Chapter 18Chapter 18

Thermodynamics: Directionality of Chemical Reactions

Ludwig Boltzmann 1844-1906.Famous for his equation statistically defining entropy.

Josian W. Gibbs 1839-1903.Pioneered concepts of chemical thermodynamics and free energy.

So far, we have tried to answer the following questions:(1) What are the energetics (heat) of a reaction? Is it exothermic (H= -) or endothermic (H= +)?

(2) How fast (kinetics) and how (mechanism) does the reaction go?

(3) To what extent does it go? (equilibrium)

(4) Does it go, i.e., is it spontaneous?

This is the subject of this chapter.

And finally now ……..

Spontaneous processes: defined descriptively as a processthat occurs by itself (and the reverse does not occur by itself)

hot cold

The opposite: hot cold is not spontaneous,

but, it is possible (how does a refrigerator work?).

Other spontaneous processes (ask yourself: does reverse ever occur by itself?)

nail rustingeggs breaking (Humpty Dumpty)paper burningwater freezing at -10oCice melting at +10oCgases mix

heat

heat

is spontaneous,

All of these spontaneous processes are also described as:

irreversible

There are reversible processes, but the systems must be at equilibrium. heat + ice → water at +10oC Spontaneous, irreversible

heat + ice ← water at -10oC Spontaneous, irreversible

heat + ice water at 0oC Reversible; equilibrium

Both ice and water coexist at 0oCEither process, → or ← can occur at equilibrium

Irreversibility ═ Spontaneity

What makes a process spontaneous (irreversible)?

Exothermic reactions tend to be spontaneous(exception, dissolving ammonium salts),and increasing entropy (randomness) tends to causeprocesses to be spontaneous; but overallGibbs Free Energy must decrease in orderfor a process to be spontaneous.

AB

G=(-)

G = H - TSFreeenergy Enthalpy Entropy

Expansion of an Ideal GasExpansion of an Ideal Gas FG19_004.JPG

This is a statistical explanation of why increasing entropy is spontaneous.

Consider an initial state: two flasks connected by a closed stopcock. One flask is evacuated and the other contains 1 atm of gas.

The final state: two flasks connected by an open stopcock,and the gas distributes itself equally in both flasks; each flaskNow contains gas at 0.5 atm.

Why does the gas expand?

How many ways? A,B,C,D W=1 way

How many ways? A,B,C D A,B,D C A,C,D B B,C,D A

W=4 ways

(none)

How to distribute 4 particles (A,B,C,D) in two vessels??

Let W = number of waysA configuration is possible

How many ways? A, B C,DA,C B,DA,D B,CB,C A,DB,D A,CC,D A,B

W=6 ways

W=4 ways

W=1 way

Recap:

4 0 1 way3 1 4 ways2 2 6 ways1 3 4 ways0 4 1 way

The point here is that there are more ways to have an even distribution of particles.

With more than 4 particles (say Avogadro’s number), the number of ways have an even distribution is enormous!!

(That’s why air on one side of a room doesn’t suddenly rush into the other side, asphyxiating everyone in the airless side).

for 4 particles

Left Right

An equal distribution (2 and 2) has the greatest number of ways of distributing particles (6 ways).

So, again, why does thegas expand?

Because there are many more ways of having gas molecules evenly divided in number between two chambers than having them all in one chamber.

There is a greater and natural tendency toward randomness and disorder.

Boltzmann: S = k ln W

Other examples:Ice melting – similar to gas expansion – more randomness and disorder, even though process is endothermic

Ink drops in water – ink becomes evenly distributed in water; increase in randomness and disorder.

Decay of biological organisms – increase in randomness and disorder.

Dissolving of salts in water – increase in randomness and disorder

To Summarize: what contributes to spontaneity?

1. Exothermic processes (heat is evolved).

2. Any process which increases randomness and disorder.

The thermodynamic quantity which describes randomness and

disorder is called ENTROPY and denoted as S

The SECOND LAW OF THERMODYNAMICS postulates the existence of entropy; it also states that the entropy of the universe is constantly increasing. It is not a conserved quantity.

1. Gases have more entropy than liquids, which have more entropy than solids.

2. Corollary: Melting, or vaporization, increases entropy.3. Corollary: In a chemical rx., increasing the number of moles

of a gas, increases the entropy (e.g., H2O(g) H2(g) + ½O2(g)).4. Dissolving or mixing increases entropy.5. Corollary: precipitation decreases entropy.6. Increasing the temperature increases entropy.

