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

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Air Pollution in Los Angles