Chapter 10: Chemical Bonding I: Basic Concepts

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Hello and welcome back to the Deep Dive.

Today we are actually trying something a little bit different.

We're kicking off what we are calling the Last Minute Lecture Series.

Which I have to say sounds incredibly ominous.

It sort of sounds like the frantic lecture you listen to while you're literally sprinting across campus to the exam hall.

It's not ominous.

I mean, it's practical, right?

Look, we know the reality of being a student.

Sometimes you sit in class and you nod along and you diligently copy down all the diagrams, but the actual mechanics of how the universe is put together just doesn't click.

Right.

Or maybe, you know, you have a huge test tomorrow on general chemistry,

specifically Chapter 10, and you need that aha moment right now.

So what we are going to do is take a very specific, very dense topic, Chapter 10, chemical bonding,

one basic concepts from the general chemistry principles and modern applications text, and we are going to completely deconstruct it.

And when we say deconstruct, we mean we're going to walk through it exactly as the text lays it out.

We aren't skipping the hard stuff.

We aren't connect the qualitative ideas like, oh, Adam's just like to hold hands to the actual quantitative reasoning, the real math, the graphs and the three dimensional models, which means we really have to talk about drawing.

We have to talk about geometry and three dimensions.

And most importantly, we have to talk about why any of this actually matters.

Right.

And the text actually opens with a really strong hook on that exact front.

It makes this critical distinction between stoichiometry and structure.

Yes.

And this is a crucial framing for the listener.

Up until this point in your chemistry journey, you might have just been balancing equations.

You know that two hydrogens plus one oxygen makes water.

Exactly.

You can do the math.

You can calculate the molar masses and yield.

You can be a very competent chemist on paper without having any real idea what a water molecule actually looks like in space.

You can basically follow the recipe without truly understanding the ingredients.

Exactly.

But the text makes the fundamental point that shape defines chemistry.

Period.

If water had a different shape, like if the atoms were arranged in a perfectly straight line instead of being bent,

water wouldn't be a liquid at room temperature.

It wouldn't dissolve salt.

It wouldn't form cell membrane.

Right.

Life as we know it simply wouldn't exist.

So, you know, no pressure, but the geometry we're discussing today is quite literally the reason you are alive to listen to this conversation.

It really is the difference between a universe full of boring, lifeless gas and a universe capable of complex biology.

So, yeah, it matters a lot.

Okay, let's unpack this.

We're starting right at the beginning.

Section 10 -1 Lewis theory.

This is essentially the origin story of chemical bonding.

It takes us back to a very specific window of time between 1916 and 1919.

You have Gilbert and Lewis, along with Irving Langmuir and Walter Kossel.

These guys are at the periodic table and they're noticing something really strange about the noble gases.

Helium neon argon.

The snobs of the periodic table.

In a way, yes.

They are chemically aloof.

They don't react with anything.

They just don't form compounds under normal conditions.

Lewis and his colleagues proposed that this wasn't just some random accident.

Right.

They suggested that the electron configuration of these gases, specifically the number of electrons residing in their shell,

is exactly what makes them so incredibly stable.

And that leads directly to the core proposal of Lewis theory.

Right.

The proposal is that every other atom on the periodic table is jealous.

Every other atom is chemically insecure.

They're trying to mimic the cool kids.

Essentially, yes.

They bond with each other specifically to achieve that exact same stable electron configuration that the noble gases just have naturally.

And this brings us to the four fundamental ideas of Lewis theory.

The first one is the concept of valence electrons.

We hear this term a lot, but let's define it strictly for the listener.

Sure.

So an atom has layers of electrons.

The ones deep inside closest to the nucleus are the core electrons.

They are buried.

They do not interact with the outside world at all.

They're irrelevant to bonding.

Exactly.

The valence electrons are the ones in the absolute outermost shell.

They are the ones actually doing the business of bonding.

Lewis theory basically says just ignore the core entirely, focus entirely on the valence.

Okay.

So that is the who.

What about the how?

That leads to the next two fundamental ideas.

You can get that stable noble gas configuration in two different ways.

The first is ionic bonding.

This is where electrons are actually physically transferred.

Usually a metal literally gives an electron away to a non -metal.

