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Spontaneity & Equilibrium II

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Transformation under Constant Temperature & Pressure 0:08
    • Transformation under Constant Temperature & Pressure
    • Define: G = U + PV - TS
    • Gibbs Energy
    • What Does This Say?
    • Spontaneous Process & a Decrease in G
    • Computing ∆G
  • Summary of Conditions 21:32
    • Constraint & Condition for Spontaneity
    • Constraint & Condition for Equilibrium
  • A Few Words About the Word Spontaneous 26:24
    • Spontaneous Does Not Mean Fast
    • Putting Hydrogen & Oxygen Together in a Flask
    • Spontaneous Vs. Not Spontaneous
    • Thermodynamically Favorable
    • Example: Making a Process Thermodynamically Favorable
  • Driving Forces for Spontaneity 31:35
    • Equation: ∆G = ∆H - T∆S
    • Always Spontaneous Process
    • Never Spontaneous Process
    • A Process That is Endothermic Can Still be Spontaneous

Transcription: Spontaneity & Equilibrium II

Hello and welcome back to and welcome back to Physical Chemistry.0000

Today, we are going to continue our discussion of spontaneity and equilibrium.0004

Let us go ahead and jump right on in.0008

In the previous lesson we talked about this general condition of spontaneity and we talked about an isolated system, 0010

we talked about a system where the temperature is held constant.0016

We introduced this thing called the Helmholtz energy.0020

Let us talk about conditions under constant temperature and pressure.0023

Transformations under constant temperature and pressure, let us go ahead and write that out.0029

I will go ahead and work in blue.0034

Transformations under constant T and P so conditions of constant temperature and pressure 0042

are going to be the most important conditions because that is usually how most reactions are run.0058

When you are just running a reaction in a room of not covered up in a flask or anything, 0062

its constant temperature for the most part and constant pressure.0068

This is going to be the most applicable situation.0071

We have got P external DV = PDV.0078

When the pressure is constant we have PDV so I can actually write that as D, I can go ahead and put the V together.0092

Again, it is actually if I take some differential change in the pressure × the volume, 0100

I can pull this pressure out because now we are holding the pressure constant.0106

We also have the following, we also had TDS = D of TS.0111

We have seen that before.0117

Let us go ahead and start our derivation.0119

We have - DU our general condition of spontaneity - DW + TDS this could be ≥ 0.0122

We have - DU - PDV - DW other + TDS ≥ 0.0134

I just express the work as pressure, volume, work and any other kind of work.0151

I got -DU - PDV + TDS.0157

I’m going to go ahead and move the work over to the other side, DW other.0167

This is going to be - DU - D of PV + DTS ≥ the DW of other.0173

I'm going to go ahead and factor out the differential operator.0189

It is going to be - D U + PV - TS ≥ W other.0191

This thing right here U + PV - TS it shows up so much, we give it a special name.0204

Define G that gives energy, U + PV – TS.0213

If I take the energy of the system, if I add to what the product of its pressure and volume of the system and 0228

if I subtract from it the product of the temperature and entropy of the system I end up with something called the free energy of the system in that state.0233

Free energy is just another composite function.0242

Enthalpy was H + PV.0245

Helmholtz energy A = U – TS.0247

Let us put those together now.0251

G I have U + PV - TS it is a composite function.0252

U there are different ways of expressing it U + PV - TS that is the definition of the energy.0259

However, you know what U + PV is, U+ PV this part = H.0269

I can write it as H - TS it is also the same thing.0275

Now U - TS = A so I can also write it is A + PV.0279

Each of these three but this is the definition.0291

This is because H = U + PV and this one is because A = U – TS.0297

Like A, G, is called the Gibbs and like A is a state function.0316

It is called the Gibbs energy and is a state function.0324

It does not depend on the path.0338

It is called the Gibbs energy and is a state functions.0342

We have - DU + PV - TS ≥ D the work any other work so - DG ≥ work other.0348

Or if we integrate we end up with - DG ≥ any other work.0373

If I want to express in a different way I can flip the signs and write it this way.0382

What does this say?0390

These are our equations.0392

Spontaneous process, free energy, this is a relationship.0399

What does this say?0404

Here is what it says, I will write this in blue.0406

In given spontaneous process at constant temperature and pressure, the work done above 0421

and beyond pressure, volume, work ≤ the decrease in Gibbs energy.0449

Gibbs energy is referred to as free energy which is also just generally refer to as the free energy.0494

In a given spontaneous process, at constant temperature and pressure the work that is done above and 0508

beyond any pressure volume work that is done is ≤ the decrease in the Gibbs energy for the transformation.0514

The Gibbs energy accounts for any pressure, volume, work, that is done.0528

It takes care of it.0532

The free energy that is available is work, is energy that is available to do any other kind of work if I needed it.0536

