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Welcome to the Deep Dive.
Today we're tackling a big one, Thorodynetics.
Our mission is to break down that key A -level chemistry chapter on entropy and Gibbs free energy.
And we're going to get into all of it.
The concepts, the calculations, and that all -important question, will a reaction actually be feasible?
Right.
And to start, we have to get beyond this idea that reactions only happen to release heat.
I mean, think about a stretched rubber band.
You let it go and it snaps back.
It snaps back all by itself,
spontaneously.
And it's not really about releasing energy about enthalpy.
It happens because that coiled up relaxed state is just, it's more random.
The molecules have way more ways to arrange themselves.
And that randomness is what we call entropy, the capital S.
Now, disorder is a good starting point, but we need to be a bit more precise for your A -level, right?
We do.
Entropy S is fundamentally a measure of the number of ways you can arrange the particles and their energy.
The more possible arrangements, the higher the entropy.
It's all about statistical probability.
Which brings us to, I guess, the ultimate rule in this universe, the second law of thermodynamics.
It sounds grand, but the idea is simple.
For any spontaneous change, the total entropy of the universe has to increase.
Things just tend towards disorder.
And to make that manageable, we split the universe into two parts for our reaction.
Exactly.
You have the system, that's the chemical reaction itself.
And then you have the surroundings, which is literally everything else.
The beaker, the air, the solvent,
everything.
Okay.
So let's stick with idea of statistics.
Diffusion is a perfect example.
You spray some perfume in a corner.
Why does it spread out?
It's just the numbers.
It's pure probability.
Imagine you have two connected gas jars, A and B, and just say three molecules of gas in jar A.
Okay.
Well, there are two choices for each molecule, jar A or jar B.
So that's two to the power of three, which is eight possible ways they can arrange themselves.
And only one of those eight ways has them all stuck back in jar A where they started.
Precisely.
The chance of them staying put is only one in eight.
Now imagine you have 50 molecules, that's two to the power of 50.
That is a ridiculously huge number.
So the odds of them all staying in one jar become, for all practical purposes, zero.
Exactly.
They spread out simply because there are vastly more ways for them to be spread out than to be ordered in one place.
That's it.
That's a spontaneous change.
So more ways to arrange energy or more ways to arrange particles, those are the two routes to higher entropy.
That's the core of it.
Right.
Now for the calculations, we need a level playing field.
We use standard molar entropy, S naught or S plimsoll, measured at 298 Kelvin and 100 ,000 Pascals.
And the units are a bit strange at first glance.
Joules per Kelvin per mole,
JK to the minus one, mole to the minus one.
It's energy spread out per unit of temperature, basically.
And a key thing to note when you look at data tables is that elements are not zero for entropy.
Right.
Unlike enthalpy of formation, we're measuring from a theoretical perfect crystal at absolute zero, but you don't really need to worry about that.
For predictions, you just need a few generalizations.
Okay.
What's rule number one?
State of matter.
It's the biggest one.
Gases have huge entropy values.
Liquids are much lower and solids are very, very low, much more ordered.
Makes sense.
Rule two.
Complexity.
A simple molecule like carbon monoxide, CO, has a lower entropy than something more complex like carbon dioxide, CO2 or calcium carbonate.
More atoms just means more ways to vibrate and rotate.
And the third one is about how those atoms are arranged.
Yeah.
Think about carbon.
Diamond has a really rigid, tight structure.
So its entropy is much lower than graphite, which has those layers that can slide around.
It's less constrained.
We see this so clearly in phase changes.
When you melt ice or boil water, you're massively increasing the disorder.
Huge jump in entropy.
And the reverse, condensing or freezing, is a big decrease in entropy.
You're forcing order onto the system.
Now, dissolving a solid seems like it should always increase entropy, right?
You're spreading particles out.
Usually, yes.
But there's a catch.
If you have very highly charged ions, they can actually grab onto water molecules and arrange them into these really ordered shells around themselves.
Ah.
So the ordering of the water can sometimes outweigh the disordering of the solid spreading out.
It's a subtle point, but it's a good one to know.
For chemical reactions, though, the main thing to look for is much simpler.
Let me guess.
Gas.
Gas.
It's always about the gas.
Look at the change in the number of moles of gas.
Okay.
So example one, decomposing calcium carbonate.
Solid calcium carbonate gives you solid calcium oxide and one mole of carbon dioxide gas.
You're going from zero moles of gas to one mole of gas.
That's a huge increase in disorder.
Delta S for the system will be positive, for sure.
And the other way, the Haber process.
One mole of nitrogen gas plus three moles of hydrogen gas.
Gives you just two moles of ammonia gas.
You've gone from four moles of gas down to two.
You're literally compressing them into a more ordered state.
So delta S for the system is negative.
And to get the actual number, the sum of the standard mole entropies of the products minus the sum for the reactants.
And don't forget to multiply by the stoichiometry, the big numbers in the equation.
Let's take an example.
Two moles of solid calcium plus one mole of oxygen gas makes two moles of solid calcium oxide.
When you do the map, you find the system entropy change is negative.
It's about minus 208.
Right.
It's negative.
The system has become more ordered.
But wait, we know this reaction is spontaneous.
Calcium burns fiercely in oxygen.
So how can it be feasible if the system's disorder is going down?
This is the critical moment.
This is what we have to look at the surroundings.
If the system is getting more ordered, the surroundings must be getting more disordered and by an even greater amount.
And how does the reaction make the surroundings more disordered?
By dumping heat into them.
That reaction is highly exothermic.
It has a very negative delta H.
That release of energy makes the particles in the surroundings, the air, the container move faster more randomly.
So an exothermic reaction makes the surroundings more chaotic, which increases the entropy of the surroundings.
