Chapter 20: Entropy, Free Energy, & Reaction Direction

Welcome to Last Minute Lecture.

This free chapter overview is designed to help students review and understand key concepts.

These summaries supplement not replaced the original textbook and may not be redistributed or resold.

For complete coverage, always consult the official text.

Have you ever noticed how some things just happen naturally?

You know, like that old copper statue turns green all on its own, or sugar dissolving in your coffee.

You stir it, boom, it's gone.

But it never ever spontaneously reforms back into a neat little cube, does it?

No, definitely not.

Or think about gasoline burning to power your car.

Those exhaust fumes, they never just decide to turn back into gasoline.

It feels like the universe has a preferred direction, doesn't it?

It really does.

It feels like a one -way street for a lot of processes.

It absolutely is.

And these everyday things, you know, a book falling, a plant growing, even like stars burning out eventually,

they all point to this fundamental universal principle, what dictates the direction of change.

Exactly.

And this isn't just chemistry, you know, it applies everywhere.

Today we're going to try and unravel this.

We'll dive into it using the powerful ideas of thermodynamics,

specifically things called entropy and free energy.

Perfect.

So our mission for this deep dive is to take those, let's be honest, sometimes pretty dense chemistry concepts from the Silberberg and Amethyst chapter on thermodynamics.

Yeah, it can be.

And really turn them into something clear, something engaging, you know, podcast style.

We want to arm you, our listener, whether you're maybe a college student cramming for an exam or just someone curious about how stuff works with the knowledge to actually predict and understand why things happen spontaneously.

We'll break down the complex bits, use analogies instead of diagrams, make it digestible.

Sounds like a plan.

Let's do it.

Okay.

So first things first, what do we actually mean by a spontaneous change?

It kind of sounds like instantaneous, but that's not quite it, is it?

No, that's a common trip up.

In thermodynamics, spontaneous is simpler.

It just means a change that occurs under a specific set of conditions without needing a continuous energy push from outside the system.

Right.

Like it'll happen eventually on its own.

Exactly.

Think of that book falling off your desk that's spontaneous and it's But fruit ripening, that's also spontaneous, but definitely not instantaneous.

Good point.

Takes its sweet time.

It just means it will happen given the right conditions and enough time.

Once it starts, it keeps going.

Okay.

And this is where some maybe common misunderstandings come in, like with energy.

Yeah, exactly.

The first law of thermodynamics, everyone learns that one, energy is conserved.

Can't be created or destroyed.

Right.

The total energy of the universe is constant.

Delta E universe equals zero.

So gasoline burning converts potential energy to kinetic, releases heat, energy is conserved.

Fine.

But the first law doesn't tell us why those exhaust fumes won't just turn back into gasoline or why an ice cube melting in your hand won't spontaneously refreeze, even though energy would still be conserved if it did.

Huh.

So the first law tracks the energy, but not the direction.

Precisely.

It accounts for the amount of energy, but not the direction of change.

Okay.

So if it's not just energy conservation, what about heat?

You know, exothermic reactions releasing heat, endothermic ones absorbing it.

Is that the key?

Well, that was the initial thought for a long time.

People figured exothermic reactions, the ones that release heat, were delta H is negative.

Delta H, the enthalpy change.

Right.

They thought those must always be spontaneous and endothermic ones absorbing heat, delta H positive, must be non -spontaneous.

Makes intuitive sense, kind of.

Things cooling down seem natural.

It does seem intuitive, but it turns out, nope.

We've got loads of spontaneous processes that actually absorb heat.

Like the ice cube melting in your hand again.

Exactly.

That's endothermic.

It needs heat from your hand to melt, but it certainly happens spontaneously above freezing or water boiling at 100 degrees C.

Also endothermic needs heat, but spontaneous.

Okay.

There's a really dramatic demo example dissolving ammonium nitrate salt in water.

It gets so cold because it absorbs heat like crazy from the surroundings that the beaker can literally freeze itself to a wet piece of wood.

It's spontaneous, but powerfully endothermic.

Freezing a beaker to a board?

That's nuts.

So releasing heat isn't the whole story either.

Not by a long shot.

The sign of delta H alone just isn't a reliable predictor for spontaneity.

So, okay.

If it's not just conserving energy and it's not just releasing heat,

what is driving these changes?

What makes the universe prefer one direction?

