Chapter 6: Energy and Chemical Change

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Have you ever stared at a pot boiling maybe?

Or felt the warmth coming off a fire and just wondered about the, you know, the invisible stuff happening?

Or even how your car actually moves or why ice melts in your drink?

Exactly.

It's all about energy.

It's constantly moving, changing form, but well, you don't always notice it unless things get hot or cold or something, you know, moves.

So today we're taking a deep dive into thermochemistry.

It's that really essential branch of chemistry that kind of unrolls the secrets of heat.

Heat in chemical reactions, heat in physical changes, all of it.

Our goal here is to really pull back the curtain on this hidden world, give you a hopefully crystal clear picture of how energy flows and crucially do it without getting bogged down in like tons of dense equations.

Yeah.

Think of this as your shortcut.

We want to help you truly understand the energy dynamics that power pretty much everything.

Okay.

And our mission for you, our curious learner, is to give you a solid foundation.

How does energy behave?

How do we measure it?

And maybe most importantly, why does knowledge actually matter?

Because it's not just for textbooks, is it?

Not at all.

It's profoundly important for everything.

Powering cars, understanding your own metabolism, even tackling the really big challenges like climate change.

Wow.

Okay.

So we're going to try and simplify these powerful concepts, connect them to some maybe surprising real world applications and help you grab the most crucial insights from your chemistry sources without feeling totally overwhelmed.

Sounds good.

So where do we start?

Well, we'll begin with the absolute fundamentals, the language of energy, defining the system and its surroundings.

Right.

System and surroundings.

Then how energy actually moves between them.

We're talking heat and work.

Okay.

Heat and work.

Got it.

Then we'll unpack a really crucial concept called enthalpy and show you how chemists actually measure these energy changes in the lab.

It's pretty deep.

Enthalpy is measurement.

Okay.

And finally, we'll equip you with some predictive tools.

Things like Hess's law,

standard enthalpies of formation.

And then we'll tie it all back to those big energy challenges we mentioned.

Cleaner fuels, global warming, that sort of thing.

Excellent roadmap.

So let's jump in.

The basics.

System and surroundings.

What's a system in chemistry?

So a system is basically just

the specific part of the universe we decide to focus on.

It could be the chemicals reacting inside a beaker maybe.

Or like the fuel burning in an engine.

Exactly.

Yeah.

Or even something tiny like the molecules involved in one step of photosynthesis.

It's whatever you define as your area of interest.

Okay.

So you draw a line around it conceptually and everything outside that line.

That's the surroundings.

Simple as that.

So if your system is the reaction in the flask.

Then the flask itself, the air, the lab bench, me watching it.

Yep.

All surroundings.

It's just defining your focus.

Makes sense.

So inside that system, there's energy, right?

Oh yeah.

Every particle in there has energy.

Kinetic energy because it's moving.

Potential energy stored in its bonds.

The grand total of all that energy, that's its internal energy.

We use a capital E for that.

D for internal energy.

Okay.

And that usually changes during a reaction.

Almost always.

When a chemical or physical change happens, that internal energy shifts.

And that shift, that change, that's where delta comes in.

Precisely.

That little triangle delta always means change in.

So D is just the final energy state minus the initial energy state.

Okay.

So if E is negative,

what does that tell us?

Energy left the system.

Exactly.

The system released energy to the surroundings.

It lost energy overall.

Think of it like, I don't know, letting air out of a balloon.

Okay.

And if E is positive.

Then the system absorbed energy from the surroundings.

It gained energy.

Like a sponge soaking up water.

Right.

Absorbed energy.

And you said this energy transfer between the system and surroundings, it happens in two main ways.

Heat and work.

That's right.

Heat, which we symbolize with Q.

And work, symbolized by W.

So what's the key difference?

What makes something heat?

Heat Q is specifically energy transferred because of a temperature difference.

That's the key.

Hot coffee cooling down.

That's heat flowing from the coffee system to the cooler air surroundings.

Okay.

Temperature difference, heat.

Got it.

So work W is everything else.

Any other energy transfer?

Pretty much.

Work is energy transferred when something moves against an opposing force.

Like a gas expanding and pushing a piston in an engine.

That gas, the system is doing work on the piston, part of the surroundings.

Right.

Movement against a force.

Okay.

Let's nail down the signs here because this is where it can get a bit counterintuitive maybe.