So it is transaction.

I give you a take and that creates ions.

One becomes positive because it lost an electron and one becomes negative because it gained one.

And then opposite charges attract each other.

Okay.

And the second way, covalent bonding.

This is where electrons are shared.

No atom gives it up completely.

We just agree to hold onto the electrons together.

And the fourth idea is the rule that governs this whole process, the octet rule, the relentless drive to acquire eight outer shell electrons.

Eight is the magic number because that is exactly what neon and argon have.

Now, Lewis didn't just write this out in dense paragraphs.

He drew it.

And we really have to talk about Lewis symbols.

This is the famous dot system.

It is a beautifully simple visual system.

You take the chemical symbol, say capital C, lowercase L for chlorine.

That text symbol represents the nucleus and all those deep core electrons we said we don't care about.

Then you place dots around the symbol to represent only the valence electrons.

But you can't just throw the dots on the page like confetti.

There is a rigid system.

How do I know how many dots to actually draw?

You look directly at the periodic table, specifically the group number at the top of the column.

For the main group elements, those are the tall columns on the left and right.

The group number essentially tells you the valence count.

So group one like lithium gets one dot.

Group two gets two dots.

Then you jump across that middle dip of transition metals.

Group 13 has three dots.

Group 14 has four.

All the way over to group 17, the halogens, which have seven dots.

And group 18, the noble gases has eight.

Except helium.

Helium is the little exception.

It only has two dots.

But for helium, that first small shell is totally full.

So it is perfectly happy with just two.

Okay.

So let's say I am drawing nitrogen.

I look at the table.

It is in group 15.

So I drop the one and I know I have five dots.

How do I place them around the N?

Imagine a square box drawn around the letter N.

You have four sides, top, bottom, left, right.

You place one dot on each side first.

One, two, three, four.

You do not pair them up until you absolutely have to.

So for nitrogen, I have five.

I do four singles on the four sides and then the fifth one.

The fifth one pairs up with one of the other.

So you end up with one pair of dots on one side and three single lonely dots on the other three sides.

That seems really specific.

Does that actually matter?

It matters immensely.

Those three single dots are the hands nitrogen is reaching out to bond with.

It suggests nitrogen typically wants to form three bonds.

The pair of dots, well, that is a lone pair.

It is already satisfied.

It is just going to sit there and watch the action.

Let's apply this directly to ionic bonding first.

The text walks us through example 10 .1, which is sodium chloride.

Right.

Let's visualize it together.

Sodium is N, A.

It's in group one.

So it gets one dot.

Chlorine is C, L.

Group 17.

So it has seven dots.

It is exactly one dot away from the magic eight.

So sodium is a metal.

It is generous.

It is not just generous.

It is eager to get rid of that electron so it can drop down to a stable core shell underneath.

Chlorine is desperate to grab one.

So the dot literally physically moves from the sodium over to the chlorine.

And how do we draw the result of that transaction?

Because they aren't sharing anymore.

We use brackets.

This is a really important piece of notation.

You put the symbol for sodium inside square brackets with a plus sign outside on the top right.

And no dots, right?

Right.

No dots.

We don't draw the empty shell.

Then you put chlorine in its own set of brackets with a minus sign outside.

But inside those brackets, chlorine now has eight dots around it.

It's original seven plus the one it took from sodium.

The text also gives us example 10 -2, which complicates things just slightly.

Barium oxide or BAO.

It is the two dots to lose.

Oxygen is group 16, so it has six dots.

It needs exactly two to reach eight.

It is a perfect trade.

Barium gives both of its dots to oxygen.

So you get barium with a two plus charge and oxygen with a two minus charge in brackets.

Exactly.

But what about magnesium chloride, MgCl2?

That is the tricky one.

Magnesium is group two, so it has two dots to give.

But chlorine, as we established, can only take one.

Right.

If you forced a chlorine atom to take two electrons, it would have nine in its valence shell.

And that violates the basic rules of the universe.

It would be incredibly unstable.

So magnesium is just stuck holding an extra electron.

Well, unless it finds a second chlorine atom, and that is exactly what happens.

One magnesium atom services two separate chlorine atoms.

