entropy and free energy

Entropy and Free Energy

Driving Forces of Reactions• So far we have seen that reactions are

spontaneous if they give off heat – exothermic

• There is a natural tendency in the universe for systems to get to lowest energy state

• Why do endothermic reactions happen?– Demo with barium – Ammonium chloride dissolving in H2O -

endothermic

Natural direction• Scientists notice that there is a natural direction

for processes– Balls roll down hill, not up hill– Ice melts above 0º C, never refreezes above 0 C– A gas fills its container uniformly, never collects in one

area– Heat flows from hot to cold; hotter object doesn’t get

hotter when exposed to a colder object– Wood burns spontaneously, but CO2 and H2O don’t

form wood when heated

What makes these processes irreversible?

• All of the processes have the following in common: – in all cases you have less information about how the

particles are organized than you did before• Analogy: Why don’t we have fire drills during

lunch?– Less “information” about where students are during

lunch compared to when they are in class• Measure of “information” about a system =

ENTROPY

Entropy

• Measure of the amount of randomness or disorder in a system– Symbol: S– Units: J/K

• No matter what the process, entropy (of universe) is always increasing…

Entropy was introduced in 1865 by Rudolf J. E. Clausius, a German physicist. Clausius said he derived the term from the Greek words en trope, which means “in the transformation” He used it to describe the dissipation or apparent loss of energy available to do work as energy is transformed in a system.

Entropy Analogies

• Throw a card into the air – 2 possible positions (up or down)

• Throw a deck of cards into the air – how many possible positions? – One possibility is that they land organized in a

stack. How probable is that? • The more cards = the more entropy• MORE MOLES = MORE ENTROPY

Given the following reaction, how is entropy changing:

N2 (g) + 3 H2(g) 2NH3(g)

0% 0%0%

100%1. Increasing2. Decreasing3. Stays the same4. Need more

information

What causes entropy to increase?• Statistics…• Boltzmann Bucks Demo

– At first everyone has $1, we play rock-paper-scissors for awhile. Some people have more money than others, but • no one has all the money and • Not everyone has exactly $1

– Why not? A. There is only one way for the money to be arranged so that

everyone has $1B. There are only 9 ways for the money to be arranged so that one

person has $9 (assuming class size of 9)C. There are many ways for some people to have no money, some to

have $1 and some to have $2 or $3.D. So there is a higher probability that the $ will be arranged as

described in C• Nature spontaneously proceeds to the state that has the

highest probability of existing.• Highest probability = most disordered

Entropy Changes

• Increase moles• Dissolving and mixing• Increasing temperature• Increase volume• Solid to liquid or liquid to gas (or S to G)• More complicated molecules have higher

S than simpler molecles

Which one of the following does not generally lead to an increase in

entropy of a system?

0%

100%

0%0%

1. Increase in total number of moles or particles

2. Formation of a solution3. Formation of a gas4. Formation of a solid

Given the reaction below, how is entropy changing?

Br2(l) Br2(g)100%

0%0%0%

1. Increasing2. Decreasing3. Stays the same4. Need more info


Ag+1(aq) + Cl-1(aq) AgCl(s)

10%0%0%

90%1. Increasing 2. Decreasing 3. Stays the same4. Need more info

Given the following reaction, how is entropy changing: 2NO2(g) N2O4(g)

10%0%0%



CO(g) + H2O(g) CO2(g) + H2(g)

0% 0%0%



H2(g) + F2(g) 2HF(g)

0% 0%0%0%

1. Increasing 2. Decreasing 3. Stays the same4. Need more info

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

Given the following reaction, what is the sign for ΔS:

NaCl(s) NaCl(aq)

0% 0%0%0%

1. positive 2. negative3. 04. Need more info

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30


2OH-(aq) + CO2(g) H2O(l) + CO32- (aq)

0% 0%0%0%

1. Increasing 2. Decreasing 3. Stays the same4. Need more info

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

Which of the following has the largest increase in entropy?