Now we're getting to the heart of it.

It comes down to something more subtle.

The freedom of motion of particles and how their energy is spread out or dispersed.

Freedom of motion.

Like how much particles can wiggle around.

Exactly.

Think about states of matter.

In a solid, particles are pretty locked in place, restricted.

Yeah, vibrating, but stuck.

Then in a liquid, they gain more freedom.

They can slide past each other, move around more.

More options.

And in a gas, they're just going wild, flying all over the place, filling the whole container.

Maximum freedom.

Maximum dispersal of energy.

So solid to liquid to gas.

That progression shows increasing freedom.

Precisely.

And that increasing freedom, that dispersal of energy, that's the real driving force we've been looking for.

Okay.

This feels important.

Is there a way to measure this freedom, this dispersal?

There is.

And this is where we introduce entropy.

It's usually symbolized by S.

Entropy is the thermodynamic variable that quantifies this dispersal of energy and freedom of motion.

Entropy.

S -gas.

Got it.

How does it work?

Well, think about the particles in a system, atoms,

molecules.

They have energy, right?

And that energy isn't just one thing.

It's distributed among how they move through space.

That's translational motion, how they rotate, how they vibrate, even the energy levels of their electrons.

Lots of ways to have energy.

Loads.

Each unique combination, each specific way the total energy can be distributed among all these motions for all the particles is called a microstate.

A microstate.

Okay.

The more possible microstates a system can access or occupy, the more ways its energy can be spread out.

And higher entropy means more microstates are possible.

Ah, so more options for arranging the energy means higher entropy.

You got it.

Ludwig Boltzmann, brilliant physicist, he connected this directly.

He showed basically that entropy S is proportional to the natural logarithm of the number of microstates.

WS equals K times LNW.

S, K, L, and W.

So more microstates.

No.

W goes up, log of W goes up, entropy S goes up.

Exactly.

More ways energy can be arranged, higher the entropy.

The universe tends towards states with the most possible arrangements, the highest probability, the highest entropy.

Okay.

Can we visualize this microstate idea?

Yeah.

Think about say one mole of neon gas in a one liter box connected by a valve to another one liter box.

It's empty, a vacuum.

Okay.

Gas on one side, nothing on the other.

Right.

Initially, all the neon atoms are stuck in that first liter.

They have a certain number of positions they can be in, a certain number of ways their energy can be distributed.

That's a certain number of microstates.

Committed space.

Then you open the valve.

What happened?

The gas spreads out, fills both boxes.

Spontaneously.

Right.

Why?

Because now those atoms have double the volume to Roman.

The number of possible positions, the number of ways they can arrange themselves and distribute their energy, the number of microstates doesn't just double.

It increases massively, like exponentially.

Whoa.

So it's way, way more probable for them to be spread out.

Enormously more probable.

That huge increase in available microstates means a huge increase in entropy.

That's why gases spontaneously expand to fill their container.

It's pure statistics driven by entropy.

Okay, that makes sense.

And you said entropy is a state function, like energy and enthalpy.

Yes, exactly.

Delta S for the system, the change in entropy just depends on the final state and the initial state.

S final minus S initial, doesn't matter how you got there.

So we can see entropy increasing, delta S positive when say dry ice turns into CO2 gas.

Definitely.

Gas particles have way more freedom, way more microstates than solid ones.

And decreasing delta S negative when steam condenses into liquid water.

Yep.

Less freedom in the liquid.

Or when two gases react to form a solid, like ammonia and hydrogen chloride gas, making solid ammonium chloride.

Fewer particles locked in a solid big decrease in entropy for the system.

Okay.

System entropy makes sense.

But you mentioned the universe earlier.

How does the system relate to everything else?

Ah, yes.

This is absolutely crucial.

This is the second law of thermodynamics.

And it's, well, it's profound.

It states that for any real spontaneous process, the total entropy of the universe must increase.

Total entropy.

Meaning the system plus its surroundings.

Precisely.

Delta S of the universe, which equals delta S of the system, plus delta S of the surroundings, must be greater than zero for any spontaneous change.

So wait, if the system's entropy goes down,

like when water freezes.

Big example.

The surroundings entropy must go up by an even larger amount to make the total positive.

You've got it.

The universe's total entropy always has to climb for a spontaneous process.

The surroundings have to compensate.

And then some, if the system becomes more ordered.

