Chapter 17: Spontaneity, Entropy, and Free Energy

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Have you ever looked at a perfectly organized bookshelf, maybe, and just knew, yeah, that's not going to last?

Or wondered why gas always fills up at the container, but never just squishes itself back into one corner?

Right.

It seems obvious.

But why?

It's a really fundamental question.

And it goes way beyond just how much energy is involved.

There's something deeper happening.

Definitely.

A more profound principle governing, well, everything from rust forming on steel to, believe it or not, the existence of life itself.

Welcome to the deep dive.

We sift through the sources, the textbooks, the research to bring you concise, impactful insights.

And today we're jumping into a really fascinating area, spontaneity, entropy, and free energy.

We're drawing mainly from ZoomDoll, ZoomDoll, and Dacasse Chemistry 11th edition.

Our mission, as always, is to unpack these core chemical ideas,

these somewhat tricky concepts, connect them to the world around you, and hopefully give you a few aha moments, all without needing diagrams or charts.

Yeah.

Let's see if we can make thermodynamics click just using words.

Okay.

So let's start with something familiar.

The first law of thermodynamics.

You'll remember this one.

It's basically just energy conservation, right?

Energy can't be created or destroyed.

Exactly.

It only changes form.

Think of it like the universe keeping its energy books balanced.

Like when methane burns,

the energy in the bonds gets released as heat.

Total energy stays the same.

Just rearranged.

Precisely.

But here's the thing.

The first law doesn't tell us.

It gives us zero clue about why something happens in one direction, like the methane burning, but not the reverse.

Why doesn't ash and CO2 spontaneously turn back into methane and oxygen?

Right.

Or why does a pen fall down but never jump back up?

Energy could still be conserved in theory.

But it just doesn't happen.

So the first law tracks the energy but doesn't explain the direction of change.

Okay.

So that brings us to this idea of a spontaneous process.

That's just something that happens without any outside help, right?

Without continuous intervention.

Correct.

But, and this is a really key distinction, spontaneous does not mean fast.

Ah yeah.

The classic example.

Diamond turning into graphite.

Right.

Thermodynamically speaking, it's spontaneous.

It should happen.

But thankfully for anyone with a diamond ring, it's unbelievably slow.

It's under what we call kinetic control.

The energy barrier to get started is huge, even though the overall process is favorable.

So that's a critical point.

Thermodynamics tells us if it can happen.

The yes or no, based on start and end states.

Well, kinetics tells us how fast it happens.

Looking at the pathway, the reaction mechanism, the activation energy.

You need both pictures to really understand what's going on.

Absolutely.

Okay.

So thinking about everyday spontaneous things.

Steel rusting, gas filling a room, heat flowing from your coffee cup to the air, wood burning.

What's the common thread?

Well, the first thought the logical guess early scientists had was maybe it's about releasing heat.

Exothermicity.

Makes sense.

A lot of spontaneous things do release heat.

Burning wood, for example.

Sure.

But it can't be the whole story.

Think about ice melting above zero degrees Celsius.

Right.

That happens on its own.

Spontaneous.

But it's endothermic.

It absorbs heat from the surroundings to melt.

Ah.

So releasing heat isn't the universal driver.

There must be something else.

Something more fundamental pulling the strings.

And there is.

After a lot of observation and thinking, scientists pinned it down.

The common factor in all spontaneous processes is an increase in a property called entropy, usually shown as S.

Entropy.

The universe's tendency towards messiness.

Disorder.

That's a great way to think about it.

Initially, it's a measure of randomness or disorder at a molecular level.

Like your room analogy, it just naturally tends towards messy.

Exactly.

Why?

Because there's only maybe one or a few ways for everything to be perfectly in its place.

There are countless ways for things to be out of place.

Scattered around.

Disordered.

So the messy state is just far, far more probable.

Statistically more likely.

So entropy is linked to probability.

Deeply linked.

More technically, entropy relates to the number of possible arrangements, positions, energy levels available to a system.

We call these microstates.

The more microstates a particular state corresponds to, the higher its entropy, and the more probable that state is.

Nature tends towards the most probable state.

Okay, let's take that gas example again.

Gas in one half of a box, vacuum in the other.

You open the barrier.

It spreads out.

Instantly fills the whole box.

Spontaneously.

It's because there are vastly more ways, more microstates, for the gas molecules to be spread throughout the entire volume.

Than for them all to be huddled in one corner.

That spread out state has higher positional probability.

Higher entropy.

And does that explain states of matter too?

Solid, liquid, gas.

Absolutely.