0% 0%0%0%

1. Pb(NO3)2(s) Pb(NO3)2(aq)2. CaCO3(s) CaO(s) + CO2(g)3. 2NH3 (g) 2H2(g) + N2(g)4. H2(g) + Br2(g) 2HBr(g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

Spontaneity

• Spontaneous change:– Occurs w/o continuous input of energy

• Spontaneous reactions occur when– Reaction is exothermic ( ΔH < 0)– Increase in entropy for the system (ΔS >0)

• But which is more important? ΔH or ΔS ?

Total Entropy• System vs. Surroundings vs. Universe

– Suniverse = Ssystem + Ssurroundings– Suniv is always increasing.

• Two spontaneous processes: – CaCl2(s) Ca2+(aq) + Cl-1(aq) ΔH = -66kJ

• Ssys is increasing• Ssurr is increasing because heat is released to surroundings

– NH4Cl(s) NH4+ + Cl-(aq) ΔH = 15 kJ

• Ssys is increasing• Ssurr is decreasing b/c surroundings are losing heat

• Non-spotaneous– Na(s) Na (l) ΔH =2.59 kJ

• Ssys = increasing• Ssurr = decreasing

A. NH4Cl(s) NH4+ + Cl-(aq) ΔH = 15 kJ

B. Na(s) Na (l) ΔH =2.59 kJC. Na+(g) + Cl-(g) NaCl(s) ΔH = -771 kJ

• Why is A spontaneous, but not B?– Entropy is much greater for A

• Why is C spontaneous?– Enthalpy is large

How do you know if enthalpy or entropy will make the reaction more

spontaneous?

• Remember: Suniverse = Ssystem + Ssurroundings

• Ssurr depends on temperature• The lower the surrounding temperature, the more significant

adding heat is• The higher the surrounding temp, the less significant adding

heat is.– Analogy

• Imagine you give $1 to someone w/ only $10 to their name? • Imagine the effect of giving $1 to a millionaire.• Who is affected more? sys

surr

HS

T

• Exothermic reactions that release heat to the surroundings are a a stronger driver of reactions when the surrounding temperature is low.

• At high temperatures, an exothermic reaction isn’t such a strong driving force, entropy is more important.

Negative sign b/c ΔH defined in terms of system: exothermic reaction from system’s perspective causes increase in entropy of surroundings. • Suniverse = Ssystem + Ssurroundings

Entropy of system

Determined by ΔH of system

syssurr

HS

T

• Suniv = Ssys + Ssurr

• Substitute: - ΔHsys/T for Ssurr

• Multiply by (-T)• Define new quantity

– Free energy: ΔG = -T ΔSuniv– Free energy tells whether a rxn will be spontaneous at

a given temperature.– Measures the maximum energy available to do useful

work– Reactions at equilibrium have ΔG = 0

syssurr

HS

T

-T ΔSuniv = ΔHsys - T ΔSsys

ΔG = ΔHsys - T ΔSsys

Based on the previous slides and derivation of ΔG, rxns will be

spontaneous if ΔG is75%

0%13%13%

1. Less than 02. Greater than 03. Equal to 04. Spontaneity has

nothing to do with ΔG.

Under which conditions will reactions ALWAYS be spontaneous?

0%11%

78%

11%

1. ΔH > 0, ΔS >02. ΔH > 0, ΔS < 03. ΔH < 0, ΔS >04. ΔH < 0, ΔS <0


Under which conditions will reactions NEVER be spontaneous?

0% 0%0%

100%



Under which conditions will reactions be spontaneous at high temps?

(other than when they are always spontaneous)

100%

0%0%0%



ΔH > 0, ΔS >0• A large positive value for the term (TΔS) can

make ΔG negative if it is bigger than ΔH

• Reaction is endothermic so the entropy of surroundings is decreasing. At high temps, this won’t make as big of a difference as it would at lower temps.


syssurr

HS

T

Under which conditions will reactions be spontaneous at low temps?

