Chapter 6: Chemical Equilibrium

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Welcome to the Deep Dive.

Today we are cracking open one of the most critical ideas in physical chemistry, chemical equilibrium.

If you ever wondered how much product you can actually make in a reaction, not just what the equation says you could make, well this is the deep dive for you.

Exactly.

We're pulling the key ideas straight from topic six of Atkins Molecular Thermodynamics and Kinetics.

This chapter really provides that crucial thermodynamic link mostly through Gibbs energy to understand how far a reaction really goes, you know, in the lab.

Yo.

Okay, right.

So let's unpack this a bit.

Our mission today really is to get a handle on how this thing called Gibbs energy G kind of acts like the ultimate driving force, how it pushes a reaction towards this stable dynamic equilibrium state, that point where reactants and products just coexist and the net change stops.

Yeah, and the core concept, physically speaking, is actually quite elegant.

It boils down to this.

If you keep temperature and pressure constant, the mix inside your reaction vessel will always shift around compositionally.

It keeps changing until the total Gibbs energy G hits its absolute minimum.

You can think of reactions as sort of rolling downhill, looking for the lowest energy valley to rest in.

Okay, I like that valley analogy.

Yeah.

But if we're rolling down, how do we track like how far we've gone?

How do we quantify that progress along the valley floor?

Ah, good question.

For that, we use something called the extent of reaction.

It's got this Greek symbol.

It looks like a little squiggle.

It basically measures, usually in moles, how much the reaction has actually proceeded from wherever it started.

But the real engine driving things, the thing telling us which way to roll, is the reaction Gibbs energy, delta G.

Right.

So delta is where we are.

And a delta G is like the steepness of the hill at that point.

It tells us which way is down.

Precisely.

Think of delta G as the slope on a graph where you plot the total Gibbs energy against that extent of reaction.

If that slope, delta G, is negative, the reaction goes forward spontaneously.

It's rolling downhill towards that minimum G.

Okay.

So the reaction just keeps pushing forward, making products until that slope flattens out, until it hits zero.

But when the slope is zero, does that mean everything just stops?

Like chemically dead?

Or is it more like a really well -managed traffic flow?

It's definitely the traffic flow.

And that's such a crucial point, the difference between a dead stop and dynamic equilibrium.

When delta G hits zero, it doesn't mean molecules stop reacting.

It means the potential for net chemical change is perfectly balanced.

For a simple reaction, like A goes to B, A right left their prunes dollars, it means the chemical potential of A, new wool dollars, equals the chemical potential of B.

Molecules are absolutely still converting back and forth, A to B and B to A, but the rates are equal.

So the overall amounts, the net amounts of A and B, stay constant.

Got it.

And there's some specific terminology for this potential, this drive, isn't there?

If the reaction is rolling downhill spontaneously.

We call that exergomic.

Delta Dagger G is negative.

It means the reaction can, in principle, do work, it's work producing.

And the flip side, if the forward reaction means going uphill energetically, if delta GI is positive, we call it endergonic.

It's non -spontaneous.

It actually requires work input to proceed.

I also found the analogy helpful here, thinking about coupled weights.

Like an exergonic reaction is a heavy weight falling down naturally.

And you can use that maybe with a pulley system to pull a lighter weight up.

That uphill pull is the endergonic reaction.

Exactly.

And that coupling is absolutely fundamental, especially in biology.

Think about it, the exergonic oxidation of sugars like glucose in our cells, that's the falling weight.

And that energy release is coupled to drive all sorts of endergonic uphill processes essential for life, like building proteins.

Chemistry, especially biochemistry, is all about cleverly coupling these downhill reactions to make the necessary uphill ones happen.

Okay, that makes sense.

So, we have this inherent drive, Dilton deal.

Now, how do we connect that drive to what we actually see in the beaker, the mixture of reactants and products?

How do we link the drive to the composition?

Right.

That's where the reaction quotient Q enters the picture.

Q is like taking a snapshot of the reaction at any given moment.

It's that familiar ratio.

Yeah.

You take the activities, think effective concentrations for now of the products, multiply them together, each raised to the power of its stoichiometric coefficient from the balanced equation.

And you divide by the same thing for the reactants.

Activities of reactants multiplied, raised to their powers.

And the key relationship, the bridge, is this.

The current drive of the reaction, delta G, depends on both its inherent standard drive, delta G and where it is right now, which is captured by that REST -T -L -N -Q term.

The equation is delta G, delta G plus RT -L -N -Q.

