Thermodynamics

Spontaneity• What does it mean when we say a process

is spontaneous?• A spontaneous process is one which

occurs naturally with no external influence.

• The reverse process will not occur naturally under the same conditions!

Spontaneity, Cont.

• Spontaneous processes may occur slowly or quickly, spontaneous does not mean that it is an instantaneous process.

• What are some examples of spontaneous processes?

Spontaneity, Cont.

• So, how can you tell whether a chemical rxn or physical process will occur spontaneously (naturally with no external influence)?

• Also, why is a rxn spontaneous and under what conditions (temperature, etc.)?

Spontaneity, Cont.

• To answer this, we need to talk about the two factors of spontaneity: – enthalpy (a measure of the heat energy

change in a system) and – entropy (a measure of the randomness or

disorder of a system)

Entropy

• Entropy, S, is a measure of the molecular disorder or randomness.

• Like enthalpy, entropy is a state function, so it is independent of path.

• ΔS is the change in entropy of a system, ΔS = Sf – Si, and this value is also independent of path.

Entropy

• You can see from the above equation, that if the entropy of a system increases, then ΔS is positive, while it will be negative if the entropy decreases.

• It is true that chemical systems tend to move spontaneously in the direction which will increase the randomness or entropy of the system.

Entropy• So one indicator of spontaneity is the

entropy change of a system: it is likely to be spontaneous if ΔS is +.

• How can you predict whether ΔS is increasing or decreasing?

• Well first of all, use your common sense and knowledge: which state is the most disordered: solid, liquid, or gas?

Entropy• So you can eyeball many processes or

rxns and see whether more or less gas molecules are being formed: the side with the most disorder is favored.

• Also, mixing processes tend to increase the disorder of a system (although these are 2 or more steps, and not all of the steps have favorable entropy changes).

Entropy• Changing the temperature increases

molecular motion and velocity, which increases entropy.

• This is because of the Third Law of Thermodynamics which states that the entropy of a perfectly ordered crystal is 0 at 0K.

Entropy• Changing the volume of a gas (at

constant T) changes the entropy: increasing the volume gives the gas more space in which to move, so entropy increases.

Entropy• Likewise, changing the pressure of a gas

(at constant T) changes the entropy: here increasing the pressure, by decreasing the volume, forces the molecules closer together into a more ordered state.

Entropy• Problem: Predict the sign of ΔS for the

following processes. • Which are likely to be spontaneous?

Entropy• In reality, entropy is really a function of

statistics and probability: the most likely, most statistically probable state is a disordered state!

Entropy• Mathematically, there is an equation:

S = k lnW or S = k lnΩ, where k is Boltzmann’s constant and W or Ω is the number of ways the system can be arranged.

• So the more ways a system can be arranged, the higher the entropy.

Entropy• This also means that the more molecules

or particles in the system, the more ways a system can be arranged. So the more particles in the system, the higher the entropy.

Entropy and the Second Law of Thermodynamics• The Second Law of Thermodynamics

states that for any process to be spontaneous, the overall entropy of the Universe MUST increase.

• Now we have to think beyond the entropy of the system itself to the entropy of the surroundings and the overall entropy of the universe.

Entropy and the Second Law• What this means is this:

ΔSuniverse = ΔSsys + ΔSsurr

• For a process to be spontaneous, ΔSuniverse must be +.

• How do we find ΔSuniverse?

Entropy and the Second Law

• Finding ΔSsys is easy:ΔSsys = ΔSrxn = Sproducts – Sreactants

• As standard molar entropies, S°, at 25°C are easy to find in Tables, we calculate ΔS°rxn

Entropy and the Second Law

• Ex: Find ΔSsys for the following rxn at 25°C:

Entropy and the Second Law

• OK, it’s easy to find ΔSsys, but how do you find ΔSsurr?

Back to Enthalpy!

• Enthalpy Change, ΔH, measures whether heat is absorbed or released by a process.

• Just like ΔSsys , we find ΔHrxn :

Back to Enthalpy!