Solids have molecules locked in place.

Very few possible positions.

Low entropy.

Liquids, they can move around more.

More positions.

Higher entropy.

And gases.

Molecules flying everywhere.

Huge volume available.

Way more positions.

Highest positional entropy.

So generally, stalgus is much greater than sliquid, which is greater than solid.

Even dissolving something increases entropy.

Like sugar and water.

The shimmer molecules go from an ordered crystal to being randomly dispersed among the water molecules.

More positions available.

More randomness.

Higher entropy for the system.

Okay, this is making sense.

It's all about increasing the ways things can be arranged.

The universe likes options.

You could say that.

And this leads directly to the second law of thermodynamics.

It's one of the most fundamental laws in physics.

It states that for any spontaneous process, the entropy of the universe always increases.

Not just the system we're looking at, but the whole universe.

The whole universe.

Energy is conserved, first law, but entropy is always increasing, second law.

The universe is constantly getting, in a sense, more disordered overall.

Wow.

Okay, so how do we track that?

Universe is kind of a big place.

We cheat a bit.

We divide the universe into the system, the reaction, the ice cube, whatever we're studying.

And the surroundings.

Yeah.

Which is literally everything else.

Right.

And the total entropy change universe is just the sum of the change in the system and the change in the surroundings.

The universe equal system plus surroundings.

And for a process to be spontaneous, that total change, universe, must be positive.

Greater than zero.

That's the rule.

That's the thermodynamic condition for spontaneity.

Okay, but wait.

This raises a question.

What about life?

Living cells?

Aren't they building complex, incredibly ordered things, proteins, DNA from simpler building blocks?

That sounds like decreasing entropy, creating order.

Ah, the classic apparent paradox.

How can life exist if the universe demands increasing disorder?

Yeah.

How does that work?

It's all about that system versus surroundings distinction.

While the system, the cell, the organism, is indeed creating order and decreasing its own entropy.

The processes of life are, well, messy in other ways.

Think about metabolism.

You eat complex food molecules.

And break them down into simpler waste products like CO2 and water.

And release a lot of heat.

Exactly.

That breakdown and heat release drastically increases the entropy of the surroundings.

So the decrease in entropy within the cell is more than compensated for by a much larger increase in the entropy of the surroundings.

So the universe is still positive.

Life doesn't break the second law.

It just cleverly exports disorder.

Precisely.

And sometimes, interestingly, maximizing entropy in one part, like the surroundings, can actually drive ordering in the system itself.

It's called entropic ordering.

Kind of counterintuitive.

Okay.

You mentioned heat flow affecting the surroundings entropy.

Can we quantify that?

We can.

The change in entropy of the surroundings, L's surroundings, is directly related to the heat flow into or out of the system, which we call enthalpy change, AH.

So if the system releases heat, it's exothermic, AH is negative.

That heat flows into the surroundings, increases the random motion of the molecules there.

So A's surroundings is positive.

More disorder.

And if the system absorbs heat, endosermic, positive.

It takes heat from the surroundings, slows their molecules down, decreases their entropy.

A's surroundings is negative.

Makes sense.

But you also mentioned temperature matters.

Hugely.

Think about the impact of adding a certain amount of heat.

Let's say 50 joules.

Adding 50 joules to surroundings that are already very hot, with molecules whizzing around super fast, doesn't increase the randomness that much, relatively speaking.

But adding that same 50 joules to very cold surroundings where molecules are moving sluggishly.

That makes a much bigger relative difference in the random motion.

A bigger increase in disorder.

It's like the textbook's analogy.

Giving $50 to a millionaire versus giving $50 to a broke college student.

Bigger impact for the student.

Exactly.

So the entropy change in the surroundings is inversely proportional to the absolute temperature, T.

The equation is X surroundings in your H, T.

The negative sign is because X age is defined from the system's perspective.

Heat leaving the system, negative H, increases the surroundings entropy.

Got it.

So an exothermic process, negative H, contributes more strongly to overall spontaneity, more positive universe, when the temperature is low.

That's right.

Okay, so tracking universe works.

But calculating low surroundings all the time can be a bit cumbersome.

Especially since we're usually more focused on our chemical system.

Precisely.

So chemists developed another thermodynamic function that's often more convenient, especially for reactions at constant temperature and pressure, which is like most benchtop chemistry.

And that would be?

Free energy or Gibbs free energy, named after Josiah Willard Gibbs, symbol G.

Right, G.

And it elegantly combines the enthalpy and the entropy factors.

It does.

The definition is G equals HTS, enthalpy minus the product of absolute temperature and entropy.