Precisely.
And an endothermic reaction does the opposite.
It sucks heat in, cooling the surroundings and making them more ordered.
And there's an equation for this.
The entropy change of the surroundings is equal to minus the enthalpy change of the reaction divided by the temperature.
T.
Yes.
Delta sominus surroundings frac delta honus reaction.
And here comes the single biggest mistake students make.
The units.
I know this one.
The units.
Your enthalpy, delta H, is almost always given in kilojoules per mole.
But entropy is always in joules.
So you have to multiply your delta H value by a thousand to get it into joules before you do anything else.
You absolutely must.
If you don't, your answer will be off by a factor of a thousand and almost certainly the wrong sign.
Okay.
So once we have the system entropy change and the surroundings entropy change, we just add them together to get the total entropy change.
Delta sominus system plus delta sominus surroundings.
And the rule is simple.
If that total is positive, the universe has become more disordered overall and the reaction is feasible.
It can happen.
That's the fundamental law.
Take burning methane.
The system entropy actually goes down a tiny bit, but the reaction is so exothermic.
The delta S of the surroundings is huge and positive, completely overwhelming the system's change, which is why it's so spontaneous.
And just quickly at equilibrium, everything's in balance.
There's no net change.
So the total entropy change is zero.
Right.
But calculating two separate things, system and surroundings is a bit of a pain, which is why chemists came up with a shortcut, a very elegant shortcut.
It's called Gibbs free energy.
Delta G named after Josiah Willard Gibbs.
And this one value basically combines everything for us.
It does.
We get to it from the total entropy, but the final famous Gibbs equation you need to know is delta H miss delta H missed H Wilman S system.
So it pulls together the enthalpy change, delta H and the system's entropy change, delta S all in one.
What's the new golden rule?
It's the opposite of the entropy rule.
If delta G is negative less than zero, the reaction is feasible.
Negative delta G feasible,
positive delta G not feasible.
And if delta G is zero, you're at equilibrium.
It's that simple.
Let's try it with a tricky one.
The decomposition of zinc carbonate.
It's endothermic.
So delta H is positive.
Yeah.
And it produces a gas.
So delta S of the system is also positive.
So you've got a competition.
The positive delta H is unfavorable, but the positive delta S is Who wins depends on the temperature.
At room temperature, 298 Kelvin, we plug in the numbers
remembering to convert delta H to joules.
And you find that the big positive delta H term wins out.
Delta G comes out as positive.
So not feasible at room temperature.
Not at all.
And this leads to four key scenarios based on the signs of delta H and delta S.
Okay, let's run through them.
Case one, delta H is negative.
Delta S is positive.
Easy.
Exothermic and getting more disordered.
Both factors are favorable.
Delta G will always be negative.
Always spontaneous.
Case two, delta H is positive.
Delta S is negative.
Endothermic and getting more ordered.
Both factors are unfavorable.
Delta G is always positive.
Never spontaneous.
Okay, the tricky ones.
Case three.
Yeah.
Both are negative.
Exothermic but getting more ordered.
Here, it's only spontaneous at low temperatures.
You need to keep the T in that minus T delta S term small so the unfavorable entropy part doesn't cancel out the favorable enthalpy part.
And finally, case four.
Both are positive like our zinc carbonate.
Endothermic but getting more disordered.
This is spontaneous only at high temperatures.
You need T to be big so that the now favorable entropy term minus T delta S becomes a large negative number that can overcome the unfavorable positive enthalpy.
Which is why the zinc carbonate decomposes if you heat it strongly even though it won't at room temp.
At, say, 1200 Kelvin, delta G flips to being negative.
Exactly.
Now, besides that main Gibbs equation, there's another way to calculate delta G, isn't there?
A bit like Hess's law.
That's right.
You can use standard molar Gibbs free energy of formation, delta Gf.
And the formula is just what you'd expect.
Sum of delta Gf of the products minus the sum of delta Gf of their reactants.
And just like with enthalpy, the delta G formation for an element in its standard state is zero.
Yep.
It's just another tool in your toolbox.
So we know delta G predicts feasibility, but what is it physically?
It's the free energy.
It's the portion of the total energy change, the delta H, that is actually available to do useful work like run a motor or charge a battery.
The rest, the T delta S part, is the energy that's sort of inevitably lost to disorder.
Which brings us to the final connection, electrochemistry.
Standard cell potential, E cell, also predicts feasibility.
So they must be linked.
They are.
The equation is delta Geo minus NF E ominous cell.
Okay, break that down.
E ominous.
Moles of electrons transferred in the redox reaction.
And F is the Faraday constant, 96 ,500.
Just a number you're given.
So this gives us a really clear link.
If your E cell is positive, which we know means a feasible reaction.
Then because of that minus sign in the equation, your delta G must be negative.
It all ties together perfectly.
Okay, a whirlwind tour.
Let's recap.
Yeah, the big idea is that feasibility isn't just about energy.
It's about disorder.
The second law says total entropy must always increase.
We can predict the system's entropy change by looking at gases mainly, but we also have to account for the surroundings.
And that's where enthalpy delta H comes in.
Gibbs free energy, delta G wraps it all up in the one value.
And the golden rule to remember for a reaction to be feasible, delta G must be negative.
Oh, and watch those kilojoule to joule conversions.
Please do.
And a final thought to leave you with, feasible does not mean fast.
Delta G can be massively negative, telling you a reaction is incredibly favorable, but it might not happen for a million years.
Because of activation energy.
Because of kinetics and activation energy, thermodynamics tells you where you'll end up.
Kinetics tells you how long it'll take to get there.
You still might need a spark.
A perfect distinction to end on.
Thank you for diving deep with us into the world of thermodynamics.
Now go out there and ace those calculations.