That seems important for understanding, well, everything, like life.

We seem to create order, right?

We build complex things.

That's a classic question.

Organisms look like they defy the second law locally, creating incredibly ordered structures from simpler molecules.

Yeah, seems like decreasing entropy.

But living things are open systems.

And our metabolic processes, like, you know, breaking down food for energy, are highly exothermic.

They release a lot of heat into the surroundings.

Wow, the surroundings again.

That heat released increases the entropy of the surroundings, all the air molecules, water molecules bouncing around more energetically by a huge amount, way more than the decrease in entropy from building the organism itself.

So locally ordered, but overall the universe still gets messier.

Exactly.

Life exists because it can dump entropy into its environment, ensuring the total entropy of the universe increases.

Phew.

Mind blown.

Okay.

So how do we put numbers on this?

How do we measure entropy?

Is there a zero point?

There is.

That's the third law of thermodynamics.

It provides our baseline.

It states that a perfect crystal, perfectly ordered at absolute zero temperature, that's zero Kelvin,

or negative 173 .15 Celsius.

The coldest possible temperature.

Has zero entropy.

S equals zero.

Everything is locked in its lowest energy state, perfectly arranged, no randomness, no disorder, theoretically.

A perfect starting point.

So we can measure entropy relative to that.

Exactly.

This gives us absolute standard entropy values, usually called S0, for substances at standard conditions, typically 25 degrees C and one atmosphere pressure.

That little knot circle means standard state.

Okay.

S0.

What affects those values?

Several things.

First, temperature.

Higher temperature means more kinetic energy, particles move faster, vibrate more, rotate more, more energy levels become accessible.

So more microstates, higher S0.

Makes sense.

Heat things up, they get more agitated, more entropy.

Yep.

Second, physical state.

This is a big one.

Gases have much higher entropy than liquids, which have higher entropy than solids.

Think S0 solid is much less than S0 liquid, which is much less than S0 gas.

Like our water example.

Ice, liquid, steam, big jumps in entropy at melting and boiling.

Huge jumps.

Third, dissolving.

Generally, dissolving a solid or liquid increases entropy.

The particles mix, spread out, more freedom.

Usually.

Usually.

But there are exceptions.

Sometimes dissolving very small, highly charged ions like aluminum 3 plus assay can actually decrease the overall entropy.

Because those tiny charged ions organize the water molecules around them really tightly into hydration shells.

That increased order of the water can outweigh the increased disorder of the ions spreading out.

Interesting twist.

What about dissolving gases?

Ah, dissolving a gas in a liquid almost always decreases entropy.

The gas particles lose a ton of freedom when they're confined in the liquid phase.

Okay.

What else influences S0?

Atomic size and molecular complexity.

Within a group in the periodic table, heavier atoms tend to have higher S0.

More electrons, energy levels are closer together, more accessible microstates.

Heavier means higher entropy.

Generally.

And molecules with more atoms usually have higher entropy than simpler ones, because there are more ways for the molecule to vibrate and rotate.

Think NO versus NO2 versus N2O4.

More atoms, more entropy.

More complex, more ways to move.

Also, structure matters.

Like, a straight chain hydrocarbon generally has slightly higher entropy than a cyclic one with the same number of atoms, because the chain can rotate more freely around its bonds.

Okay.

Lots of factors.

But what's the most important one?

Oh, definitely the physical state.

The difference between gas, liquid, and solid usually swamps the effects of molecular complexity.

Methane gas, CH4, has much higher entropy than liquid ethanol, C2H5OH.

Even though ethanol is a bigger, more complex molecule, gas always wins pretty much.

Good rule of thumb.

Gas trumps complexity.

Okay, so knowing these trends, can we predict entropy changes for reactions?

Often, yes.

At least the sign.

A really useful trick is just to look at the change in the number of moles of gas.

Moles of gas.

Yeah.

If a reaction produces more moles of gas than it consumes, delta S for the reaction, delta S0 reaction is usually positive.

More gas, more disorder, more entropy.

And fewer moles of gas means?

Usually a negative delta S0 reaction, less gas, more order, lower entropy like making ammonia.

N2 gas plus 3H2 gas goes to 2NH3 gas.

You start with 4 moles of gas and with 2.

Fewer gas moles.

So delta S should be negative.

And it is.

It's a pretty reliable quick check.

Cool.