Okay, so for a process occurring at constant temperature, we look at the change in free energy.

Exactly.

And that change is given by a super important equation, G, H, D.

Crucially, all those terms, 8HT and SD, now refer just to the system.

Yes, that's the beauty of it.

AG incorporates the system's enthalpy change, related to heat flow affecting surroundings, and the system's own entropy change, all in one value that tells us about spontaneity from the system's viewpoint.

And how does it tell us?

What's the rule for gaity?

This is the chemist's spontaneity scorecard.

For a process at constant T and P, if AG is negative, the process is spontaneous in the forward direction.

If AG is positive, the process is non -spontaneous.

Actually, the reverse process is spontaneous.

And if AG is zero, the system is at equilibrium, no net change occurring.

Simple as that.

Negative day means go.

Positive D means no go, or go backwards.

Zero day means stop balance.

You got it.

Let's revisit the ice cube with this.

Melting ice.

H2O solid to H2O liquid.

Okay.

Melting is endothermic, so AG is positive.

It also increases disorder.

Liquid is more random than solid, so H is positive.

So GbA becomes gray, positive value.

T, positive value.

Right.

Now think about temperature.

Above 0 degree C, 273 K, T is large enough that the positive T's term becomes bigger than the positive H term.

Making the T's term more negative when subtracted, so G becomes negative overall.

And melting is spontaneous.

Below 0 degree C, T is small.

The negative T's term doesn't overcome AG, so gray is positive.

Meaning melting is non -spontaneous, and freezing, the reverse, is spontaneous.

And right at 0 degrees.

The H and T's terms balance perfectly.

AG is zero.

Equilibrium.

Ice and water coexist.

Beautiful.

It shows how temperature acts as the deciding factor when H and S have

opposing tendencies regarding spontaneity.

Like if a reaction is endothermic H0 but increases disorder, it only works, only becomes spontaneous at high T.

Correct.

High temperature favors the entropy term.

Conversely, if it's exothermic 800 but creates order, it's spontaneous only at low T.

Like many reactions where gases form solids, maybe.

Exactly.

This AG equation governs phase transitions like boiling points, too.

The normal boiling point is just the temperature where AG for vaporization equals zero at one adenine pressure.

Okay, let's think about chemical reactions now.

Can we predict the sign of AG for a reaction just by looking at it?

Often yes, especially if gases are involved.

Gases have much higher entropy than liquids or solids.

So if a reaction reduces more moles of gas than it consumes, R -MOS is generally positive.

More gas molecules mean more positional randomness.

And if it consumes more gas than it produces,

fewer gas molecules.

Then K less is likely negative.

Less randomness.

Makes sense.

Now, to actually calculate entropy values, we need a starting point, right?

A zero.

We do.

And that's where the third law of thermodynamics comes in.

It states that the of a perfect crystal at absolute zero, zero Kelvin, is zero.

Perfect order, minimum, possible entropy.

That gives us a baseline.

So we can measure how entropy increases as temperature rises and calculate standard entropy values, S degrees, for different substances.

Right.

And once we have those tabulated S degree values, we can calculate the standard entropy change for any reaction.

It's just the sum of the standard entropies of the products minus the sum of the standard entropies of the reactants weighted by their stoichiometric coefficients.

Like S is law, but for entropy.

Pretty much.

An interesting side note, more complex molecules generally have higher standard entropy values than simpler ones because they have more ways to rotate and vibrate.

More internal microstates.

Okay, so we can calculate A S.

We often know A degrees from calorimetry or Hess's law.

So we can then calculate the standard free energy change using 8 H degrees, A G H T degrees.

That's one way.

Super useful if you have A degrees and A S degrees.

Are there other ways to get A G?

Yep.

Just like H degrees, you can use a Hess's law type approach if you know A G degrees for other reactions that add up to your target reaction.

And the third way involves those formation values again.

Exactly.

We use standard free energies of formation, A G def.

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

And A G D raise for an element in its standard state is zero, just like H degrees.

So you calculate A G degrees reaction the same way you'd calculate A G degrees reaction using heats of formation.

Sum of A degrees of products minus sum of A D G H F of reactants times their coefficients.

Okay, so we can calculate D G D.

But what if it turns out to be positive?

The reaction is non -spontaneous under standard conditions.

Are we stuck?

Can we never make it happen?

Oh, absolutely not.

Just because it won't happen on its own doesn't mean we can't force it to happen.

Well, the most direct way is to supply external energy.

Think about electrolysis.