Okay.

So Q tells us the current state.

And then when the reaction finally rolls into that valley bottom, when the drive stops, delta G deleters town.

That's when Keeler stops changing too, and we give it a special name.

Deleter is the thermodynamic equilibrium constant.

Precisely.

And setting delta G to zero in that equation gives us one of the absolute cornerstones of chemical thermodynamics, delta G -circ RT -10, or rearranging, delta G -circ RT -techo.

This is huge.

It means we can look up standard Gibbs energy values, delta G -circ in tables data determined under standard conditions, and directly calculate the equilibrium constant dollars for that reaction.

If delta G -circ is negative, delta G is positive, meaning delta is greater than one.

Products are favored at equilibrium.

If delta G's are positive, del R is less than one.

Reactants are favored.

Now you mentioned activities when defining Q and K.

That's often a sticking point.

Can you clarify what an activity is briefly and why it matters for how K looks?

Sure.

Activity, A -J, is basically the thermodynamically correct measure of a substance's contribution.

It's like an effective concentration or pressure adjusted for non -ideal behavior, interactions between molecules, that sort of thing.

But the crucial thing for this discussion is that activities are defined as dimensionless ratios.

They compare the substance's current state to a standard state because activities have no units.

The reaction Q -dollar and the equilibrium constant dollars are also dimensionless.

They're just numbers, which is essential mathematically because you can only take the logarithm of a dimensionless quantity.

Ah, right.

The Dave Van Kue term.

Exactly.

And another key consequence of using activities, the activity of any pure solid or pure liquid in its standard state is defined as exactly one.

Since they're constant, as long as some solid or liquid is present, they effectively drop out of the expression for Q and K.

Think about calcium carbonate decomposing.

Protects the cavernous, tex -CaO plus tex -CaO.

Both tex -CaO and tex -CaO are solids.

Their activities are one.

So the equilibrium constant dollar for this reaction simplifies beautifully.

It's just equal to the activity of the tex -DO2 gas, which, if we assume ideal gas behavior, is essentially just the numerical value of the partial pressure of tex -DO2 at equilibrium relative to the standard pressure.

Wow.

Okay.

That simplifies things a lot.

Now, one more point on this Gibbs energy curve.

If we just looked at the energy of pure reactants and pure products, you might expect the Gibbs energy to just drop in a straight line if the reaction is favorable.

But we always see this curve, this dip, this minimum somewhere in the middle.

You're saying that minimum exists because of mixing.

Nature actually prefers a bit of a mix.

You've nailed it.

That U shape, that minimum in the Gibbs energy plot that isn't at pure reactants or pure products arises almost entirely because of

mixing, delta mix G.

Mixing things together always increases the entropy of the system, think randomness, disorder.

Thermodynamics loves entropy.

So even if the pure products are much lower in enthalpy energy than the reactants, the thermodynamic drive towards maximum entropy achieved by mixing reactants and products pulls the minimum Gibbs energy away from the pure product side.

It forces the system to settle in that mixed state, that compromise, at the bottom of the graph.

Okay.

So we've established the why Gibbs energy minimum.

But for chemists, for engineers, the big question is always how do we control it?

How do we push the equilibrium where we want it?

Which brings us to controlling reaction conditions, right?

Like pressure.

Yes.

Let's start with pressure.

Now remember, dollar itself, the equilibrium constant, is calculated from delta G, which is defined at a standard pressure, usually one bar.

So fundamentally, dollar is independent of the actual pressure you apply to the system.

Wait, so changing the pressure doesn't change K, but surely it changes the amounts of stuff at equilibrium.

Ah, yes.

It absolutely can change the composition and equilibrium, even though K is constant.

The key is how you change the pressure and whether gases are involved.

This is where Le Chatelier's principle comes in.

The system, when disturbed, will shift in a way that minimizes the disturbance.

The system fights back.

Exactly.

So imagine you have a reaction involving gases and you increase the pressure by, say, compressing the volume.

The system wants to relieve that pressure stress.

How does it do that?

It shifts the equilibrium towards the side of the reaction that has fewer moles of gas.

Fewer gas molecules mean less pressure.

Take our old example, right, left, there are two BGA.

One mole of gas on the left, two moles on the right.

If you crank up the pressure, it shifts left towards A to reduce the total number of gas molecules.

Precisely.

To minimize the pressure increase.

Conversely, if you decrease the pressure, it would shift right, making more B, trying to fill the space.

Okay.