Can we calculate the exact value too?

Absolutely.

Just like Hess's law for enthalpy changes, we can calculate delta S0 for the reaction using the standard molar entropies, the S0 values, from tables.

You sum up the S0s of all the products, multiply each by its coefficient in the balanced equation, and then subtract the sum of the S0s of all the reactants, again multiplied by their coefficients.

Products minus reactants.

Standard procedure.

Got it.

But we keep forgetting the surroundings.

How do they fit into the calculation?

The second law needs delta S universe.

Right, you are.

We need delta S of the surroundings.

Think of the surroundings as this huge reservoir that can absorb or release heat from the system without changing its own temperature much.

Like the ocean?

Kind of.

And the impact of heat transfer on the surroundings entropy depends heavily on the temperature of the surroundings.

There's a great analogy for this.

Think about money.

If you have only $10 in your account and someone gives you $100, that's a huge relative change, right?

Makes a big difference.

But if you have getting another $100, hmm,

meh, barely notice it.

Okay, I see where you're going.

Heat is like that money.

Transferring a certain amount of heat to cold surroundings, low energy, like the $10 account, causes a big change in their entropy.

Transferring the same heat to hot surroundings, high energy, like the million dollar account, makes much less of a difference to their entropy.

So the entropy change in the surroundings depends on how much heat is transferred and

Exactly.

And there's an equation for it.

Delta S of the surroundings is equal to the negative of the system's enthalpy change, minus delta H of the system, divided by the absolute temperature T.

Delta S, sir, you'll delta HST.

Okay, why the minus sign?

Because if the system releases heat, exothermic negative delta H, sir, that heat goes into the surroundings, increasing their energy and therefore their entropy, positive delta S, sir.

The minus sign flips the sign correctly.

Ah, makes sense.

Heat out of system, heat into surroundings.

So this is really key.

An exothermic reaction, negative delta H says,

always increases the entropy of the surroundings, positive delta S, sir.

This explains how a process can be spontaneous even if the system's entropy decreases, negative delta S says.

As long as the surroundings entropy increases more.

Precisely.

If the heat released to the surroundings creates enough entropy there, especially at low temperatures because T is in the denominator,

it can overwhelm a negative delta SS and make delta S universe positive overall.

So exothermic reactions are often spontaneous, especially at low T, even if they create more order in the system itself.

That's a major takeaway.

And conversely, an endothermic reaction, positive delta SS, negative delta S, sir, can only be spontaneous if the system's own entropy increase, positive delta SS, is large enough to overcome the decrease in the surroundings entropy.

This usually happens at higher temperatures.

Okay.

This is starting to connect delta H and delta S to spontaneity via the surroundings and temperature.

What about equilibrium?

Equilibrium is the balancing point.

It's when the drive for the system to change is perfectly matched by the drive for the reverse change.

In terms of entropy, it's when the total entropy change of the universe is zero.

Delta S universe equals zero.

So at equilibrium, delta S system must equal negative delta S surroundings.

They perfectly cancel out.

Exactly.

The system is stable.

No net change occurs.

Phew.

Okay.

It's a lot to track system entropy, surroundings, entropy, enthalpy, temperature.

Is there a simpler way, a single value that tells us if something is spontaneous under specific conditions?

You've anticipated the next brilliant step.

Yes, there is.

It's called the Gibbs free energy, usually just called free energy symbol G named after Josiah Willard Gibbs, an absolute giant in thermodynamics.

You have free energy G.

What does it do?

It cleverly combines enthalpy H and entropy S into a single state function that directly predicts spontaneity for the system itself without you having to explicitly calculate delta S for the surroundings.

It's beautiful.

Sounds useful.

What's the equation?

The change in Gibbs free energy, delta G is defined as delta G equal is delta H T delta S where delta H and delta S are for the system and T is the absolute temperature.

Delta G, delta H T delta S.

Wow.

So it combines the heat term delta H and the disorder term T delta S.

Exactly.

And the sign of delta G tells you everything you need to know about spontaneity at constant temperature and pressure.

Okay.

Lay it on me.

If delta G is negative less than zero, the process is spontaneous in the forward direction.

Delta G negative spontaneous.

Go.

If delta G is positive greater than zero, the process is non -spontaneous as written.

The reverse process would be spontaneous.

Delta G positive non -spontaneous.

No go in that direction.

