Dr. S. M. Condren Chapter 5 The Gaseous State
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Dr. S. M. Condren
Chapter 5
The Gaseous State
Dr. S. M. Condren
Properties of Gases• can be compressed
• exert pressure on whatever surrounds them
• expand into whatever volume is available
• easily diffuse into one another
• can be described in terms of their temperatures and pressure,the volume occupied, and the amount (number of molecules or moles) present
Dr. S. M. Condren
Mercury Barometer
Dr. S. M. Condren
Composition of Air at Sea Level
Dr. S. M. Condren
Important Units of Pressure
Conversion factor to learn
Dr. S. M. Condren
Boyle’s LawAt constant temperature and mass of gas:
V1/P
V = a * 1/P
where a is a proportionality constant
thus
VP = a
V1P1 = a = V2P2
V1P1 = V2P2
Dr. S. M. Condren
Boyle’s Law
Dr. S. M. Condren
Boyle’s Law
Dr. S. M. Condren
Effect of Pressure Differential
Dr. S. M. Condren
Charles’ Law
At constant pressure and mass of gas:
VT
V = b * T
where b is a proportionality constant
V/T = b
V1/T1 = b = V2/T2
V1/T1 = V2/T2
Dr. S. M. Condren
Charles’ Law
Dr. S. M. Condren
Combined Gas LawAt constant mass of gas
VT/P
V = d * (T/P)
where d is a proportionality constant
(VP)/T = d
V1P1 = d = V2P2
T1 T2
V1P1 = V2P2
T1 T2
Dr. S. M. Condren
Avogadro’s LawAt constant pressure and temperature
Vn
V = c * n
where c is a proportionality constant
V/n = c
V1/n1 = c = V2 /n2
V1/n1 = V2 /n2
Dr. S. M. Condren
Ideal Gas LawV(n * T)/P
V = R * (n * T)/P
where R is proportionality constant
P * V = n * R * T
(P*V)/(n*T) =R
Thus,
(P1*V1)/(n1*T1) = (P2*V2)/(n2*T2)
Dr. S. M. Condren
What will be volume of an ideal gas at absolute zero?
- 10 mL/mole
0 mL/mole
10 mL/mole
Dr. S. M. Condren
Ideal Gas Constant
R = 0.08205 L*atm/mol*K
R has other values for other sets of units.
R = 82.05 mL*atm/mol*K
= 8.314 J/mol*K
= 1.987 cal/mol*K
Dr. S. M. Condren
Molar Massfrom Gas Densitygas density = #g/V = d
PV = nRT
where n = #g/MM
PV = (#g/MM)*RT
MM = (#g*R*T)/(P*V)
MM = (#g/V)*((R*T)/P) = (d*R*T)/P
Dr. S. M. Condren
Dalton’s Lawof Partial Pressures
The total pressure of a mixture of gases is equal to the sum of the pressures of the individual gases (partial pressures).
PT = P1 + P2 + P3 + P4 + . . . .
where PT => total pressure
P1 => partial pressure of gas 1
P2 => partial pressure of gas 2
P3 => partial pressure of gas 3
P4 => partial pressure of gas 4
Dr. S. M. Condren
Dalton’s Law of Partial Pressure
Dr. S. M. Condren
Collecting Gases over Water
Dr. S. M. Condren
Example: What volume will 25.0 g O2 occupy at 20oC and a pressure of 0.880 atm?
(25.0 g)(1 mol)n = ---------------------- = 0.781 mol
(32.0 g)V =?; P = 0.880 atm; T = (20 + 273)K = 293KR = 0.08205 L*atm/mol*K
V = nRT/P= (0.781 mol)(0.08205L*atm/mol*K)(293K)
0.880atm = 21.3 L
Dr. S. M. Condren
Example A student generates oxygen gas and collects it over water. If the volume of the gas is 245 mL and the barometric pressure is 758 torr at 25oC, what is the volume of the “dry” oxygen gas at STP?
Pwater = 23.8 torr at 25oC; PO2 = Pbar - Pwater = (758 - 23.8) torr = 734 torr
P1= PO2 = 734 torr; P2= SP = 760. torr
V1= 245mL; T1= 298K; T2= 273K; V2= ?
(V1P1/T1) = (V2P2/T2)
V2= (V1P1T2)/(T1P2)
= (245mL)(734torr)(273K) (298K)(760.torr)
= 217mL
Dr. S. M. Condren
Kinetic Molecular Theory
Matter consists of particles (atoms or molecules) in continuous, random motion.
Dr. S. M. Condren
Kinetic Molecular Theory: Gases
• particles in continuous, random, rapid motion• collisions between particles are elastic• volume occupied by the particles is negligibly
small effect on their behavior• attractive forces between particles have a
negligible effect on their behavior• gases have no fixed volume or shape, take the
volume and shape of the container
Dr. S. M. Condren
Maxwell’s Distribution of Speeds
Dr. S. M. Condren
Real Gases
• have a finite volume at absolute zero
• have attractive forces between gas particles
Dr. S. M. Condren
Van der Waals Equation
(P + a/V2)(V - b) = nRT
where a => attractive forcesb => residual volume
Dr. S. M. Condren
Real versus Ideal Gases
0
0.5
1
1.5
2
2.5
0 100 200 300 400 500 600 700 800 900
Pressure, atm
Vob
s/V
idea
l
ideal
H2
O2
N2
CH4
CO2
SO2
Cl2
H2O
Dr. S. M. Condren
Real versus Ideal Gases
0.9820.9840.9860.9880.990.992
0.9940.9960.998
11.0021.004
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Pressure, atm
Vob
s/V
idea
l
ideal
H2
O2
N2
CH4
CO2
SO2
Cl2
H2O
Dr. S. M. Condren
Carbon Dioxide and Greenhouse Effect
Dr. S. M. Condren
Some Oxides of Nitrogen• N2O
• NO
• NO2
• N2O4
2 NO2 = N2O4
brown colorless
• NOx
Dr. S. M. Condren
Air Pollution in Los Angles
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