Previously in Chem104:

•What determines reaction spontaneity?

•Entropy

Today in Chem104:

• A recap

• The 2nd Law & No Free Lunch

• What chemists really use- free energy

• Worksheet: “What’s keeping you alive?”

Hypothesis 1: Spontaneous reactions are exothermic

HCl + NaOH Na+ + Cl- + H2O

got warm so Hrxn <0 YES!!!

Ba(OH)2.8H2O + 2NH4NO3 Ba(NO3)2 + 2NH3+

10H2Ogot COLD so Hrxn> 0 NO!!!

Conclusion 1: Spontaneous reactions can beexothermic or endothemic

Next, we encountered ENTROPY

ENTROPY:the concept An increase in disorder

An increase in energy dispersal

symbol S

ENTROPY:its magnitude

Depends on state of matter, solid< liquid<gas

Depends on temperature

Depends on complexity of molecule/matter

calculated like enthalpy: Srxn = Sprdt - Srgt

Hypothesis 2: Spontaneous reactions have increased entropy

HCl (g) + NH3 (g) NH4Cl(s)

Entropy reagent gases >> Entropy solid prdt, Srxn< 0 NO!!!

Ba(OH)2.8H2O + 2NH4NO3 Ba(NO3)2 + 2NH3+

10H2O

Srxn> 0 YES!!!

Conclusion 2: Spontaneous reactions can havea decrease in entropy!

Srxn = Sprdt - Srgt

Srxn = [150 + 2(70) + 10(192)] - [500 + 2(151)]Srxn = +432 J/K mol

So,J/K mol = 500 2(151) 150 2(70) 10(192)

Hypothesis 3: Reaction Spontaneity depends on entropy AND enthalpy

HCl (g) + NH3 (g) NH4Cl(s)

Heat released goes to surroundings?!!

Srxn = Sprdt - Srgt

Srxn = [94.6] - [187 + 193]Srxn = - 285 J/K mol

So,J/K mol = 187 193 94.6

Hrxn = Hprdt - Hrgt

Hrxn = [-315] - [-92.3 + -46.3]Hrxn = - 176 kJ/mol

Hof,kJ/mol = -92.3 -46.3 -315

ENTROPY DECREASED

ENTHALPY DECREASED

HCl (g) + NH3 (g) NH4Cl(s)

Heat released to surroundings should increase SSURR

And the net entropy change is:Snet = SSURR + SSYS = SUNIVERSE

SUNIVERSE = 591 - 285 J/K mol = 206 J/K mol

THE ENTROPY of UNIVERSE INCREASED

How much? Use this relationship of enthalpy and entropy:SSURR = -Hsys / T

So the addition of 176 kJ/mol heat to surroundings corresponds to:SSURR = - (-176 kJ/mol) / 289 = 0.591 kJ/K molSSURR = 591 J/K mol

This is the fundamental requirement

long version: a spontaneous change is accompanied by an increase in the total entropy of the system and the surroundings STOTAL = SSURR + SSYS

THE ENTROPY of UNIVERSE INCREASED

This is the 2nd Law of Thermodynamics

shorter version: total entropy change must be positive for a spontaneous reactions

shortest version: the entropy of the universe is constantly increasing

This is the fundamental requirement

Paul’s version: No Free Lunch

This means, a spontaneous exothermic reaction is not just creating heat ( or energy). The price is Entropy—more disorder in the Universe .… or a greater distribution of energy

THE ENTROPY of UNIVERSE INCREASED

This is the 2nd Law of Thermodynamics

Paul Grobstein’s version: The 1st Law: You can’t win.The 2nd Law: You can’t break even.The 3rd Law: You can’t leave the game.

Chemists rarely use this:

Why? Using this fundamental relationship:STOTAL = SSURR + SSYS

it’s too hard—impossible, really—to calculate SSURR

THE ENTROPY of UNIVERSE MUST INCREASE

to predict what will happen

So how do they predict what will happen? A new thermodynamic quantity was derived:

Free Energy“wait a minute - how can you have free energy when you can’t have a free lunch?”

Blame it all on Josiah Gibbs.

This is how he figured it: “If the universe obeys:”

SUNIVERSE = STOTAL = SSURR + SSYS

“And we can replace SSURR :” STOTAL = -HSYS / T + SSYS

“It’s all in terms of the system and we can measure it. Yeah!!”

JosiahWillardGibbs

1839-1903

Blame it all on Josiah Gibbs:

“It’s all in terms of the system. Yeah!!” STOTAL = -HSYS / T + SSYS

“Now if we do some algebra:”T x STOTAL = -HSYS + T SSYS

“And change the signs:”- T x STOTAL = HSYS - T SSYS

“We can name the result after me!” -T x STOTAL = GSYS = HSYS - T SSYS

Gibbs Free Energy, GSYS

“Is this supposed to be an improvement?”

Gibbs Free Energy, GSYS GSYS = HSYS - T SSYS

How do I tell when a spontaneous event occurs?

STOTAL > 0 is still the Law

Since -T x STOTAL = GSYS

when STOTAL >0, GSYS < 0Spontaneous reactions & processes occur whenGibbs Free Energy is negative, GSYS < 0

“Interpretation, please!”

STOTAL > 0 is still the Law

if -T x STOTAL = GSYS

Spontaneous reactions & processes occur whenGibbs Free Energy is negative, GSYS < 0

it means: the disorder in the universe

came from the system

The best part?

Grxn is calculated exactly like Hrxn and Srxn

Grxn = Gprdt - Grgt

Let’s do it!