And if delta G is zero.

Equilibrium.

Then go.

Delta G equals zero means the system is at equilibrium.

No net change.

That is elegant.

One number, delta G tells you go, no go or equilibrium.

Takes enthalpy, entropy and temperature all into account.

It's incredibly powerful.

It's the ultimate criterion for spontaneity under typical lab

Okay.

So can we calculate a standard free energy change like we did for H and S, a delta G naught?

Yes, we can.

Two main ways.

First, if you already know the standard enthalpy change, delta H naught, and standard entropy change, delta S naught, for a reaction at a specific temperature, usually 298 K, which is 25 C, you can just plug them into the Gibbs equation.

Delta G naught, delta H naught, T delta S naught.

Okay.

Use the definition.

What's the other way?

Similar to Hess's law again,

there are tabulated values called standard free energies of formation, delta G naught F.

These represent the free energy change when one mole of a compound is formed from its elements in their standard states.

Oh, like delta H naught F.

Exactly like that.

You can calculate delta G naught for a reaction by summing the delta G naught F values of the products times their coefficients and subtracting the sum of the delta G naught F values of the reactants times their coefficients.

Products minus reactants again.

We can use this for, say, that potassium chloride decomposition in fireworks.

Absolutely.

You can calculate its delta G naught either from delta H naught and delta S naught or from the delta G naught values, and you should get the same answer.

It tells you how spontaneous that decomposition is under standard conditions.

Very cool.

Now, I've heard free energy linked to work.

Yes, that's another crucial aspect.

Delta G represents the maximum amount of useful work that a system can perform during a spontaneous process at constant temperature and pressure.

Maximum useful work.

Why useful?

Useful work means work other than the simple expansion work P delta V work.

Think electrical work from a battery or mechanical work from an engine.

Delta G tells you the theoretical limit of how much energy you can extract from a spontaneous process to do something useful.

The theoretical maximum implies we don't usually get that much.

Almost never in real life.

Real processes are always irreversible to some extent.

This means some of the free energy change is always lost, usually as heat dissipated to the surroundings due to friction, inefficiency, things not happening infinitely slowly.

Entropy strikes again.

The universe demands its tax.

You could say that.

So a car engine burning gasoline has a certain negative delta G representing the maximum work possible, but a lot of that energy just ends up heating the engine

You never get the full delta G out as motion.

Same with a battery.

Short circuit it and all the free energy becomes heat.

Run a motor with it and you get some useful work, but still less than the theoretical maximum delta G.

So delta G is the ideal potential, but reality always falls short.

Got it.

Now let's revisit temperature.

You said delta G equals delta H T delta S.

That T looks really important, especially if delta H and delta S have the same sign.

Hugely important.

The temperature determines the magnitude of the entropy contribution, nanoHT delta S, relative to the enthalpy contribution, delta H.

This leads to those four distinct scenarios for spontaneity.

Okay, let's break them down.

Scenario one.

Delta H is negative, exothermic, and delta S is positive, more disorder.

What happens when you plug those into delta G equal delta H T delta S?

Let's see.

Negative delta H and then you're subtracting positive term.

T is always positive, delta S is positive.

So a negative minus a positive.

Delta G will always be negative regardless of T.

Exactly.

Always spontaneous at all temperatures, like hydrogen peroxide decomposing, releases heat and increases entropy.

Liquid to liquid plus gas always wants to happen.

Okay.

Scenario two.

The opposite.

Delta H is positive, endothermic, and delta S is negative, more order.

Okay.

Positive delta H and now we're subtracting a negative term, T times negative delta S.

A positive plus another positive.

Delta G will always be positive.

Right again.

Never spontaneous at any temperature, if it were a reaction anyway.

The reverse reaction would be always spontaneous.

Think of forming ozone, O3 from oxygen, O2, takes energy and decreases entropy.

Three moles gas to two moles gas.

Doesn't happen on its own.

Okay, those are the straightforward cases.

What about when the signs are the same?

Case three.

Both delta H and delta S are positive.

Endothermic but increasing entropy.

Delta G, positive delta H.

T, positive delta S.

Now it's a competition.

The positive delta H makes it non -spontaneous, but the negative key delta S term makes it spontaneous.

Which one wins depends on T.

Precisely.

At low T, the delta H term dominates.

Delta G is positive, non -spontaneous.