It can seem that way, but there's a simple convention.

Energy entering the system is positive.

Energy leaving the system is negative.

Always from the system's point of view.

Okay.

Systems perspective.

Can you give us that bank account analogy again?

I like that.

Sure.

Think of your bank account as the system.

A deposit is money in.

So that's positive for your account balance.

Make sense.

Withdrawals, money out.

So that's negative for your balance.

Same idea for energy.

Heat absorbed by the system.

That's like a deposit.

Q is positive.

Okay.

Heat released by the system.

Like a withdrawal, Q is negative.

Work done on the system.

Positive W.

Work done by the system.

Negative W.

Deposits positive, withdrawals negative.

Got it.

If my coffee is cooling, it's withdrawing heat.

Q is negative for the coffee.

Perfect.

Perfect.

And all this energy moving around,

it leads to a really fundamental law, doesn't it?

The first law of thermodynamics.

Energy conservation.

Absolutely.

One of the science.

The core message is, well, incredibly simple, but also profound.

Energy cannot be created or destroyed.

Can't make it.

Can't break it.

Exactly.

You can only change its form or move it from one place to another.

The total energy of the system plus its surroundings stays absolutely constant.

That still kind of blows my mind.

If energy is conserved, why do we worry about an energy crisis or running out of energy?

It sounds like it should always be there.

That's a brilliant question.

It touches on a common confusion.

We're not actually losing energy from the universe.

The first law holds true.

What we are doing is converting energy into forms that are less useful or less concentrated.

Okay.

Less useful.

Like waste heat.

Precisely.

When gasoline burns in your car engine, the chemical energy stored in the gasoline doesn't vanish.

It transforms into mechanical energy to move the car, maybe some electrical energy for lights and sound, but a lot of it becomes heat.

Right.

The engine gets hot.

And that heat just dissipates into the surroundings.

It's still energy.

The total amount is conserved, but you can't easily use that dispersed heat to, say, drive another mile.

So the quality or usability of the energy decreases even though the quantity doesn't.

That's the crux of our energy challenges.

That's a fantastic clarification.

It's about useful energy versus dispersed energy.

Okay.

Now, when we measure this energy, what units are we talking about?

The standard scientific unit, the SI unit, is the joule, abbreviated J.

Joule.

But you'll very often see kilojoules, KJ, which is just 1 ,000 joules, more convenient for chemical reactions.

And then there's the calorie, calagical.

And when you see on food labels, the nutritional calorie with a capital C.

Yeah.

That's different.

That's actually a kilocalorie, Kcal.

So one calorie equals 1 ,000 of.

Good to know.

A capital C makes a big difference.

Okay.

What else is fundamental about how energy behaves?

You mentioned state functions.

Yes.

State functions.

This is a really important concept.

A state function is a property of the system that depends only on its current state,

its conditions right now, like temperature, pressure, volume, amount of substance.

So it doesn't matter how it got to that state.

Exactly.

It's path independent.

Think about climbing a mountain.

Your final altitude depends only on where you end up, not whether you took the steep direct path or the long winding trail.

Altitude is a state function.

Ah, okay.

Like my bank balance again.

The final number is the same, whether I made one big deposit or lots of small ones.

Perfect analogy.

Internal energy, E, is a state function.

Its value depends only on the current state of the system.

But heat, Q, and work W, they're not state functions.

Wait, why not?

Because the amount of heat transferred or work done often does depend on the specific path taken between the initial and final states, like your deposits and withdrawals.

The individual transactions depend on how you managed your account.

Okay, that makes sense.

Q and W depend on the journey, but their sum, EE, only depends on the start and end points because E is a state function.

You've nailed it.

That's a key insight.

EE equals Q plus W, but the specific values of Q and W can change depending on the process, even if EE stays the same for the same overall change.

Right.

And one specific type of work often pops up in chemistry, doesn't it?

Pressure volume work, PV work.

Yes, especially when gases are involved.

PV work happens when a system's volume changes against an external pressure.

Like the gas expanding in a cylinder.

Exactly.

If a gas expands, it pushes against the surroundings, like pushing a piston out.

The system is doing work on the surroundings.

In this case, work W is negative for the system because energy is leaving it as work.

Okay.

Expansion is negative work for the system, so compression.

Compression is the opposite.

If the surroundings push a piston in, compressing the gas, then work is being done on the system.