(other than when they are always spontaneous)

0%

80%

10%10%



ΔH < 0, ΔS < 0• A small negative value for the term (TΔS) can

still make ΔG negative if it is smaller than the absolute value of ΔH

• Reaction is exothermic so the entropy of surroundings is increasing. At low temps, this will make a bigger difference than it would at higher temps.


syssurr

HS

T

Calculating ΔG

• For a reaction at 25 C, ΔH = 100 kJ and ΔS = 80 J/K, determine if the reaction is spontaneous.

• For a reaction with a ΔH = 100 kJ and a ΔS of 80 J/K, at what temperature will the reaction become spontaneous?

Watch your units!! Put temps in Kelvin and make sure you aren’t trying to add Joules to Kilojoules!

• 100 KJ – (298*80/1000) = 76.2 kJ = not spontaneous

• 0 = 100 - (x*80/1000) 100 = x(. 08)• x = 1250 K, reaction becomes

spontaneous at temperatures above 1250 K

Calculations of ΔS°rxn, ΔH°rxn and ΔG°rxn

• Standard Entropy of Formation Tables (ΔS°f )– Σ n(ΔS°f )products - Σ n(ΔS°f )reactants

• Standard Gibbs Free Energy of Formation Tables (ΔG°f )– Σ n(ΔG°f )products - Σ n(ΔG°f )reactants

• Standard Gibbs Free Energy of Formation Tables (ΔG°f )– Σ n(ΔG°f )products - Σ n(ΔG°f )reactants– Only good for standard conditions! – For ΔG at non-standard conditions, use

ΔG = ΔH - TΔS

• Calculate the free-energy change, G°, for the oxidation of ethyl alcohol to acetic acid using standard free energies of formation.

CH3CH2OH(l) + O2(g) CH3COOH(l) + H2O(l)

CH3CH2OH(l) + O2(g) CH3COOH(l) + H2O(l)

Gf°, kJ/mol –174.8 0 –392.5 –237.2 n, mol 1 1 1 1nGf°, kJ –174.8 0 –392.5 –237.2 –174.8 kJ –629.7 kJ

G° = –454.9 kJ

G° = –629.7 – (–174.8)

• Sodium carbonate, Na2CO3, can be prepared by heating sodium hydrogen carbonate, NaHCO3:

2NaHCO3(s) Na2CO3(s) + H2O(g) + CO2(g)

Estimate the temperature at which the reaction proceeds spontaneously at 1 atm.

See Appendix C for data.

2NaHCO3(s) Na2CO3(s) + H2O(g) + CO(g)Hf°, kJ/mol –947.7 –1130.8 –241.8 –393.5n, mol 2 1 1 1nHf°, kJ –1895.4 –1130.8 –241.8 –393.5

–1895.4 kJ –1766.1 kJH° = 129.3 kJ

Sf°, J/mol K 102 139 188.7 213.7n, mol 2 1 1 1nSf°, J/K 204 139 188.7 213.7

204 J/K 541.4 J/KS° = 337.4 J/K

SHT

ΔΔ

KJ 337.4

J 10 129.3 3T

K 383T

C110T

Use ΔG to get K

• Equilibrium position represents the lowest free energy value available to a particular reaction system

ΔG and K• Standard free energy change is related to the

thermodynamic equilibrium constant, K, at equilibrium.– IF a reaction is NOT at equilibrium, it is proceeding in some

direction (forward or reverse) depending on Q, reaction quotient. – That means there exists energy to do work (make reaction

proceed)• ΔG = Δ G° + RT ln Q

• At equilibrium:– Δ G = 0, because there is no ability to do any more useful work – and Q = K

• So we get: – Δ G° = –RT ln K

• Calculate the value of the thermodynamic equilibrium constant at 25°C for the reaction

• N2O4(g) 2NO2(g)• The standard free energy of formation at 25°C is

51.30 kJ/mol for NO2 and 97.82 kJ/mol for N2O4(g).

RTGK

ln

K) (298K mol

J 8.315

)mol

J 10 (4.78 ln

3K

929.1 ln K

0.145K

G° = 2 mol(51.30 kJ/mol) – 1 mol(97.82 kJ/mol)

G° = 102.60 kJ – 97.82 kJ

G° = 4.78 kJ

entropy and free energy

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