That is why we call it free energy.0545

It is energy that I can use to actually do any kind of work that I want.0547

I have to do the work it just means it is there for me to use.0552

The decrease in the Gibbs energy is going to be available for work.0556

Notice that G = U + PV – TS.0570

δ G accounts for any PV work that is done.0580

When I say change δ PV it is also again because the pressure is constant, I can write this as P δ V.0600

This definition of free energy it accounts for any pressure, volume, work that is done.0608

Therefore, the only work left over is other kind of work.0615

Therefore, δ G is the maximum, it is the max amount of work, 0624

I should say the max amount of energy available to do other work that is why we called it free energy.0641

It is why the word free is used.0661

The δ Q of the system, if there is a decrease in the δ G of the system.0665

That δ G already accounts for any pressure, volume, work that is done.0671

I have this certain amount let us say that the δ G is -50 kJ.0677

The 50 kJ is free and available to do other kinds of work if I need it that is why we call it free energy.0683

That is a relationship that exists here.0693

The other work that is done is going to be less than or = the change in free energy, 0697

that is why we call it the maximum amount of work that is available.0705

If I have 50 kJ of free energy available I'm probably only to be able to harness 40 kJ of it, I’m going to lose the rest of it the heat.0708

It is not going to be the ideal condition that is why we call it the maximum amount of energy that is available to do other work.0719

It is the maximal free energy I have under conditions we are not going to be able to achieve that max 0726

but it is available for us if we need it up to that amount.0732

Since we are not concerned with other work, since we are only concerned pressure, volume, work, we said -DG ≥ DW of the other.0741

The DW of the other = 0 so we get -DG ≥ 0 or we get - DG ≥ 0 or the one that you are familiar with 0773

if I multiply both sides by -1 that is the equation we are familiar with.0787

Under conditions of constant temperature and pressure, since the definition of the free energy already accounts for the pressure, volume, work, 0794

and we are not concerned with any other work that is done this is the condition of spontaneity.0803

If I have a process and if I can calculate as δ G is less than 0 that is a spontaneous process, it will happen naturally under the right circumstances.0809

I do not have to help it along, it is spontaneous.0819

If there is a spontaneous process and I know that it is happening without me doing anything, I automatically know that the δ G ≤ 0.0825

If I have a way of actually harnessing the δ G, that energy I can use that maximum amount of energy to do some other kind of work.0839

I’m going to go back to black.0854

Any spontaneous process is accompanied by decrease in G.0861

In other words, the δ G for the process is less than 0.0883

This amount of energy is free and available to be harnessed if I want it to be harnessed for some kind of work if we wanted.0892

You do not have to have it because it is there if we need it.0931

As long as the system is in a state such that G can decrease further, spontaneous change will continue to occur.0939

Spontaneous change can occur in that direction when G reaches the lowest value that can be for the particular process.0976

When G reaches its lowest value DG = 0 the minimum, the maximum, the derivative is 0.1000

You remember this from calculus DG = 0 that means we have reached equilibrium.1019

DG = 0 if δ G = 0 you are at equilibrium.1028

You are not going to move forward or back.1033

Most chemical and phased transformations, not all but most of them take place under conditions of constant temperature and pressure.1044

Therefore, G and δ G are profoundly important for chemistry.1084

If we happen to be doing work where we are holding temperature constant and volume constant, 1104

the G that gives energy we are going to look at the Helmholtz energy.1111

It is just the question of what you are looking at.1116

We are concerned with δ G because it is under conditions of constant temperature and pressure and1118

already accounts for the pressure, volume, work.1123

I want to know what is left over to do real work.1126

If we can compute δ G for a given process here is what we get.1133

If δ G > 0 the process is spontaneous as written.1140

In other words, if I write some reaction from left to right, it will go from left to right.1149

If δ G = 0 it is under equilibrium.1157

It is not going to go anywhere.1159

This is just a review of what you know from General Chemistry.1163

If the δ G is greater than 0 then it is spontaneous from right to left as written spontaneous in the reverse direction of what I want.1165

Not of what I want but what the δ process is spontaneous and reverse.1175

There is nothing strange here.1183

We said G = U + PV - TS that means δ G = δ U + P δ V - T δ S.1185

The pressure is constant and temperature is constants, I can pull them out of this δ PV and δ TS to become P δ V.1203

This is my basic relationship.1215

If I know δ U, P δ V and T and δ S, I can calculate δ G.1221

Since we have this, we also know that H = U + PV, δ H = δ U + P δ V, δ G = δ H - T δ S.1229

This is a very important equation and there are many other ways to derive this equation.1259

This just happens to be one of them.1262

We talk about isolated conditions, we have talked about constant temperature conditions, 1267

we need reference to in the last lesson of this thing constant volume sometimes depends if the pressure, volume, work is 0.1271