But as T gets higher, the 90 delta S term becomes more negative and eventually overwhelms delta H.

Delta G becomes negative.

So spontaneous only at high temperatures.

Like melting ice.

Endothermic, positive delta H.

More disorder, positive delta S.

Only spontaneous above zero degrees C.

High enough T.

Perfect example.

Or the oxidation of N2O gas becomes spontaneous above about 994 K.

Okay.

Last case, scenario four.

Both delta H and delta S are negative.

Exothermic but decreasing entropy.

Delta G equals negative delta H.

T, negative delta S.

Negative delta H wants it to be spontaneous, but the 90 T delta S term becomes minus minus, so plus T delta S.

That term wants it to be non -spontaneous.

Another competition.

Yep.

At low T, the negative delta H term dominates, making delta G negative, spontaneous.

But as T increases, the positive plus T delta S term grows and eventually makes delta G positive, non -spontaneous.

So spontaneous only at low temperatures.

Like freezing water.

Exothermic, negative delta H.

More order, negative delta S.

Only spontaneous below zero degrees C.

Low enough T.

Exactly.

Or the formation of rust, iron thronoxide.

Very exothermic, but less entropy solids and gas forming solid.

Spontaneous at room temperature, but would become non -spontaneous at extremely high temperatures.

Above 3000 K or so.

This temperature dependence is fascinating.

Is there a specific temperature where it flips from spontaneous to non -spontaneous or vice versa?

Yes.

That's the crossover temperature where delta G equals zero, the equilibrium point between spontaneous and non -spontaneous.

Since delta G equals delta H delta S, if delta G is zero, then delta H over T delta S.

So you can calculate that crossover T by dividing delta H by delta S, T equals delta H delta S.

T equals delta H over delta S.

That tells you the switching point.

Assuming delta H and delta S don't change much with temperature, yes.

For example, reducing copper i -oxide with carbon to get copper metal.

It's endothermic, but increases entropy.

Solid plus gas.

Calculating T equals delta H delta S gives about 352 K.

Which is 79 degrees Celsius.

Right.

So above 79 C, delta G becomes negative and the reaction becomes spontaneous.

That's a pretty moderate temperature for metal extraction achievable, practically.

That's really useful for industrial processes.

What about, can you force a non -spontaneous reaction to happen?

Well, besides changing the temperature, there's a really important strategy called coupling reactions.

You can link a non -spontaneous reaction, positive delta G, to a separate highly spontaneous reaction, very negative delta G.

How does linking them help?

If the second reaction's negative delta G is larger in magnitude than the first reaction's positive delta G, then the overall delta G for the combined process will be negative.

So the favorable reaction essentially pulls or drives the unfavorable one along.

Like using a downhill reaction to power an uphill one?

Exactly like that.

And this is absolutely fundamental to life.

Ah, biology again.

How does it use coupling?

The universal energy currency in cells is ATP, adenosine triphosphate.

The hydrolysis of ATP to ADP and phosphate has a very negative standard free energy change, about negative 30 .5 kilojoules per mole.

It's highly spontaneous.

ATP breaking down releases energy.

Releases free energy.

And cells couple this highly spontaneous ATP hydrolysis reaction to drive countless other reactions that are essential for life but are non -spontaneous on their own, like building proteins or transmitting red signals or the first step in glucose metabolism, phosphorylating glucose.

So attaching a phosphate to glucose is uphill, not spontaneous.

Yep, positive delta G.

But coupling it with ATP hydrolysis makes the overall process spontaneous.

It's how life pays its energy bills to create order and function.

Amazing.

Okay, we've talked about delta G predicting spontaneity and standard delta G0.

But reactions don't always start with standard conditions, right?

What if you have different amounts of reactants and products?

Excellent point.

That's where equilibrium comes back in, more formally.

The actual free energy change, delta G, not delta G0, depends not only on the standard change but also on the current concentrations or pressures of reactants and products, relative to their equilibrium values.

How far you are from equilibrium matters?

It does.

We use the reaction quotient Q to describe the current state.

Q has the same form as the equilibrium constant K, but uses the actual non -equilibrium concentrations or pressures.

Okay, Q tells us where we are now.

K tells us where equilibrium is.

Exactly.

And the relationship between the actual free energy change, delta G, the standard free energy change, delta G0, and Q is given by delta G equals delta G0 plus RT LNQ.

