Previously in Chem104: What determines reaction spontaneity? Entropy

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Previously in Chem104: What determines reaction spontaneity? Entropy

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Previously in Chem104: What determines reaction spontaneity? Entropy

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- 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 DHrxn <0 YES!!!

Ba(OH)2.8H2O + 2NH4NO3

Ba(NO3)2 + 2NH3+ 10H2O

got COLD so DHrxn> 0 NO!!!

Conclusion 1: Spontaneous reactions can be

exothermic or endothemic

Next, we encountered ENTROPY

ENTROPY:

the concept

An increase in disorder

An increase in energy dispersal

symbol S

calculated like enthalpy: DSrxn = DSprdt - DSrgt

ENTROPY:

its magnitude

Depends on state of matter, solid< liquid<gas

Depends on temperature

Depends on complexity of molecule/matter

Hypothesis 2: Spontaneous reactions have

increased entropy

HCl (g) + NH3 (g)

NH4Cl(s)

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

DSrxn = DSprdt - DSrgt

Ba(OH)2.8H2O + 2NH4NO3

Ba(NO3)2 + 2NH3+ 10H2O

DSrxn = [150 + 2(70) + 10(192)] - [500 + 2(151)]

DSrxn = +432 J/K mol

DSrxn> 0 YES!!!

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

Conclusion 2: Spontaneous reactions can have

a decrease in entropy!

Hypothesis 3: Reaction Spontaneity depends on

entropy AND enthalpy

HCl (g) + NH3 (g)

NH4Cl(s)

So,J/K mol = 187 193 94.6

DSrxn = DSprdt - DSrgt

DSrxn = [94.6] - [187 + 193]

DSrxn = - 285 J/K mol

ENTROPY DECREASED

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

DHrxn = DHprdt - DHrgt

DHrxn = [-315] - [-92.3 + -46.3]

DHrxn = - 176 kJ/mol

ENTHALPY DECREASED

Heat released goes to surroundings?!!

Heat released to surroundings should increase DSSURR

How much?

Use this relationship of enthalpy and entropy:

DSSURR = -DHsys / T

So the addition of 176 kJ/mol heat to surroundings corresponds to:

DSSURR = - (-176 kJ/mol)/ 289 = 0.591 kJ/K mol

DSSURR = 591 J/K mol

HCl (g) + NH3 (g)

NH4Cl(s)

And the net entropy change is:

DSnet = DSSURR + DSSYS = DSUNIVERSE

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

THE ENTROPY of UNIVERSE INCREASED

This is the fundamental requirement

THE ENTROPY of UNIVERSE INCREASED

This is the 2nd Law of Thermodynamics

long version: a spontaneous change is accompanied by an increase in the total entropy of the system and the surroundings DSTOTAL = DSSURR + DSSYS

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

THE ENTROPY of UNIVERSE INCREASED

This is the 2nd Law of Thermodynamics

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

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:

THE ENTROPY of UNIVERSE MUST INCREASE

to predict what will happen

Why?Using this fundamental relationship:

DSTOTAL = DSSURR + DSSYS

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

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.

Josiah

Willard

Gibbs

1839-1903

This is how he figured it:

“If the universe obeys:”

DSUNIVERSE = DSTOTAL = DSSURR + DSSYS

“And we can replace DSSURR :”

DSTOTAL = -DHSYS / T + DSSYS

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

Blame it all on Josiah Gibbs:

“It’s all in terms of the system. Yeah!!”

DSTOTAL = -DHSYS / T + DSSYS

“Now if we do some algebra:”

T xDSTOTAL = -DHSYS + T DSSYS

“And change the signs:”

- T xDSTOTAL = DHSYS - T DSSYS

“We can name the result after me!”

-T xDSTOTAL = DGSYS = DHSYS - T DSSYS

Gibbs Free Energy, DGSYS

“Is this supposed to be an improvement?”

Gibbs Free Energy, DGSYSDGSYS = DHSYS - T DSSYS

How do I tell when a spontaneous event occurs?

DSTOTAL > 0 is still the Law

Since -T xDSTOTAL = DGSYS

when DSTOTAL >0, DGSYS < 0

Spontaneous reactions & processes occur when

Gibbs Free Energy is negative, DGSYS < 0

“Interpretation, please!”

DSTOTAL > 0 is still the Law

if-T xDSTOTAL = DGSYS

it means: the disorder

in the universe

came from

the system

Spontaneous reactions & processes occur when

Gibbs Free Energy is negative, DGSYS < 0

The best part?

DGrxn is calculated exactly like DHrxn and DSrxn

DGrxn = DGprdt - DGrgt

Let’s do it!