So W is positive for the system.

It's gaining energy in the form of work.

Got it.

And there's an equation for that.

There is.

For constant external pressure, WE equals Nash FPV.

The negative sign is crucial.

It ensures that work is negative when volume increases.

W is positive.

And positive when volume decreases, AV is negative.

Okay.

W equals Nash PV.

Good to remember.

So wrapping up this first part, understanding system surroundings, internal energy, heat, work, state functions.

This is really the foundation, isn't it?

It absolutely is.

It's like learning the grammar of energy.

Once you have these terms down, you're incredibly well equipped to understand pretty much any discussion about energy transfer, which is, well, everywhere.

Okay.

Great foundation.

Now you mentioned another term that's super useful, especially for chemists working in labs.

Enthalpy?

Yes.

Enthalpy, symbolized by H.

See, most chemical reactions, especially the ones you might do in a typical lab or even processes in our bodies, happen under conditions of constant atmospheric pressure.

Right.

Open beakers, things like that.

Not usually sealed containers.

Precisely.

And under constant pressure, enthalpy becomes a really convenient way to track energy changes, specifically the heat flow.

How so?

What's the connection between enthalpy and heat?

Here's the key thing.

The change in enthalpy, if AH, is exactly equal to the heat absorbed or released at constant pressure.

We often write this heat as QP, Q sub P.

So AH equals QP.

Whoa.

Okay.

So if a reaction is happening open to the air, the heat you'd measure is just

the enthalpy change.

That seems much simpler than tracking both heat and work.

It really is.

It simplifies things tremendously.

We often care most about the heat given off or taken in.

And at constant pressure, AD tells us exactly that.

We don't usually need to worry about calculating the PV work separately, unless there's a big change in the number of moles of gas during the reaction.

And usually AD is pretty close to eight anyway.

Often, yes.

For reactions involving only liquids and solids, the volume changes are tiny, so PV work is negligible, and H is almost identical to QI.

Even with gases, unless the change in gas moles is huge, the heat term QP is usually much larger than the work term.

So H is still a very good approximation of the total energy change.

Okay.

That's incredibly useful.

So focusing on H at constant pressure leads us to two really important classifications, exothermic and endothermic.

Remind us what those mean.

Sure.

An exothermic process is one that releases heat to the surroundings.

Think exo like exit.

Heat exits the system.

So the system loses energy as heat.

Its enthalpy goes down.

H must be negative.

Spot on.

Burning fuel, a campfire, even your body metabolizing food, those are exothermic.

You feel the heat coming off them.

H is negative.

Okay.

And endothermic?

Endothermic is the opposite.

Endo like enter.

An endothermic process absorbs heat from the surroundings.

The system gains energy as heat.

So its enthalpy goes up, meaning H must be positive.

Exactly.

Think of ice melting.

It needs to absorb heat from the surroundings to turn into liquid water or those instant cold packs you snap.

They get cold because the chemical reaction inside is absorbing heat from your hand in the air.

OH is positive.

Exothermic, heat out, H negative.

Endothermic, heat in, H positive.

Got it.

Like energy going downhill versus uphill.

That's a great visual.

So how do scientists actually measure these heat changes?

You can't just stick a thermometer in the chemical bonds, right?

No, not quite.

We use a technique called calorimetry, and the device is a calorimeter.

The whole idea hinges on measuring temperature changes in the surroundings, usually water.

Okay.

Measure the surroundings.

How does that work?

It relies on a property called specific heat capacity, usually symbolized with a lower case C.

This is the amount of heat energy required to raise the temperature of exactly one gram of a substance by one degree Celsius or one Kelvin.

Specific heat capacity, different for different materials.

Oh, very different.

Water, for instance, has a very high specific heat capacity.

Metals tend to have low ones.

And there's a formula, right?

Q equals mass.

And the one.

Heat Q equals mass times specific heat capacity C times the change in temperature.

If you measure the mass and temperature change of, say, water surrounding a reaction, and you know water specific heat capacity, you can calculate the heat the water absorbed or lost.

Oh, okay.

And that heat, the water gain or loss must have come from or gone into the reaction system.

Exactly.

Assuming the calorimeter itself doesn't absorb much heat, which we try to ensure the heat change of the system is equal in magnitude, but opposite in sign to the heat chain of the water surroundings.

