The Gaseous State

1
The Gaseous State

• Chapter 5

2
Pressure-Force exerted by molecules in motion

• 1 Pascal 1 N/m2
• 101,325 Pa 760 mm Hg
• 760 mmHg 1 atm

P Force/unit area
3
The Gas Laws

• Boyles Law
• V ? 1/P (constant n and T)
• Charless Law
• V ? T (constant n and P)
• Avogadros Law
• V ? n (constant T and P)

P Force/unit area
4
The Ideal Gas Law
PV nRT
P is pressure V is volume n is number of atoms
(moles) R is universal gas constant 0.08206
L.atm/K.mole T is temperature
5
Ideal Gas Law

• An experiment calls for 3.50 moles of chlorine,
  Cl2. What volume would this be if the gas volume
  is measured at 34oC and 2.45 atm?

6
Ideal Gas Law

• An experiment calls for 3.50 moles of chlorine,
  Cl2. What volume would this be if the gas volume
  is measured at 34oC and 2.45 atm?

nRT (3.50 mol)(0.08206 L atm/K mol)(307 K)

V

P
2.45 atm
35.99 36.0 L
7
A Problem to Consider

• A sample of methane gas that has a volume of 3.8
  L at 5.0 oC is heated to 86.0 oC at constant
  pressure. Calculate its new volume and mass.

8
Solution

• First, determine which values in the ideal gas
  equation are fixed PV nRT
• Rearrange to group constants V/T nR/P
• Add new conditions and unknown V1 V2
  nR/P T1 T2

9
Solution

• Solve for unknown quantity

V2
3.8 L

nR/P
359.0 K
278.0 K
Note Temperature must be in Kelvin
10
Solution

• Solve for unknown quantity

V2
3.8 L

nR/P
359.0 K
278.0 K
3.8 L
x
359.0 K V2 4.9 L
278.0 K
11
Standard Temperature and Pressure (STP)

• By defining STP several new equations can be
  derived that yield constants or other information
  about a sample.

Standard Temperature 0 oC Standard Pressure
1 atmosphere
12
Gas Stoichiometry-at STP

• Molar Mass g/mole just like molecular
  weight P dRT/molar mass (where d is the
  density in g/V)
• Molar Volume
• V nRT/P 22.42 L 1.3 basketballs

13
Partial Pressures of Gas Mixtures

• PTotal P1 P2 P3
• The pressure of a mixture of gases is the sum of
  the partial pressure exerted by each gas.
• DALTONS LAW OF PARTIAL PRESSURE

14
Gas Mixtures

• Given a mixture of gases in the atmosphere at
  760 torr, what is the partial pressure of N2 (?
  .7808) at 25 Co?

15
Gas Mixtures

• Given a mixture of gases in the atmosphere at
  760 torr, what is the partial pressure of N2 (?
  .7808) at 25oC?

? is the mole fraction of a gas.
? n1 / nTotal
16
The Result
n1
?
nTotal
17
The Result
n1
?
nTotal
P1(V/RT)

P1(V/RT) P2(V/RT) P3(V/RT) . . .
18
The Result
n1
?
nTotal
P1(V/RT)

P1(V/RT) P2(V/RT) P3(V/RT) . . .
P1
?
PTotal
19
So . . .

• PN2 PTotal x ?N2
• 760 torr x .7808
• 593 torr

20
Kinetic-Molecular Theory A simple model based on
the actions of individual atoms

• Volume of particles is negligible
• Particles are in constant motion
• No inherent attractive or repulsive forces
• The average kinetic energy of a collection of
  particles is proportional to the temperature (K)

21
Grahams Law of Effusion

• Diffusion - is the transfer of a gas through a
  space or another gas over time.
• Effusion - is the transfer of gas through a
  membrane or orifice.

22
Grahams Law of Effusion

• Diffusion - the transfer of a gas through a
  space or another gas over time.
• Effusion - the transfer of a gas through a
  membrane or orifice.

Rate of effusion for gas 1
(M2/M1)1/2
Rate of effusion for gas 2
23
A Problem to Consider

• Samples of ammonia and hydrochloric acid are
  placed at either end of a 1 meter tube. A
  reaction to form ammonium chloride solid will
  occur closer to which end of the tube?

24
A Problem to Consider

• Samples of ammonia and hydrochloric acid are
  placed at either end of a 1 meter tube. A
  reaction to form ammonium chloride solid will
  occur closer to which end of the tube?

Rate of Effusion of NH3
(17.04)-1/2

1.463
Rate of Effusion of HCl
(36.46)-1/2
25
A Problem to Consider

• Samples of ammonia and hydrochloric acid are
  placed at either end of a 1 meter tube. A
  reaction to form ammonium chloride solid will
  occur closer to which end of the tube?

Rate of Effusion of NH3
(17.04)-1/2

1.463
Rate of Effusion of HCl
(36.46)-1/2
NH4Cl will form closer to the HCl since it moves
slower than NH3
26
Stoichiometry with Gas Volumes

• Lithium hydroxide, LiOH, is used in spacecraft to
  recondition the air by absorbing the carbon
  dioxide exhaled by astronauts. The reaction
  is What volume of carbon dioxide
  gas at 21oC and 781 mmHg could be absorbed by 348
  g of lithium hydroxide?

2LiOH(s) CO2(g) Li2CO3(s) H2O(l)
27

• Use the equation to obtain the moles of CO2

2LiOH CO2 LI2CO3 H2O
1 mol LiOH
1 mol CO2
348 g LiOH x
x

23.95 g LiOH
2 mol LiOH
7.2651 mol CO2
28

• Use the equation to obtain the moles of CO2 and
  then the ideal gas law to obtain the
  volume.

2LiOH CO2 LI2CO3 H2O
1 mol LiOH
1 mol CO2
x

348 g LiOH x
23.95 g LiOH
2 mol LiOH
7.2651 mol CO2
(7.2651 mol)(0.08206 L.atm/K.mol)(294 K)
V
171 L
781 mm Hg
760mm Hg/atm
29
Real Gases

• Real gases do not follow PVnRT perfectly. The
  van der Waals equation corrects for the non-ideal
  nature of real gases.

(P n2a/V2)
(V - nb) nRT
a corrects for interaction between atoms
b corrects for volume occupied by atoms