It gives one electron to the first chlorine and the other electron to the second chlorine.

That makes sense.

That is why the formula is MgCl2.

Now, there is a very important conceptual point the text makes here regarding figure 10 -1.

We write NaCl or MgCl2, but these aren't discrete molecules, are they?

No, and students get this wrong all the time.

An ionic compound isn't a little independent unit of one sodium and one chlorine floating around holding hands.

It is a crystal lattice.

A giant grid.

A massive infinite grid.

Every positive sodium ion is surrounded on all sides by negative chloride ions, and every chloride is surrounded by sodiums.

It extends in all three dimensions.

The formula NaCl is really just the empirical ratio.

It just tells you that for every one sodium in the giant pile, there is one chlorine.

It doesn't describe a distinct physical object the way H2O describes a single water molecule.

That is a fantastic transition to section 10 -2, covalent bonding, because here we actually are talking about distinct independent molecules.

Now we have to ask the obvious question.

Why do atoms share?

Why doesn't hydrogen just give its electron to chlorine the way sodium did?

Hydrogen is really small, and it is not a metal.

Correct.

Hydrogen has a very high ionization energy.

That means it holds onto its one electron very tightly.

It flat out refuses to give it up completely, but it still desperately wants to fill its shell.

And chlorine also wants to fill its shell.

So they compromise.

They share.

The text calls the diagram for this the broken circles diagram.

It is a brilliant way to visualize the accounting fraud that is covalent bonding.

Imagine drawing a circle around the hydrogen atom that includes the shared pair of electrons.

Hydrogen points to the circle and says, look, I have two electrons.

I am stable like helium.

And then you draw a circle around the chlorine.

Right.

You draw a circle around the chlorine that also includes that exact same shared pair.

Chlorine says, look, I have eight electrons.

I am stable like argon.

They are double counting the money in the joint bank account.

Precisely.

And that shared pair of electrons is what we call the bond.

We need to make sure we get the terminology straight here.

We have bond pairs and lone pairs.

Right.

So a bond pair is the shared electrons between the atoms.

We usually represent this with a straight line or a dash drawn between the symbols.

One dash always equals two dots.

A lone pair consists of the electrons that belong to just one atom.

They are not involved in the bond at all.

They are just sitting there.

Yeah.

They are usually just drawn as standard dots.

So in the HCl molecule, you have a solid line between the H and the Cl.

And then around the chlorine.

You still have those three pairs of dots that didn't do anything.

Three lone pairs.

The text mentions the octet rule in action for molecules like chlorine gas, which is Cl2, water H2O, and dichlorine monoxide Cl2O.

But there is a glaring exception right out of the gate with hydrogen.

Hydrogen follows what we call the duet rule.

It only has one shell, the 1S shell.

And physically, that shell can only hold a maximum of two electrons.

So hydrogen never wants eight.

It only ever wants two.

It wants to be like helium.

Before we move on to polarity, there's this really interesting concept mentioned here called the coordinate covalent bond.

This is a fascinating little nuance in bonding.

Usually in a standard covalent bond, it is a potluck dinner.

I bring a dish, which is an electron, and you bring a dish, and we share the meal.

But in a coordinate bond, I bring the entire meal, and you just show up to eat.

One atom contributes both electrons to form the shared pair.

The text uses the ammonium ion NH4 plus as the primary example.

Let's build that so the listener can picture it.

Okay, start with a regular ammonium molecule,

NH3.

You have a nitrogen in the middle with three single bonds to three hydrogens.

And nitrogen has a lone pair of dots sitting on top of it.

It has eight electrons.

It is full, and it is happy.

Then along comes a hydrogen ion,

an H plus.

Which is literally just a naked proton.

It has absolutely zero electrons.

It is chemically desperate.

The nitrogen looks at it and says, don't worry, I have a lone pair right here, not doing anything.

We can share mine.

So nitrogen pays for the whole dinner.

Basically, yes.

But here is the absolutely key concept the text stresses.

Once that coordinate bond is formed, you cannot tell it apart from the other regular bonds.

In the final ammonium ion, all four N to H bonds are identical in length and identical in strength.

It doesn't matter where the electrons came from originally.

Exactly.