Brand system dash water.

You mentioned water's high specific heat capacity.

Does that have bigger implications like for the planet?

Absolutely huge implications.

Yeah.

Think about why coastal areas have milder climates than inland areas at the same latitude.

Yeah.

San Francisco versus Kansas.

Yeah.

Very different.

Right.

It's because water can absorb massive amount of heat without its temperature changing drastically.

And it releases that heat slowly too.

Oceans act like giant thermal buffers, soaking up solar energy and releasing it gradually, which moderates global temperatures and drives weather patterns.

It's incredible.

Wow.

That one property, water's high C, basically shapes our climate.

Okay.

Back to the lab.

What do these calorimeters look like?

Is it fancy equipment?

Well, it can be, but a simple version for measuring H called a constant pressure calorimeter can be made from, believe it or not, two nested styrofoam coffee cups.

Seriously.

Seriously.

Styrofoam is a great insulator.

You put your reactants, usually in water, inside, put on a lid with holes for a thermometer and a stirrer and measure the temperature change.

Since it's open to the atmosphere through the small holes, it's at constant pressure.

So the temperature change directly relates to H.

Okay.

The coffee cup calorimeter for these, what about really precise measurements, like finding the energy content of food or fuel?

For that, you need something more robust.

A constant volume calorimeter, often called a bomb calorimeter.

A bomb.

Sounds intense.

It is, sort of.

It's a strong sealed steel container, the bomb, where you place your sample, like a phenup or a bit of fuel, in pure oxygen.

You seal it, place the sample electronically.

Okay.

So it burns completely inside this sealed bomb.

Volume is constant.

So it measures.

It measures the heat released at constant volume, which directly gives you E, the change in internal energy.

Because system usually makes surroundings at constant volume, EQV.

Ah, so the bomb gives E, while the coffee cup gives AE.

But you said H and E are often close.

Very close.

Especially for combustion reactions, where the heat release is usually huge, compared to any PV work term.

So the A measured in a bomb calorimeter is extremely useful for understanding the energy content, which we often report as AH anyway.

So calorimetry isn't just some obscure lab thing.

It's literally how they figure out the calories on your nutrition labels and the energy rating of fuels.

Absolutely.

It's fundamental to understanding energy in practical terms.

Okay.

Measurement is key.

But what if you can't easily measure a reaction's enthalpy change?

Maybe it's too slow or too dangerous.

Are there ways to predict it?

Yes, definitely.

This is where thermochemical equations and Hess's law come in.

Thermochemical equations.

That's just a balanced equation with the age value written next to it.

Exactly.

Like CH4 gas plus 202 gas, yield CO2 gas plus 2H2O liquid, AHE's negative 890 kilo J.

That applies to those specific amounts, one mole of methane reacting with two moles of oxygen.

Okay.

And those H values, they follow rules, right?

Like if you run the reaction backwards.

If you reverse the reaction, like decomposing water instead of forming it, you just flip the sign of AJ.

Same magnitude, opposite sign.

Makes sense.

And if you use double the amount of methane?

You get double the heat out.

The magnitude of AJ is directly proportional to the amount of substance reacting or being produced.

It scales.

So age acts like another stoichiometric factor.

You can use it in calculations just like mole ratios.

Precisely.

You can calculate the heat produced by burning, say, 10 grams of methane using the molar mass and that age value.

They are thermochemical equivalents.

Okay.

Very useful.

Now, Hess's law.

This sounds important.

What's the big idea?

The big idea comes back to enthalpy being a state function.

Remember, state functions are path independent.

Right.

Only the start and end points matter.

Hess's law applies that logic.

It states that if a reaction can be expressed as the sum of series of individual steps, the overall enthalpy change for the reaction is simply the sum of the enthalpy changes for each of those individual steps.

Okay.

So if I want to find the age for reaction AC, but I only know the age for AB and BC.

You stand them up.

AHAB plus ADBC.

It doesn't matter that it happened in steps.

The overall change from A to C is the same.

Like that trip analogy again, New York to LA direct has the same change in location as NY to Chicago, then Chicago to Denver, then Denver to LA.

The total displacement is the same.

Exactly.

Hess's law is incredibly powerful because it lets us calculate AG for reactions that are difficult or impossible to measure directly just by manipulating and combining the known AG's values of other reactions.

How do you manipulate them?

