Entropy = S

Entropy is disorderor randomness

2nd Law of Thermodynamics

Suniverse

spontaneous = no external intervention

positional disorder energetic disorder

for spontaneous processes

Ssystem Ssurroundings

> 0

Energetic DisorderP.E. K.E.

ordered random

reactants

products

P.E.

a) endothermic reactionb) exothermic reaction

Hsystem 0Hsurroundings 0Ssurroundings > 0

a) b)

<>

Ssurr =

Ssurr

high T small effect

heat surroundings

low T relatively larger effect

- Hsystem

T

depends on T

(J/K)

Positional Disorder

(1/2)(1/2)(1/2)(1/2)(1/2)(1/2) = 1/64

With 1 mole of gas,

Not probable

Positional Disorder

ordered states low probabilitydisordered states high probability

low Shigh S

Ssystem Positional disorder

Increases with number of possible positions

Ssolids < Sliquids << Sgases

(energy states)

BoltzmanW = degrees of freedomS = k ln W

Entropy

System 1

System 2

w = -182 J

w = 0

E = 0

E = 0

q = +182 J

q = 0

(J/K)[heat entering system at given T]

T = 298 K

Pext = 1.5 atm

Pext = 0 atm

convert q to S

System 3

P1 = 6.0 atm P2 = 1.5 atmV1 = 0.4 L V2 = 1.6 L T1 = 298 K = T2

Pext =

reversible process - infinitely slow

wr=

Pint + dP

- Pext = dV =- nRT dV V - nRT ln (V2/V1)

V2

V1

Ssystem

System 1Pext = 1.5 atmw = -182 Jq = +182 JS =

System 2Pext = 0 atmw = 0q = 0S =

System 3Pext = Pint + dPwr =qr =S =

= - 1120 J+ 1120 J

Ssurr = - Hsystem

T= 1120 J 298 K

3.77 J/K 3.77 J/K3.77 J/K

Ssystem = qr

T

-nRT ln (V2/V1)

3rd Law of Thermodynamics

Entropyof a perfect crystallinesubstance

at 0 K= 0

Entropy curve

S

qr

T

Temperature (K)

solid liquid gas

00

fusion

vaporization

EntropyAt 0K, S = 0 Entropy is absolute

S 0 for elements in standard states

S is a State Function

Sorxn = nSo

products - nSoreactants

S is extensive

Increases in Entropy1. Melting (fusion) Sliquid > Ssolid

2. Vaporization Sgas >> Sliquid

3. Increasing ngas in a reaction

4. Heating ST2 > ST1 if T2 > T1.

5. Dissolution Ssolution > (Ssolvent + Ssolute)?

6. Molecular complexity number of bonds

7. Atomic complexity e-, protons and neutrons