We use electrical energy to drive non -spontaneous reactions like splitting water into hydrogen and oxygen.

Or charging a battery.

Or charging a battery.

Another huge example is photosynthesis.

Right.

Planes making glucose from CO2 and water using sunlight.

That reaction, C6H12O6 formation, has a massively positive G degrees, about plus 2080 kilojoules per mole.

Highly non -spontaneous.

So the sunlight energy is what drives it.

The light energy provides the necessary input to overcome that positive A degree.

Nature also uses a really elegant strategy called coupling reactions.

Coupler.

Like linking two reactions together.

Exactly.

You pair a thermodynamically unfavorable reaction, positive E, with a highly favorable one.

Very negative G.

If the overall A G for the couple process is negative, then the unfavorable reaction can be pulled along.

How does that work in biology, say, with photosynthesis?

Well, the initial light energy capture is used to make molecules like ATT.

The breakdown of ATP back to ADP is highly exergonic, meaning it has a very negative BATD.

That energy release from ATP breakdown is then used to power the energetically expensive steps of actually building the glucose molecule.

So the favorable ATP breakdown is coupled to the unfavorable glucose synthesis.

Clever.

Very clever.

It's how life powers almost everything.

Another chemistry example.

Silver chloride, AGCl, barely dissolves in water.

AGE is positive for dissolving.

But if you add ammonia, AGCl dissolves readily.

Why?

Because the silver ions then react with ammonia to form a stable complex ion AGNH32 plus G.

Ah, and that complex formation reaction must have a very negative DG.

Exactly.

It's favorable enough to pull the silver chloride into solution, even though dissolving AGCl itself isn't favorable.

The overall coupled process has a negative D.

Okay, that makes sense.

So systems naturally try to reach the lowest possible free energy state, like a ball rolling downhill.

Right.

And for chemical reactions, that lowest point isn't necessarily pure products or pure reactants.

It's equilibrium.

It's equilibrium.

Remember, our re -degree values are for standard conditions, usually one at Oripimera pressure for gases, one M concentration for solutions.

But reactions don't always happen under standard conditions.

Nope.

To find the free energy change under any set of conditions, we use the equation.

DG plus RTLNQ.

Where R is the gas constant, T is absolute temperature, and Q is?

Q is the reaction quotient.

It's like the equilibrium constant expression K, but uses the actual non -equilibrium pressures or concentrations at any given moment.

Okay, so G changes as the reaction proceeds and concentrations change, changing Q.

Exactly.

And the system keeps reacting, spontaneously changing, DG is negative, until it reaches that point of lowest possible free energy.

Which is equilibrium, where the tendency for the forward reaction equals the tendency for the reverse reaction.

Thermodynamically speaking, equilibrium is the state where G is 0.

There's no longer any net driving force for change.

The system has reached its minimum free energy for those conditions.

So at equilibrium, G is 0, 0.

And at equilibrium, the reaction quotient Q becomes equal to the equilibrium constant K.

Correct.

So substitute G, 0, and Q into our equation, a GEG plus RTLNQ.

We get 0 equals plus RTLNK.

Rearrange that, and you get one of the most important equations in chemical thermodynamics.

G degrees, NezhrTLNK.

Wow.

That directly links the standard free energy change, a measure of the intrinsic thermodynamic drive of a reaction to the equilibrium constant K, which tells us the position of equilibrium.

It's incredibly powerful.

It bridges thermodynamics and equilibrium.

So what does this equation tell us about K based on our G degree?

Well, think about it.

If AG degrees is negative, spontaneous under standard conditions.

Then LNK must be positive for the equation to hold, meaning K must be greater than 1.

Right.

Products are favored at equilibrium.

The reaction proceeds significantly towards products.

And if AG degree is positive,

non -spontaneous under standard conditions.

LNK must be negative, meaning K is less than 1.

Reactants are favored at equilibrium.

The reaction doesn't proceed very far.

And if AG degrees happens to be exactly 0.

Then LNK is 0, which means K is 1.

Products and reactants are roughly equally favored at equilibrium under standard conditions.

So for rusting iron, where dG degrees is hugely negative.

K is astronomically large.

Equilibrium lies almost completely on the side of rust.

The reaction goes essentially to completion.

This equation also lets us see how K changes with temperature.

Because the AG degree depends on temperature through the T's term.

Exactly.

We can derive the van't Hoff equation from this, which explicitly shows the temperature dependence of K based on the reaction's H degrees.

Super important for controlling reaction outcomes.

Okay, one last piece.

What does free and free energy actually mean?

Is it like energy we get for free?

Huh.

If only.