You find known reactions that contain the reactants and products you need.

You might need to reverse one of the known reactions if you do.

You flip the sign of its age.

You might need to multiply a known reaction by a factor like two or 12 to get the right stoichiometry if you do.

You multiply its age by the same factor.

Okay.

Reverse means flip sign.

Multiply means multiply H.

Then you add the manipulated equations together.

If you've done it right, the intermediate substances should cancel out, leaving you with your target reaction.

And the H for your target reaction is just the sum of the H values from your manipulated step reactions.

That sounds like a puzzle, but a really useful one.

A chemical calculation cheat sheet.

It kind of is.

It allows chemists to predict reaction heats without ever running the reaction.

Now, to make sure everyone's comparing results fairly, you mentioned standard states earlier.

What's that little degree symbol mean again?

Right.

The degree symbol means the reaction is carried out under standard conditions.

It's a set of reference conditions chemists agreed on for consistency.

Which are?

For gases, it's one atmosphere of pressure.

For aqueous solutions, it's one molar concentration.

And for elements or compounds, it's their most stable form at one atmosphere pressure and usually a specified temperature, most commonly 25 degrees Celsius, which is 298 Kelvin.

Okay.

One at Aram and one M most stable form at 25 degrees C.

So H diger means the enthalpy change under those specific conditions.

Precisely.

It allows us to tabulate and compare values reliably.

And this leads to standard enthalpy of formation.

H degrees.

What's being formed?

Good question.

A formation equation shows the formation of exactly one mole of a compound directly from its constituent elements in their standard states.

Okay.

One mole of product from elements in standard states, like forming water, H2O from H2 gas and O2 gas.

Exactly.

The enthalpy change for that specific reaction is its standard enthalpy of formation, H degrees of core.

So for H2G plus 12 O2G minus H2OL, the H degrees is the H degree of liquid water.

And here's a key point, right?

What's the H degrees for an element in its standard state, like graphite carbon or O2 gas?

By definition, it's zero.

They are the reference points.

We define their formation enthalpy as zero because, well, they're already formed.

Makes sense.

Zero baseline.

Okay.

So we have these tables of H degrees values for lots of compounds.

How do we use them?

This is another incredibly powerful predictive tool.

We can calculate the standard enthalpy change for almost any reaction H degrees arcs in just using the H degrees values of the reactants and products.

How?

Is it just adding them up again?

Almost.

The rule is H degrees arc SN equals the sum of the H degrees values of all the products minus the sum of the H degrees F values of all the reactants.

Remember to multiply each degrees off by the stoichiometric coefficient from the balance equation.

So sum of products minus sum of reactants.

Yeah.

H degrees products.

Why does that work?

It works because of Hess's law again.

You can imagine the reaction happening in a hypothetical two -step process.

First, all the reactants break down into their constituent elements in their standard states,

which is the reverse of their formation.

So it involves nanosecond degrees F.

Then those elements recombine to form the products,

which involves plus dearest degrees for the products.

Since enthalpy is a state function, this hypothetical path gives the same overall H degrees arc SN as the direct reaction.

Wow.

That's elegant.

So Hess's law and standard enthalpies of formation are like the ultimate toolkit for predicting reaction heats without a calorimeter.

They really are.

They allow scientists to assess the feasibility of reactions, design industrial processes, understand biological energy flows, all based on tabulated data in these fundamental principles.

Okay.

Let's shift gears now and connect all this theory systems and the Hess's law to the real world, specifically our energy challenges.

Right.

Because thermochemistry isn't just academic, it's absolutely central to understanding energy production, consumption, and its environmental impact.

So the big one, fossil fuels, coal, oil, natural gas.

Thermochemically, what's the story?

Well, the story is they store a huge amount of chemical potential energy, originally captured from sunlight millions of years ago.

Burning them releases that energy very effectively.

That's an exothermic process with a large negative acreage.

That's why they're so useful.

But the main product of burning carbon -based fuels is carbon dioxide, CO2,

and releasing massive amounts of CO2 into the atmosphere is the primary driver of the enhanced greenhouse effect and global warming.

Explain that connection again.

The greenhouse effect itself isn't bad, right?

No, the natural greenhouse effect is vital.

Gases like CO2, water vapor, and methane in the atmosphere trap some of the heat radiating from Earth's surface, keeping the planet warm enough for life, like a natural blanket.