Once they are in the bond, they are just a shared pair holding two atoms together.

Okay, let's move into section 10 -3.

This is where things start getting colorful.

Polar covalent bonds and electrostatic potential maps.

This section is critical because it debunks a massive binary myth that students hold.

People often think a bond is either strictly ionic where it is transferred, or strictly covalent where it is shared equally, black or white.

But chemical reality is a spectrum.

Most bonds fall somewhere in between those extremes.

Right.

Unless you have two completely identical atoms pulling on the electrons like in Cl2, the sharing of the electrons is not going to be perfectly equal.

One atom is always going to pull harder on the rope.

This unequal sharing creates what we call a polar covalent bond.

And we denote this unequal distribution with that lowercase Greek symbol delta, right?

Delta plus and delta minus.

Exactly.

Delta plus means partial positive and delta minus means partial negative.

It is not a full -blown integer charge like an ion.

It is not a plus one or a minus one.

It is a fraction.

Maybe a plus 0 .2 or a minus 0 .2.

It is just a skew in the electron cloud.

The text relies really heavily on electrostatic potential maps to illustrate this.

Since our listeners obviously can't see the textbook, paint a picture for us.

The text calls it the rainbow model in figure 10 -4 and 10 -5.

Imagine a fuzzy 3D blob shape representing the entire molecule.

The color of the blob tells you exactly where the electron density is concentrated.

Red represents the low electrostatic potential end, which somewhat counterintuitively means high electron density.

Think of red as hot with electrons.

It is the negative side.

Exactly.

And blue represents low electron density.

It is the positive side, positive potential.

Then green or yellow is just intermediate neutral territory.

If we look at the map for C -A -L, two chlorine gas mess.

It is totally uniform, just a solid color, usually shown as a yellowish green blob in the text because the electrons are shared perfectly equally between the two identical chlorines.

It is entirely nonpolar.

There is no red side and no blue side.

If you look at sodium chloride, N -A -C -L.

You see a very distinct blue sphere representing the sodium cation sitting right next to a very distinct red sphere representing the chloride anion.

The colors don't really blend.

The electrons have totally left the building on the sodium side.

That is a purely ionic interaction.

In the middle ground.

The polar covalent H -C -L.

It looks like a gradient.

The hydrogen end of the blob is distinctly bluish and the chlorine end is yellow green shading into red.

It visually shows that the electrons are drifting heavily toward the chlorine, but they haven't completely abandoned the hydrogen yet.

So what actually drives this drift?

What makes chlorine the obvious winner in that tug of war?

Electronegativity.

This is a huge foundational concept.

It is defined specifically as an atom's ability to compete for electrons within a molecule.

How is that actually different from electron affinity?

Because we learned about that in previous chapters.

It's a great question.

Electron affinity is a measurable energy.

It is about an isolated single atom in the gas phase grabbing an electron from empty space.

It is a solo sport.

Electronegativity is an arbitrary scale about an atom in a bonded relationship pulling on a shared rope.

It is a team sport.

The text shows the periodic trends for this in figure 10 -6.

The general trend is pretty simple to remember.

Electronegativity increases as you go from the bottom left of the periodic table to the top right.

Fransium down in the corner is the lowest at 0 .7.

Fluorine up in the top right is the absolute king of electronegativity at 4 .0.

Fluorine is just the ultimate electron hawk.

Absolutely.

Oxygen is a close second at 3 .5.

Nitrogen and chlorine are tied for third at 3 .0.

So we can use the mathematical difference in these values, the delta E n, to classify bonds.

Yes.

Figure 10 -7 gives us the standard guidelines.

You just subtract the smaller number from the larger one.

If the difference is small, roughly 0 to 0 .4, we call it nonpolar covalent, like carbon, which is 2 .5, and hydrogen, which is 2 .1.

The difference is only 0 .4.

Right.

And that is exactly why oils and fats, which are just long chains of carbon and hydrogen, are nonpolar and don't mix with water.

If the difference is moderate.

Between 0 .4 and about 2 .0, it is polar covalent, like our HCL example.

The difference there is 0 .9.

And if it is large?

Greater than 2 .0, it is usually considered ionic.