Delta G, delta G0 plus RT LNQ, R is the gas constant, T is temp, LNN is natural log.

What does this tell us?

It tells us the actual spontaneity under current conditions.

Remember that delta G0 is related to the equilibrium constant K by by.

Delta G0 itself, there's RT LNK.

Ah, right.

So we can substitute that in.

You can.

If you substitute dadrush RT LNK for delta G0, you get delta G equal to LNK plus RT LNQ, which simplifies using log rules to delta G equals RT LNQ.

Delta G equals RT LNQ divided by K.

That's neat.

So the sign of delta G depends on whether Q is bigger or smaller than K.

Precisely.

So if Q is less than K, more reactants at an equilibrium, LNQK is negative, so delta G is negative, reaction goes forward towards product.

Correct.

If Q is greater than K, more products than at equilibrium, LNQK is positive, delta G is positive, reaction is non -spontaneous forward, so it goes backward towards react.

Spontaneously to the left.

Correct.

And if Q equals K, LN1 is zero, delta G is zero.

Equilibrium.

You've nailed it.

That equation perfectly connects the actual free energy change to how far the reaction mixture is from equilibrium.

And that link delta G0F dot RT LNK is powerful too.

Means if you know the standard free energy change, you can calculate the equilibrium constant K.

Absolutely.

A negative delta G0 means K will be greater than 1, product favorite at equilibrium.

A positive delta G0 means K will be less than 1, reactant favorite at equilibrium.

And because of the logarithm, even a small change in delta G0 can mean a huge change in K, right?

A massive change.

A shift of just a few kilojoules in delta G0 can change K by orders of magnitude.

It shows how sensitive the equilibrium position is to the underlying thermodynamics.

So we could calculate K for, say, NO oxidation,

or find delta G0 if we knew K for HCl decomposition.

Yep.

Standard calculations using that equation.

And that other equation, delta G equal delta G0 plus RT LNQ, let's just find the actual delta G if we're not at standard conditions.

Like for that sulfur dioxide oxidation and making sulfuric acid, if we know the partial pressures.

Exactly.

You calculate Q from the given partial pressures, plug it in with the known delta G0, R and T, and find the actual delta G under those specific industrial conditions, tells you if the reaction will still proceed forward spontaneously.

So just to wrap this up clearly, spontaneous means what, finally?

It means the system from its current state, defined by Q, will move towards the equilibrium state, defined by K, where its free energy is at a minimum.

Even if equilibrium favors reactants.

Even then, if delta G0 is positive and K is less than 1, the reaction is reactant favored.

But if you started with only products, Q is infinite, the reaction would still spontaneously proceed towards reactants until it reaches that equilibrium mixture.

The drive is always towards minimum free energy, which is the equilibrium state, wherever that might lie.

So spontaneous just means we'll proceed towards equilibrium from the current state.

Got it.

Wow.

Okay, so we've really covered some ground here.

We started with just noticing things happen one way.

Like statues turning green.

And ended up diving into energy conservation, enthalpy, the crucial idea of entropy as disorder or dispersal.

Microstates.

Microstates, the second and third laws.

And then the really elegant Gibbs free energy, delta G, as the ultimate predictor.

Delta G equals delta H minus T delta S, the key equation.

It feels like understanding these concepts really gives you, the listener, the tools to predict reaction direction.

Think about efficiency.

Even grasp the energy flow that drives life itself.

It's like a decoder ring for how the universe tends to change.

It really is.

And it leaves you with this fascinating thought, doesn't it?

The universe as a whole relentlessly marches towards greater entropy, greater disorder.

Yet within that grand trend, life creates these pockets of incredible intricate order.

By cleverly using coupled reactions and essentially paying its entropy dues to the surroundings.

Exactly.

It makes you wonder what other complex systems out there, maybe things we don't even think of in these terms, like planetary formation or maybe even social structures.

Could they also be governed or at least profoundly influenced by these same fundamental thermodynamic laws of energy, entropy, and the drive to minimize free energy?

That's a deep thought to end on.

Definitely something to mull over.

Well, thank you for joining us on this deep dive into thermodynamics.

My pleasure.

We really hope this gave you a useful shortcut to understanding these key ideas.

And maybe sparked a few aha moments along the way.

Until next time, keep digging into the fascinating world around you.

That's another deep dive.

We appreciate you tuning in.