Okay.

But burning fossil fuels has dramatically increased the concentration of CO2.

So that blanket is getting thicker, trapping more heat than usual.

That's the enhanced effect, leading to rising global average temperatures, melting ice, rising sea levels, more extreme weather.

And understanding the age of combustion helps us quantify the energy we get, but also the amount of CO2 produced per unit of energy, right?

Which helps compare fuels.

Exactly.

And it drives the search for alternatives with lower or zero carbon emissions.

It also informs strategies like carbon capture and storage, trying to grab the CO2 before it hits the atmosphere.

So what about alternatives?

Hydrogen keeps coming up as a potential clean fuel.

What's the thermochemistry there?

Hydrogen's big appeal is its combustion reaction.

H2 plus 12 O2 might H2O.

The only product is water.

Plus its H per gram is very high, much higher than fossil fuels.

Sounds perfect.

What's the catch?

The catch is producing the hydrogen in the first place.

It's not readily available like natural gas.

You have to make it.

Common methods like steam reforming of natural gas still produce CO2.

Electrolysis of water, splitting water with electricity, is cleaner if the electricity comes from renewables.

But it takes a lot of energy.

So gaming is great when you burn H2, but getting the H2 often has its own energy cost and potential emissions.

It's an energy carrier, not really a primary source yet.

Okay.

What about solar?

Tapping the sun directly.

Solar's fantastic because the energy sources, for all practical purposes, limitless and clean.

Photovoltaic cells use materials, often silicon based, that absorb photons, light energy, and convert that energy directly into electrical energy.

No combustion, no emissions at the point of use.

Right.

The main thermochemical challenge is efficiency converting sunlight to electricity isn't 100 % efficient in storage because the sun isn't always shining.

But the fundamental energy conversion process is very clean.

We can also use solar thermal systems that just capture the heat directly.

So lots of options being explored, all relying on understanding these energy transformations.

But given all this, what's maybe the most immediate thing we can do based on thermochemistry?

Honestly, energy conservation.

It sounds simple, but it's incredibly powerful.

Remember the first law says energy is conserved, but we also talked about energy becoming less useful, often lost as waste heat.

Right.

Engines get hot, light bulbs get hot.

Exactly.

The second law of thermodynamics, which is a whole of the deep dive, tells us that every energy conversion involves some waste heat.

No process is 100 % efficient.

So the simplest way to reduce our impact, extend fuel supplies, and save money is just to use less energy overall.

Better insulation, more efficient appliances, LED lights instead of incandescent bulbs.

All of that.

Passive solar building design, driving more efficient cars, or using public transport.

It all comes back to minimizing wasted energy, which is pure thermochemistry in action.

It really ties everything together.

This deep dive makes it clear that thermochemistry isn't just equations on a page.

It's the science behind heating your home, powering your phone, the food you eat, and tackling huge global issues like climate change and finding sustainable energy.

Absolutely.

Understanding how energy flows and transforms gives you such an perspective.

So let's recap.

We started with the basics.

System, surroundings, internal energy, E.

We saw energy moves as heat, Q, or work, W, and that the total energy is conserved first.

Then we focused on enthalpy, H, which is super useful because at constant pressure, H equals the heat flow, QP.

We learned exothermic, H neg heat out, and endothermic, H pose heat in.

We saw how calorimetry, coffee cups and bombs, measures these heat changes, relying on specific heat capacity, Q, M, C, T.

And we explored the predictive power of Hess's law.

H is additive because it's a state function, and standard enthalpies of formation.

H degrees product, products, H we have for reactants.

Finally, we connected all that to real world energy, fossil fuels, CO2, and climate change, and the potential and challenges of alternatives like hydrogen and solar, plus the crucial role of conservation.

So you, our listener, are now really equipped with a much deeper understanding of this fundamental area of chemistry.

It genuinely gives you a shortcut to being well informed about so many critical topics.

Definitely.

So here's a final thought to leave you with.

As we look towards a future needing sustainable solutions, think about this.

How will our fundamental grasp of energy flow of thermochemistry drive the next big breakthroughs?

What new chemical insights might totally redefine how we generate, store, or use energy?

How might you play a part in that?

A lot to think about.

Indeed.

Thank you so much for joining us on this deep dive into thermochemistry.

And from the entire last minute lecture team, thank you for being such a curious and engaged learner.