Thermodynamic CalculationsThermodynamic CalculationsWhat is ΔG for the oxidation of SO2 to SO3 at 25°C? Is the reaction spontaneous? exothermic?

SO2(g) + ½O2(g) SO3(g)ΔHf° -296.8 0 -395.2 ΔH = -98.4 kJΔS° 0.2485 ½(0.205) 0.2562 ΔS = -0.0948 kJ

ΔG = ΔH – TΔS = -98.4 – (298)(-0.0948) = -98.4 + 28.2 = -70.15 kJ The reaction is spontaneous. The reaction is exothermic.

Note: Be sure you convert ΔS values from J to kJ

What is ΔG for the decarboxylation of limestone at 25°C? Is the reaction spontaneous? exothermic?

CaCO3(s) CaO(s) + CO2(g)ΔHf° -1207.1 -635.5 -393.5 ΔH = +178.1 kJΔS° 0.0929 0.0398 0.2136 ΔS = +0.1605 kJ

ΔG = ΔH – TΔS = +178.1 – (298)(+0.1605) = +178.1 – 47.83 = +130.27 The reaction is not spontaneous. The reaction is endothermic.

Note: Be sure you convert ΔS values from J to kJ

How do we make the decarboxylation of limestone spontaneous?

Set ΔG = 0, the the crossing over point where the reaction converts from nonspontaneous to spontaneous.

ΔG = 0 = ΔH – TΔS 0 = +178.1 –T(+0.1605) T = 1109°K = 837°C

When the temperature falls below 837°C, CO2 begins spontaneously to react with CaO to form CaCO3: CaO(s) + CO2(g) CaCO3(s) At room temperature, ΔG = -130.27 kJ

Calculate the boiling point of methanol.

CH3OH(l) CH3OH(g) ΔHf° -238.7 -200.7 ΔH = +38.0 kJ ΔS +0.1268 +0.2398 ΔS = +0.113 kJ

At equilibrium, ΔG is always 0. ΔG = 0 = ΔH – TΔS =+38.0 –T(+0.113) Tb = 336°K = 63.3°C

Note: Be sure you convert ΔS values from J to kJ

→

Additional aspects of Free EnergyAdditional aspects of Free Energy• Even though a reaction has a negative G it may

occur too slowly to be observed (i.e. combustion).• Thermodynamics gives us the direction of a

spontaneous process, it does not give us the rate of the process.

• A nonspontaneous process can be driven if coupled with a spontaneous process – this is very important in life processes (i.e., respiration to form ATP), and can be used in industrial processes, such as smelting.

• To calculate K values, use ΔG° = -RT ln Keq.

This refers to the ΔG difference of the standard states of compounds, before equilibrium is attained.

Calculating KCalculating Keqeq from from ΔG valuesΔG values

R = 8.314 J/mol-K

Let’s calculate Keq from the following reaction, which we previously studied in the Equilibrium chapter:

N2O4(g) 2NO2(g)

ΔGf° 98.3 2(51.8) ΔG = 5.3 kJ

ΔG = -RT ln K

5300 = -8.314(407) ln K

ln K = -1.57 K = 0.208 -- very close to the experimental value

Let’s calculate Ksp of AgCl.

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

ΔG° = -109.70 77.11 -131.2 ΔG = 55.71

ΔG = -RT ln K

55710 = -(8.314)(298) ln K

-22.48 = ln K

Ksp = 1.7 x 10-10 – very close to the experimental value

Let’s take a look at the dissolution of NH4Cl.

NH4Cl(s) NH4+(aq) + Cl-(aq)

ΔHf° -314.4 -132.5 -167.2 ΔH = +14.7

ΔS° 0.0946 0.1135 0.0565 ΔS = +0.0754

ΔG = ΔH – T ΔS = 14.7 – (298)(0.0754)

= 14.7 – 22.47

= -7.77 kJ

The reaction is endothermic, but is spontaneous!

Hence, ammonium chloride is excellent for cold packs.

Laws of ThermodynamicsLaws of Thermodynamics

1st Law. Energy is neither created nor destroyed. In chemistry, chemical energy can be converted into heat and vice versa.2nd Law. Entropy increases spontaneous; i.e., the natural tendency is for randomization.3rd Law. The entropy of a perfect crystal at 0°K is zero (it is impossible to attain 0°K).