10 miles
0.2 atm
4 miles
0.5 atm
Sea level
1 atm
5.2
7
Boyles Law

• P a 1/V
• This means Pressure and Volume are INVERSELY
  PROPORTIONAL if moles and temperature are
  constant (do not change). For example, P goes up
  as V goes down.
• P1V1 P2 V2

Robert Boyle (1627-1691). Son of Earl of Cork,
Ireland.
8
Charless Law

• If n and P are constant, then V a T
• V and T are directly proportional.
• V1 V2
• T1 T2
• If one temperature goes up, the volume goes up!

Jacques Charles (1746-1823). Isolated boron and
studied gases. Balloonist.
9
Gay-Lussacs Law

• If n and V are constant, then P a T
• P and T are directly proportional.
• P1 P2
• T1 T2
• If one temperature goes up, the pressure goes up!

Joseph Louis Gay-Lussac (1778-1850)
10
Combined Gas Law

• The good news is that you dont have to remember
  all three gas laws! Since they are all related
  to each other, we can combine them into a single
  equation. BE SURE YOU KNOW THIS EQUATION!
• P1 V1 P2 V2
• T1 T2

No, its not related to R2D2
11
And now, we pause for this commercial message
from STP
OK, so its really not THIS kind of STP STP in
chemistry stands for Standard Temperature and
Pressure
Standard Pressure 1 atm (or an
equivalent) Standard Temperature 0 deg C (273 K)
STP allows us to compare amounts of gases between
different pressures and temperatures
12
Avogadros Law
V a number of moles (n)
V constant x n
V1/n1 V2/n2
5.3
13
Ideal Gas Equation
Charles law V a T (at constant n and P)
Avogadros law V a n (at constant P and T)
R is the gas constant
PV nRT
5.4
14
PV nRT
R 0.082057 L atm / (mol K)
5.4
15
Density (d) Calculations
m is the mass of the gas in g
d
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
Solve for n, which mass/molar mass
Or,
M
d is the density of the gas in g/L
5.4
16
A 2.10-L vessel contains 4.65 g of a gas at 1.00
atm and 27.00C. What is the molar mass of the gas?
PV nRT
2.10 L
X 1 atm
n
0.0821 x 300.15 K
n 0.0852 mol
g
n
M
5.3
17
Gas Stoichiometry
5.60 g C6H12O6
0.187 mol CO2
V
4.76 L
5.5
18
Daltons Law of Partial Pressures
V and T are constant
P1
P2
Ptotal P1 P2
5.6
19
Consider a case in which two gases, A and B, are
in a container of volume V.
nA is the number of moles of A
nB is the number of moles of B
PT PA PB
PA XA PT
PB XB PT
Pi Xi PT
5.6
20
A sample of natural gas contains 8.24 moles of
CH4, 0.421 moles of C2H6, and 0.116 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
Xpropane
0.0132
Ppropane 0.0132 x 1.37 atm
0.0181 atm
5.6
21
Bottle full of oxygen gas and water vapor
5.6
22
5.6
23
Chemistry in Action
Scuba Diving and the Gas Laws
5.6
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. 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

5.7
25
Kinetic theory of gases and

• Compressibility of Gases
• Boyles Law
• P a collision rate with wall
• Collision rate a number density
• Number density a 1/V
• P a 1/V
• Charles Law
• P a collision rate with wall
• Collision rate a average kinetic energy of gas
  molecules
• Average kinetic energy a T
• P a T

5.7
26
Kinetic theory of gases and

• Avogadros Law
• P a collision rate with wall
• Collision rate a number density
• Number density a n
• P a n
• Daltons 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

5.7
27
Deviations from Ideal Behavior
1 mole of ideal gas
Repulsive Forces
PV nRT
Attractive Forces
5.8
28
Effect of intermolecular forces on the pressure
exerted by a gas.
5.8
29
Van der Waals equation nonideal gas
5.8
30
Velocity of a Gas
The distribution of speeds for nitrogen gas
molecules at three different temperatures
5.7
31
Gas diffusion is the gradual mixing of molecules
of one gas with molecules of another by virtue of
their kinetic properties.
NH3 17 g/mol
HCl 36 g/mol
5.7
32
GAS DIFFUSION AND EFFUSION

• diffusion is the gradual mixing of molecules of
  different gases.

• effusion is the movement of molecules through a
  small hole into an empty container.

33
GAS DIFFUSION AND EFFUSION

• Grahams law governs effusion and diffusion of
  gas molecules. KE1/2 mv2

Rate of effusion is inversely proportional to its
molar mass.
Thomas Graham, 1805-1869. Professor in Glasgow
and London.
34
GAS DIFFUSION AND EFFUSION

• Molecules effuse thru holes in a rubber balloon,
  for example, at a rate ( moles/time) that is
• proportional to T
• inversely proportional to M.
• Therefore, He effuses more rapidly than O2 at
  same T.

He
35
Gas Diffusionrelation of mass to rate of
diffusion

• HCl and NH3 diffuse from opposite ends of tube.
• Gases meet to form NH4Cl
• HCl heavier than NH3
• Therefore, NH4Cl forms closer to HCl end of tube.

36
Grahams Law Problem 1

• 1 mole of oxygen gas and 2 moles of ammonia are
  placed in a container and allowed to react at 850
  degrees celsius according to the equation
• 4 NH3(g) 5 O2(g) --gt 4 NO(g) 6 H2O(g)
• Using Graham's Law, what is the ratio of the
  effusion rates of NH3(g) to O2(g)?

37
Grahams Law Problem 2

• What is the rate of effusion for H2 if 15.00 ml
  of CO2 takes 4.55 sec to effuse out of a
  container?

38
Grahams Law Problem 3

• What is the molar mass of gas X if it effuses
  0.876 times as rapidly as N2(g)?