In this particular lesson, we talked about the Gibbs energy under conditions of constant temperature and pressure.1279

Let us go ahead and put all this together and see what this looks like.1285

I will go ahead and do this and red here.1294

Here is what we have, our general condition for spontaneity that is right here.1297

This is the general condition for spontaneity.1304

-DU + PDV – TDS – DW other > 0.1308

This is the general condition of spontaneity, there is no constraint.1314

Any spontaneous process has to satisfy this relation.1318

I can distribute the negative sign if I want to, it does not matter how you write this.1325

I just decided to be nice to see to 0 on the side so you can do - DU - PDV + TDS -DW other > 0.1329

Here is what we talked about, we talked about an isolated system.1341

For an isolated system, in all these things go to 0 here is our condition for a differential change.1344

For a finite change, it is that the change in entropy has to be greater than 0.1352

In other words, the entropy have to increase if the system is isolated.1357

If we hold temperature constant for any spontaneous process the DA + DW has to be less than 0.1361

Or the change in Helmholtz energy + the work that is transferred in the process has to be less than 0.1371

If I hold temperature and pressure constant the DG + DW other has to be less than 0.1379

In the δ G + W other has to be less than 0.1389

If I hold temperature and volume constant and I set work other to 0, if the volume is constant the P δ V is 0.1395

W other is 0 that means all this work is 0 and I get just this and this, under conditions of constant temperature and volume 1407

we are not concerned with any other work of the system may or may not do.1419

The Helmholtz energy, the δ A, has to be less than 0 for a spontaneous process.1424

The spontaneous process will have a δ A less than 0.1429

If I calculate δ A is less than 0, I know that the process is spontaneous.1432

It goes both ways.1437

Here is the most important one, under conditions of constant temperature and pressure, 1438

when I'm not concerned with any other type of work that is done the δ G for the process is less than 0.1442

If the δ G for process is calculated and found to be less than 0, that process is spontaneous.1446

We should not investigate the process further to see if we can harness that energy.1455

This is what is important, this last line, this is the one that is important.1462

For our purposes this is a summary and here is the general state of equilibrium, no constraints.1467

These are the constraints, if I hold T constant and P constant then I do TV constant with W other = 0 1476

and I do TP constant with W other = 0.1481

These are conditions for spontaneity greater than 0, less than 0.1486

For conditions of equilibrium, under conditions of equilibrium this becomes an equal sign =, everything stays the same except now we have = 0.1496

Under conditions of constant temperature and pressure, when I'm not concerned with any other work of the system is doing, if the system, 1507

if the change in free energy of the system is calculated = 0 my system is already in equilibrium.1516

There is not much I can do.1522

If the system is at equilibrium, I can say unequivocally the δ G = 0 and these are the other situations.1524

This is the summary of the conditions.1534

As we said earlier, we are not going to be concerned with work other.1541

We are going to be concerned only with pressure, volume, and work.1544

For the chemist, laboratory conditions are mostly constant temperature and pressure so last line of the table is what concerns us most.1548

It is the last line we are concerned with most.1554

However, that table covers everything, that is the general condition.1557

When we teach thermodynamics in general chemistry, we talk about things generally 1561

but we are concern ourselves with free energy, the Gibbs free energy.1566

It is important to be able to see that there is a general condition for equilibrium that has no constraint.1571

When we apply the constraints that is when the different relations fallout.1578

Let us say a few words about the word spontaneous.1586

Spontaneous does not mean fast.1590

Spontaneous just means that once a reaction is set in motion, it will move forward on its own without external help.1592

Sometimes we do not have to set in motion.1601

Sometimes it set itself in motion.1603

In other words, it refers to the extent that a reaction or process wants to happen naturally.1606

Spontaneous, natural, real, irreversible, all of these words are going to be used.1612

If I put some hydrogen and oxygen together in flask, thermodynamics tells me that the reaction is highly spontaneous, it wants to move forward.1620

In other words, if I calculate the δ G of this from a table of thermodynamic data, the δ G is going to be hugely negative.1628

However, unless I somehow set the reaction in motion, I will give it a spark, the gases are just going to sit there for millions of years and never react.1635

It will never move forward.1642

Thermodynamics tells me whether reaction can move forward.1644

It says nothing about whether it will or how fast it will.1648

The latter question falls in the jurisdiction of kinetics.1653

Thermodynamics tells me what is possible not what is going to happen.1657

It just tells me that under the right conditions, if I get this reaction going it will happen and I do not have to do anything else.1661

It will go on its own.1667

It is like pushing the ball down a cliff.1668

A ball can sit on top of the thing and sit there, it wants to go down but every once in awhile, 1670

for certain reactions somebody have to push the ball over so it can start the downhill roll.1677