But what about adding an inert gas, like argon, to the container?

That increases the total pressure, doesn't it?

It does increase the total pressure, but here's the crucial distinction.

If you add an inert gas while keeping the volume constant, you haven't actually changed the partial pressures of your reacting gases.

A and B in our example, assuming they behave ideally.

Since the partial pressures haven't changed, the reaction quotient Q hasn't changed relative decay.

So adding an inert gas at constant volume has no effect on the position of the equilibrium.

It's about partial pressures, not just total pressure.

Got it.

Constant volume is key there.

Okay.

What's the other big lever we can pull?

Temperature.

Temperature.

Again, Le Chefflier gives us the qualitative picture.

If you raise the temperature, the system tries to counteract that by absorbing heat.

So raising the temperature will always favor the endothermic direction of the equilibrium, the direction that consumes heat.

If you cool it down, it favors the exothermic direction, the one that releases heat.

Makes sense trying to stabilize its temperature, but how do we quantify that?

There must be an equation for how K changes with T.

There is, and it's incredibly important.

The van't Hoff equation.

We don't need to go through the whole derivation, but the essential result is frac delta HdVa.

Look closely at that equation.

It tells you that the rate of change of the logarithm of K with temperature is directly proportional to the standard reaction enthalpy, delta Cernursersia.

Ah, so the enthalpy change dictates the temperature sensitivity.

Exactly.

And it confirms Le Chatelet perfectly.

If the reaction is exothermic, delta HdVa is negative.

That means frac TnDT is negative.

So as temperature T goes up, THA must go down.

A smaller H means a smaller K.

Equilibrium shifts towards reactants.

If the reaction is endothermic, delta HH is positive.

Frac THT is positive.

As T goes up, then whole goes up, meaning K increases.

Equilibrium shifts towards products.

And the bigger the enthalpy change, positive or negative, the more sensitive K is to temperature changes.

That is really powerful.

And it leads to a neat experimental trick, doesn't it?

If you measure K at different temperatures.

Yes.

You can use the integrated form of the Van Hoff equation.

If you plot Noctua versus Untaller, the reciprocal of absolute temperature, you should get a straight line or close to it, assuming delta H doesn't change much over that temperature range.

And the slope of that line is equal to delta HJ.

So just by measuring equilibrium compositions at different temperatures, you can determine the standard reaction enthalpy without ever needing a calorimeter.

That's brilliant.

Measuring K to find H.

Okay, this ability to determine fundamental thermodynamic properties experimentally leads us nicely into the last section, right?

The connection to electricity.

Absolutely.

Electrochemical cells think batteries, galvanic cells are a fantastic practical application of these equilibrium principles because the electrical work they can do is directly tied to the Gibbs energy change of the reaction happening inside.

Right.

I remember this.

The maximum amount of non -expansion work, like electrical work, that a system can perform at constant temperature and pressure is equal to the change in its Gibbs energy.

Delta RG.

Exactly.

And we can measure that electrical work potential very precisely as the cell potential or voltage.

A texel and e texel.

The fundamental link is delta G, F e texel.

Here too is the number of moles of electrons transferred in the balanced redox reaction for each mole of reaction extent.

And F is the Faraday constant.

Notice the minus sign.

A positive cell potential, e texel, means a negative delta G.

And a negative G means the reaction is spontaneous.

So positive voltage tells you the cell reaction will run spontaneously and generate electricity.

Okay.

Higher voltage means more spontaneous, a bigger negative delta G.

Now earlier we saw that delta G depends on composition through the reaction quotient Q.

So does the cell voltage also depend on composition?

It has to.

And that relationship is captured by the famous Nernst equation.

It basically modifies the standard cell potential.

The voltage when all reactants and products are in their standard states, usually activity one, based on the current reaction quotient Q.

The equation is beta texel frank -q RTR.

Look what happens.

As the reaction runs spontaneously, products build up, reactants get used.

This means Q increases.

As Q increases, crew Oprah increases, and that whole second term,

NNQ2, gets larger.

Since you're subtracting it, the measured cell potential, e texel, drops from its initial e tex value.

And it keeps dropping until equilibrium.

Until equilibrium is reached.

At equilibrium, we know delta G equals zellers, which means e texel must also be zero.

The battery is dead in terms of net voltage.

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

So if we set e texel in Q, ebuol, and the Nernst equation, we get $0 ebuol is e texel K.

Rearranging that gives us another incredibly useful link.

