Chapter 17 - Gibbs Free Energy and Thermodynamics

Second Law

For any spontaneous process, the entropy of the universe increases

Second Law equation

Δ𝑆𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒 = Δ𝑆𝑠𝑦𝑠𝑡𝑒𝑚 + Δ𝑆𝑠𝑢𝑟𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑠 > 0

spontaneous

A reaction/process that occurs by itself under a given set of

conditions is said to be spontaneous

does spontaneous mean instantaneouss

no

nonspontaneous process

requires some external action to be

continuously applied in order for it to occur.

What Makes a Process Spontaneous?

Spreading out of energy drives spontaneous

processes.

Entropy (S)

a thermodynamic property describing the distribution

of a system’s energy over the available energy levels

state function

greater the number of configurations among the energy levels =

the greater the entropy of the system

Entropy formula

𝑆 = 𝑘𝐵 ln 𝑊

w = # of Microstates

kb = Boltzmann constant 1.38 x 10-23 J/(K•mol)

Microstate

The particular way in which the energy of a state is

distributed within the system at a given point in time

more microstates in a state =

greater entropy

more probable

what increases Entropy

in general more microstates = more entrophy

more specifically

a) Melting

b) Evaporation

c) Temperature increase

d) Reactions in which the number of moles of gas increases

e) Dissolution (usually)

Provided:

Ssoln > (Ssolute + Ssolvent)

Third Law:

The entropy of a perfect crystal at absolute zero (0 K) is zero

zero-point energy

not same as zero energy

w =1, There is only one way to distribute this zero-point energy

Standard Molar Entropy (S ̊)

absolute entropy of 1 mole of a pure

substance in its standard state at 25 ̊C and at 1 atm.

Standard Entropy Change (∆𝑺𝒐)

the change in entropy for a

reaction/process in which all reactants and products are in their

standard states.

∆𝑆𝑜= 𝑆𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠𝑜 − 𝑆𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠𝑜

ΔS° = [npS°(products) - nrS°(reactants)]

Gibbs (Free) Energy

is the maximum amount of energy available to

do useful work in processes happening at constant pressure and

temperature.

Gibbs Free Energy formula

ΔGsys = ΔHsys – TΔSsys

criteria for spontaneous Change in accordance to ∆𝑮

∆𝑮 < 𝟎, reaction is spontaneous

∆𝑮 > 𝟎, reaction is non-spontaneous

∆𝑮 = 𝟎, reaction has reached equilibrium

what happens to spontanity when

ΔH = -

Δs = +

spontaneous for all temp

what happens to spontanity when

ΔH = +

Δs = -

non spontaneous for all temp

what happens to spontanity when

ΔH = -

Δs = -

spontaneuous at low temp

nonspontaneous at high temp

what happens to spontanity when

ΔH = +

Δs = +

nonspontaneuous at low temp

spontaneous at high temp

ΔSsys can be calculated from

standard entropy (S°)

ΔSsurr can be calculated from

∆Ssurr = –∆Hsys/T

Standard change in free energy of a reaction (ΔG°rnx)

change in free energy for a reaction in which the reactants and products are present in their standard states at 25 °C and 1 atm

Three ways to calculate: ΔG°rnx

a) From enthalpy and entropy data

b) From tabulated ΔGf° data

c) From tabulated ΔG°rxn data

ΔG°rnx From enthalpy and entropy data

ΔG°rxn = ΔH°rxn – TΔS°rxn

Method is only valid for reactions at 25 °C; however, ΔH and

ΔS are not greatly influenced by changes in T.

ΔG°rnx From tabulated ΔGf° data

hesses law

product - reactant

ΔG°rnx From tabulated ΔG°rxn data

hess law

suming

The Gibbs energy change of a reaction under NON standard

conditions (∆𝐺)

ΔG = ΔG° + RT ln Q

standard conditions ∆G =

∆Go

Under equilibrium conditions ∆G =

0

IF 𝐾 < 1 what does it mean for ∆𝐺𝑜 and spontatnity

∆𝐺𝑜 is positive

(reaction is spontaneous in the reverse direction)

IF 𝐾 > 1 what does it mean for ∆𝐺𝑜 and spontatnity

∆𝐺𝑜 is negative

(reaction is spontaneous in the forward direction)

IF 𝐾 = 1 what does it mean for ∆𝐺𝑜 and spontatnity

∆𝐺𝑜 is zero

(reaction is at equilibrium with equivalent amounts of

products and reactants)

Difference Between ΔG° and ΔG

ΔG° is a constant

Tells us whether that “standard” process would be spontaneous

in the forward or the reverse direction.

Allows K to be calculated for virtually any reaction!

ΔG represents the “distance” from the equilibrium state of a given reaction.

Magnitude of ΔG decreases over the course of the reaction to

approach ΔG = 0 at equilibrium.

Temperature Dependence of K formula

To drive a non-spontaneous reaction, there are several options

 Change the conditions (i.e. temperature)

 Electrolysis (next chapter!)

 Couple a non-spontaneous reaction with a spontaneous one

Coupled Reactions

Second reaction “drives” the first reaction