Other times, it will just go downhill.1683

But sometimes we need to get it started.1685

thermodynamics tells us what can happen.1687

It does not tell us how fast or the whether it will happen.1689

Thermodynamics tells me that a particular process is spontaneous, 1696

it may be worth our time to investigate how we can get going or speed it up or whatever else we might want to do.1700

Once I know a process is spontaneous which we investigated further, we should harness that, we should exploit it.1708

If thermo tells me that a particular process is not spontaneous then nothing we do will make it so.1715

Thermo tells us what is possible and what is impossible are not probable, that takes us to the next paragraph.1720

As a human race we do not like hearing the word no.1733

We do not like hearing the word impossible.1735

We have to find a way to make something happen even if we know they cannot happen.1739

What if we find a really great process that we absolutely have to have but it is thermodynamic unfavorable, it is not spontaneous.1742

We really like this process and we want it to happen, here is what we can do, the answer is very simple.1752

You have to find another process that is thermodynamically favorable, that is spontaneous by a greater amount in the process we want is unfavorable 1757

and you have to find a way to put the two processes together.1768

Let us look at an example, the reaction glucose + inorganic phosphate goes to glucose 6 phosphate + H2O.1773

This is the first step of glycolysis, the breakdown of sugar that you ingest in order to produce energy.1784

We want this reaction to happen, it is very important for it to happen otherwise we would not be alive.1793

This is really we want to happen and we want it to happen efficiently.1798

The problem is the δ G for this is positive, 13.8 kJ/ mol this is not a spontaneous reaction.1803

This is not going to happen no matter what we do.1809

However, there is another reaction, the breakdown of ATP the hydrolysis.1811

ATP + H2O goes to ADP + π.1817

Adenosine triphosphate + water + adenosine triphosphate + inorganic phosphate.1821

The δ G for this reaction is -30.5 kJ/ mol that is very spontaneous.1825

In fact it is more spontaneous than this is not spontaneous.1833

If I can find a way to put these two together, I’m not worried about how.1837

If I could add them I get this.1842

I end up getting what I want.1846

I end up getting glucose going to glucose 6 phosphate, that was my task but I did not do it this way.1847

I found another path.1853

I was able to cobble these because they share reactants and products in common.1855

The coupling process takes place because they actually share reactants and products.1861

I can couple these two together.1865

I can use the fact that this is highly ex organic.1867

It is highly spontaneous by more than this is non spontaneous to create a reaction that does move forward.1870

I have been able to convert this to this.1878

The coupling of these two reactions happens because they have reactants and products in common.1880

Just because a reaction is not spontaneous it does not mean that we cannot do anything with it.1884

We just have to find another path.1889

I’m going to finish up this lesson by talking about the dragging forces for spontaneity.1896

At constant temperature and pressure spontaneous process requires the δ G is less than 0.1902

G = H – TS, DG = δ H –δ H.1907

This is a profoundly important equation.1913

If you have to walk away with one equation to always carry around in your pocket as a scientist this is the equation you want to carry with you.1916

We will see this equation again because it tells a lot.1923

It says that there are three forces that contribute to making the process spontaneous, the change in enthalpy, 1928

the change in entropy and the temperature.1934

There are three things not just the H and the DS.1937

We often think about just the δ H and the δ S because we are holding the temperature constant we often think about temperature 1939

but the temperature is also important because we do not necessarily have to hold it constant.1949

We can change the temperature too.1953

The enthalpy change, the entropy change, and the temperature will always spontaneous process 1956

is one where the δ H negative and the δ S is positive.1962

If the enthalpy is negative, if we have an exothermic reaction.1967

If the δ S is positive, in other words the entropy actually rises and going from reactive products 1972

then both terms on the right are negative so δ G is always negative.1978

This is always spontaneous.1983

Never spontaneous process is when δ H is positive and δ S is negative.1988

In this case both of the terms are positive on the right, the δ G is always positive that reaction never spontaneous no matter what you do.1993

It is clear from the equation above, let me go ahead and write here.2002

δ Chi = δ H - T δ S just look at the equation.2005

A decrease in the entropy of the system even if I end up getting a negative entropy, δ S is negative the S – T, 2019

δ S ends up being a positive term it can still lead to a spontaneous process 2024

if the δ H is sufficiently negative to offset the positive quantity T δ that arises from the negative entropy change.2032

Likewise, a process that is endothermic.2041

In other words, if this is positive they can still become spontaneous if the δ S is sufficiently positive.2044

If the increase in entropy is so huge that actually allow the term that negative T δ S term to dominate the mathematics and to pull the right side below 0.2052

It is all about this equation right here, this is the most important equation for chemist as far as thermodynamics is concerned.2064

Thank you so much for joining us here at

We will see you next time.2078