E texel FNKO, we can determine the equilibrium constant K just by measuring the standard cell potential.

And this is especially useful for reactions that go almost totally to completion, right?

Where K is enormous.

Exactly.

Measuring a K value of, say, 1030 or 1040 way by directly analyzing the tiny amount of reactant left at equilibrium is basically impossible.

But the corresponding standard cell potential might be something quite reasonable, like one or 1 .5 volts, which is easy to measure accurately.

For instance, the Daniel cell, zinc and copper, has e texel around 1 .1 V, corresponding to a K around 1 .5 times room temperature.

Electrochemistry lets us probe these extreme equilibria.

OK, so we can measure these potentials.

But how do we report them in a standard way?

We can't build every possible cell combination.

Right.

We use standard electrode potentials, often called standard reduction potentials.

We need a reference point.

By international convention, the standard hydrogen electrode, SHE, involving H plus ions at unit activity and gas at one bar pressure over a platinum electrode, is defined as having a standard potential of exactly zero volts at all temperatures.

Then we measure the standard potential of a cell made from our electrode of interest and the SHE.

That measured voltage is the standard electrode potential for our half reaction.

We tabulate these ACER values.

The overall standard cell potential for any two half cells is then just the difference between their standard electrode potentials.

And these tables, the electrochemical series, let us predict reactions.

Absolutely.

The key rule is simple.

Low reduces high.

You look at the table of standard reduction potentials.

Any species on the right side of a half reaction, the reduced form, can spontaneously reduce a species on the left side, the oxidized form, of any half reaction that lies higher in the table, has a more positive seek.

For example, zinc metal, ziengenol, has a standard potential around minus of 0 .76 V.

The hydrogen electrode is zero V.

Zinc is lower than hydrogen.

So zinc metal can reduce hydrogen ions, so nine or plus dollars, to hydrogen gas, 20 gamma or two dollars.

Low reduces high.

That's a neat rule.

And electrochemistry doesn't just give us G and K, right?

It can give us other thermodynamic properties too.

Yes, it completes the picture.

Remember how delta G, delta HT, delta SA, and we know delta G -circ, there's also a thermodynamic relationship that says the change in Gibbs energy with temperature gives entropy,

partial G, partial TP.

Combining these, you find that if you measure how the standard cell potential changes with temperature, specifically the slope frat T -circ, you can directly calculate the standard reaction entropy.

And once you have delta G and delta S from its temperature dependence, you can easily calculate the standard reaction enthalpy, delta H -circ, using delta G, delta HT, delta SA.

So measurements can give you the full thermodynamic profile, G, H, and S.

Wow.

Okay, let's try to wrap this up.

We started with this seemingly abstract idea, Gibbs energy trying to find its minimum, and we've seen how that single principle explains why equilibrium happens, leads directly to the equilibrium constant K, tells us how pressure shifts things via Le Chatelier,

quantifies the temperature effect through Van Hoff and enthalpy, and even lets us measure reaction spontaneity in equilibrium position using voltages in electrochemical cells via the Nernst equation.

It all ties back to G.

That's really the heart of it.

The standard reaction Gibbs energy, delta G sets the stage.

Its sign tells you immediately whether K is big or small, whether products or reactants are favored under standard conditions.

Then the reaction enthalpy, delta HT, dictates how temperature will tune that equilibrium via the Van Hoff equation,

and electrochemistry gives us this incredibly sensitive experimental window into all of it.

So the big takeaway is that thermodynamics isn't just theoretical stuff.

It's a seriously powerful predictive toolkit for chemists and engineers.

It tells you what's possible and how to control it.

Definitely.

Which leads to a final thought, maybe something for you listeners to chew on.

We've seen how cell potentials link directly to Gibbs energy and equilibrium constants, even huge ones.

Now, think about biochemical systems like inside our cells.

Reactions happen constantly.

Concentrations can be incredibly tiny and many crucial processes like synthesizing ATP, the cell's energy currency, are actually endergonic.

They require energy input.

So how might scientists use extremely sensitive electrochemical measurements, perhaps monitoring tiny voltage shifts related to coupled reactions in something like a miniature biochemical fuel cell, to precisely track and understand these vital but non -spontaneous processes happening at minuscule concentrations within a living system?

Hmm.

Linking tiny voltages to complex life processes.

That's definitely something to mull over.

Thank you for joining us for this deep dive into the thermodynamics of chemical equilibrium.

We really hope this shortcut through Atkins helps you feel well informed and ready to tackle it.