The difference in pull is so massive that sharing simply stops and complete transfer happens.

The text works through a really interesting comparison, an example 10 -5, comparing NaH and NaF.

And this one is genuinely tricky.

It is tricky.

Both involve sodium.

Sodium fluoride, or NaF, is textbook ionic.

Fluorine is 4 .0.

Sodium is 0 .9.

The difference is a massive 3 .1.

Right.

But sodium hydride, or NaH, the difference between hydrogen at 2 .1 and sodium at 0 .9 is only 1 .2.

Technically speaking, based on the numbers that falls right in the middle of the polar covalent range.

But experimentally, we treat it as an ionic compound.

Why is that?

Why does it break the rule?

Because of the electrostatic maps.

The map for NaH shows a huge, distinct red blob for the hydrogen.

Why?

Because the hydride ion H - is structurally massive compared to the tiny little fluoride ion.

It's fluffy.

Exactly.

The electron density is spread out over a huge volume.

The text uses this specific example to remind us of a harsh reality.

Electronegativity is a great guideline, but physical size and polarizability matter just as much in the real world.

Let's get deeply practical now.

Section 10 -4, writing Lewis structures.

The text gives us a central strategy, a real step -by -step guide in figure 10 -8.

If I am a student staring at a blank exam page, how do I even start?

You absolutely need a system.

If you try to just guess where the docs go, you will fail.

Step one, count the total valence electrons.

Sum up all the valence electrons for every atom in the molecule.

Okay.

If the whole thing is an anemone and has a negative charge, you add extra electrons to your total.

If it is electrician with positive charge, you subtract electrons.

This final number is your strict budget.

You cannot spend more dots than you have in your budget.

Step two, the skeleton.

You have to decide which atom goes in the very middle.

The general rule of thumb is the central atom is usually the one with the lowest electronegativity.

It is the one that is most willing to share its electrons in multiple directions.

And what about hydrogen?

Hydrogen is strictly always terminal.

It goes on the outside.

Since it can only ever make one single bond, it can never act as a bridge in the middle of a molecule.

Step three, draw the single bonds.

Right.

Connect everything to the central atom with a single straight line.

And remember, bookkeeping is key here.

Each line you draw costs you exactly two electrons from your total budget.

Step four, fill the octets of the terminal atoms first.

Give the outside atoms enough dots to reach their eight or two for hydrogen.

Be generous to the outsiders first.

Subtract those from your budget.

Step five, dump the leftovers.

If you miraculously have any electrons left over in your budget after step four, you simply place them on the central atom as lone pairs.

And finally, step six, which I always call the fixer step.

This is the crucial troubleshooting step.

If and only if the central atom still doesn't have a full octet of eight after you have spent your entire budget, you have to borrow.

You take a lone pair of dots from one of the terminal atoms and you fold it in to make a double bond with the center.

Let's walk through this process using example 10 -6, writing the structure for cyanogen, which has the formula C2N2.

Okay, step one, count the budget.

Carbon is in group 14, so it has four.

Nitrogen is group 15, so it has five.

We have two of each.

So two times four is eight, plus two times five is 10.

Eight plus 10 gives us a total budget of 18 electrons.

Step two, the skeleton.

Carbon is less electronegative than nitrogen, so the carbons go in the middle.

Right.

So the chain looks like N connected to C, connected to C, connected to N.

Step three, draw the single bonds.

We have three connections to make.

That is three lines.

Each line is two electrons, so three times two is six.

Eighteen minus six leaves us with 12 electrons in our budget.

Step four, fill the terminal atoms.

The nitrogens on the far ends each currently have one bond, so they have two electrons.

They need six more dots each to reach their octet.

So we put six dots on the left nitrogen and six dots on the right nitrogen.

That costs exactly 12 electrons.

And our budget is now zero.

We are out of money.

But we have a huge problem.

Look at the two carbons in the middle.

Each carbon only has two single bonds attached to it.

One to a nitrogen and one to the other carbon.

That is only four electrons.

They are starving.

They desperately need eight.

So we have to use step six.

Right.

We look at the terminal nitrogens.

They have plenty of lone pairs.

The left nitrogen takes one of its lone pairs and pushes it down into the space between itself and the carbon to form a double bond.