No.

The free refers to the energy that is available, or free, to do useful work.

The change in free energy, Tehri, represents the theoretical maximum possible useful work, Wmax, that can be obtained from a process when it occurs at constant temperature and pressure.

The maximum work.

Like turning a turbine, or lifting a weight, or running an electric motor.

Yes.

Useful work.

Not just heat released into the surroundings.

Ye tells you the theoretical limit of how much useful work you could get out if the process were perfectly efficient.

Ah.

But there's always a catch, isn't there?

Theoretical maximal.

Always.

Here's the kicker.

The reality check from thermodynamics.

In any real spontaneous process, the amount of useful work you actually obtain is always less than the theoretical maximum, Wmax.

We never get 100 % efficiency.

Why not?

Because real processes aren't perfectly reversible.

Think about generating electricity from a battery.

For current to flow and do work, like starting a car, there must be some electrical resistance in the wires, right?

Sure.

Wires aren't perfect conductors.

That resistance causes some of the electrical energy to be covered into heat, frictional heating.

That heat dissipates into the surroundings.

And that heat isn't doing useful work, like turning the starter motor.

It's wasted energy.

Exactly.

It's energy that's been degraded, turned into disordered thermal motion, increasing the universe's entropy.

The faster you try to run the process, draw more current, generally the more energy you waste as heat due to these irreversible effects.

So this ties into reversible versus irreversible processes.

It does.

A reversible process is a theoretical ideal.

It proceeds infinitely slowly, always perfectly in balance, so no energy is wasted as heat.

It would extract the maximum work.

And crucially, after a full cycle, the universe would be unchanged.

No net entropy increase.

But that's just theoretical.

Purely theoretical.

All real processes are irreversible.

They happen at finite rates, involve friction or resistance, and always convert some energy into heat, thereby increasing the entropy of the universe.

After a real process runs, the universe is permanently changed.

Its overall entropy has increased.

I remember reading Harry Bent's humorous summaries of the laws.

Ah, yes.

First law.

You can't win.

You can only break even.

Second law.

You can't break even.

Because you always lose some energy's unusable heat in any real process.

Precisely.

And you can't even break even, get back to the exact starting state of the universe.

Because entropy always increases.

This sounds like it has huge implications for things like the energy crisis.

Immense implications.

The energy crisis isn't really about the amount of energy.

The first law says the total energy in the universe is constant.

We're not running out of energy itself.

So what's the problem?

It's a crisis of useful, concentrated energy.

It's an entropy problem.

When we burn fossil fuels, we take highly concentrated chemical energy, stored potential energy in those bonds.

And convert it into heat.

Thermal energy.

Yes.

Diffuse, disordered thermal energy spread out among the countless molecules of the atmosphere.

The total energy is still there, but it's degraded.

It's far less available to do useful work.

Its quality is lower.

We're taking low entropy, highly organized energy sources.

That took nature millions of years to create.

And rapidly converting them into high entropy, disordered waste heat, significantly increasing the universe's overall entropy in the process.

That really puts our energy consumption into a thermodynamic perspective.

It really does.

It's about managing entropy and the flow of useful energy.

Okay.

So let's recap.

Whether a process happens spontaneously is ultimately governed by the second law.

The drive for the universe's entropy to increase.

Right.

And for chemists working at constant TNP, Gibbs free energy becomes the practical scorecard combining enthalpy and entropy effects of the system.

Negative GG means spontaneous.

We saw how A .G.

connects to equilibrium through ADR -EGG -Gryznia's RT -LNK,

linking thermodynamics to reaction extent.

And finally, A .G.

also tells us the maximum useful work theoretically available, though real processes always achieve less due to irreversibility and entropy generation.

From diamonds to DNA, from rusting to respiration, these principles are absolutely fundamental.

They really are.

And understanding them gives you this incredible lens for viewing the universe.

You see this constant pension, the second law pushing relentlessly towards disorder.

Yet within that flow, pockets of incredible order emerge like life itself, like stars forming, like crystals growing.

It seems driven by the very process of maximizing entropy elsewhere.

That's a fascinating thought to end on.

This fundamental push and pull between order and disorder.

How does that dynamic play out in the systems you observe every day?

Technology and nature and society.

And what does it mean for how we manage our resources, which are essentially stores of low entropy?

Something definitely worth thinking about long after this deep dive ends.

Keep looking at the world through these thermodynamic eyes.

You'll be amazed at what you see.

Thank you so much for joining us on this exploration.

And a huge thank you as always to the Last Mile Lecture team for making these deep dives possible.