• If ΔH is -, then heat energy is released by the system to the surroundings

• If ΔH is +, then heat energy is absorbed from the surroundings by the system

• Which is likely to be spontaneous, a – or + ΔH?

Back to Enthalpy!• Think about what happens to the entropy

of the surroundings when the temperature changes!

• Mathematically, ΔHrxn affects the entropy of the surroundings:

Back to Enthalpy!• If ΔHrxn is -, an exothermic rxn, then ΔSsurr is +, which indicates that the rxn (or process) is likely to be spontaneous

• So there is a balance between the two factors ΔH and ΔS to determine whether a rxn is spontaneous.

Back to Enthalpy!• Also, spontaneity depends on

temperature as shown in the following:

Gibbs Free Energy

• Chemists have named a thermodynamic function of energy, Gibbs Free Energy, G or ΔG, which predicts spontaneity.

• Gibbs Free Energy is a measure of the energy which is available in a system; it is also the maximum work which a system can perform.

Free Energy

• It is defined as:

Free Energy

• If ΔG is -, it IS spontaneous in that direction;

• If ΔG is +, it is spontaneous in the REVERSE direction;

• If ΔG = 0, then the system is at equilibrium.

Free Energy

• Here is a table which shows the balance and importance of T in determining ΔG and spontaneity:

Free Energy

• Let’s look at a cold pack.• This is a dissolving process and a

hydration process!• Will this rxn be spontaneous at room

temperature and why?

Free Energy

• Now anyone who’s used a cold pack knows that it is spontaneous, but the question is why and for what temperatures?

Free Energy

• So at temperatures higher/lower (circle the correct one) than ________, this will not be a spontaneous process, instead the reverse process is!

• So the rxn is spontaneous for temperatures higher/lower (circle the correct one) than ________.

Review:

• You learned how to calculate ΔG from the enthalpy and the entropy

• You learned how to predict the spontaneity of a process from ΔG

• You learned the temperature dependence of S and ΔG

Free Energy

• Take-Home Problem: For what temperatures will the following rxn be spontaneous (greater than, lower than what)?

Calculating ΔG°

• You can calculate ΔG° from the equation: ΔG° = ΔH° - TΔS°

• But you can also calculate it from table values of ΔG°f just as you do for ΔH.

ΔG° and Rxn Composition

• ΔG° tells you which direction the given rxn is spontaneous at standard state conditions.

• But how often are you at standard state conditions?

• How do you calculate just plain ΔG at non-standard state conditions?

ΔG° and Rxn Composition

• There is a mathematical relationship between ΔG and ΔG° based on the reaction quotient, Q

• Note we adjust G° to the temperature we are actually at.

ΔG° and Rxn Composition

• What is true if we are at standard state?

The Meaning of ΔG and ΔG°

• What else does ΔG° tell us?• All rxns come to “equilibrium”, or an

end point.• So ΔG° also tells us which direction a rxn

must shift from standard state conditions in order to reach the end or “equilibrium”.

The Meaning of ΔG and ΔG°

• The magnitude of ΔG° tells us how far away it is from “equilibrium”.– If it is very positive, then the rxn must shift

far to the left.– If it is very negative, then it must shift far to

the right.

The Meaning of ΔG and ΔG°

• Lastly, ΔG° tells us what is favored at equilibrium, reactants or products.– At standard state, Q = 1.– So if ΔG° is negative, then the rxn proceeds

to the right making products, so Q is now > 1.

– So if ΔG° is positive, then the rxn proceeds to the left making reactants, so Q is now < 1.

The Meaning of ΔG and ΔG°

• ΔG tells us what direction the rxn is proceeding right now, under the current conditions!

• Unlike ΔG°, which is fixed for a given temperature, ΔG changes as the rxn progresses toward equilibrium or completion.

The Meaning of ΔG and ΔG°

• How does ΔG change as the rxn progresses and what is the value of ΔG at equilibrium?

• What is the value of Q at equilibrium?

The Meaning of ΔG and ΔG°

• This gives us a relationship between ΔG° and K: