For more information, please see full course syllabus of Physical Chemistry

For more information, please see full course syllabus of Physical Chemistry

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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
- Transformation under Constant Temperature & Pressure
- 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
- A Few Words About the Word Spontaneous
- 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

- 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

### Physical Chemistry Online Course

### Transcription: Spontaneity & Equilibrium II

*Hello and welcome back to www.educator.com 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 and*1118

*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 www.educator.com.*2075

*We will see you next time.*2078

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