Is that enough?

The carbon now has six electrons.

Still not eight.

So the nitrogen pushes another lone pair in.

Exactly.

Now we have a triple bond between the nitrogen and the carbon.

And we do the exact same thing on the other side.

So the final structure reading left to right is a nitrogen with one lone pair triple bonded to a carbon which is single bonded to another carbon which is triple bonded to a nitrogen with one lone pair.

Perfect.

Every single atom in that chain now has access to exactly eight electrons.

And we stayed perfectly within our 18 electron budget.

That is extremely satisfying.

But sometimes you can draw structure a few different ways that all seem to magically follow the octet rules.

How do we objectively know which version is the right one?

This introduces the concept of formal charge.

Formal charge is essentially an artificial bookkeeping method.

It helps us evaluate the quality of a Lewis structure.

It basically tells us if the electrons are sitting where they actually want to be based on the atom's nature.

What is the actual calculation for it?

The formula in the text is a formal charge equals the number of valence electrons the atom brought minus a sum of its lone pair electrons plus half of its bonding electrons.

Or more simply what I brought to the party minus what I physically own right now.

Example 10 -8 uses nitrosyl chloride and OCl.

We know nitrogen and oxygen are bonded together.

Yeah.

But is the chlorine attached to the oxygen or the nitrogen?

You could theoretically draw O -N -Cl or you could draw O -Cl -N.

And if you play with the double bonds and lone pairs, both of those skeletons can actually perfectly satisfy the octet rule for every atom.

But let's check the formal charges.

Okay.

In the O -Cl -N skeleton where oxygen is bonded to chlorine if you run the math, oxygen ends up with a formal charge of positive one.

Oxygen with a positive charge.

That feels wrong.

It is extremely wrong.

Oxygen is the second most electronegative element in the entire universe.

It absolutely hates being positive.

It violently wants to be negative.

So a structure that forces oxygen to bear a positive charge is inherently unstable.

It is just wrong.

But if you draw the skeleton as O -N -Cl.

In that arrangement, oxygen gets a formal charge of minus one or zero, depending on exactly where you put the double bond.

Chlorine gets zero.

Nitrogen gets zero.

This puts any negative charge squarely on the oxygen, which is exactly where it naturally belongs.

So O -N -Cl is the clear winner.

So to summarize the rules for formal charge.

One,

the sum of all the formal charges must equal the overall charge of the molecule.

Two, the smallest formal charges closest to zero are always the best.

And three, any negative formal charge should sit on the most electronegative atom.

Correct.

It is the ultimate tiebreaker for structures.

Section 10 -5 brings us to a really famous historical problem.

The structure of ozone O3.

Ah, the ozone problem.

This is a classic.

If you strictly follow the rules and draw the Lewis structure for ozone, you have 18 electrons to spend.

You inevitably end up with a central oxygen atom that has a double bond to the left oxygen and a single bond to the right oxygen.

Which would logically imply that the molecule has two completely different types of bonds.

A really short strong double bond on one side and a much longer weaker single bond on the other.

Exactly.

But experimental data, and remember in chemistry, experimental data always, always wins, shows that both bonds in the ozone molecule are completely identical.

They are the exact same length.

They are physically halfway between a single and a double bond.

So our drawing is just wrong.

The drawing is insufficient.

Static ink on paper simply cannot capture the fluid quantum reality of the electrons.

And this introduces the concept of resonance.

When a single static Lewis structure cannot describe the molecule accurately, the true reality is an average or a blend of multiple valid structures.

We draw this on paper with a double headed resonance arrow between the two options.

One drawing with the double bond on the left and one drawing with the double bond on the right.

Yes.

But, and I literally cannot stress this enough because everyone gets confused, the molecule is not rapidly flipping back and forth between the two states.

It is not a double bond on the left for one microsecond and then a double bond on the right for the next.

It is a resonance hybrid.

You actually have a really great analogy for this hybrid concept.

Think of a mule.

A mule is a genetic hybrid of a donkey and a horse.

A mule does not spend Mondays being a donkey and Tuesdays being a horse.

It is a mule 100 % of the time.

It combines the physical traits of both animals simultaneously.

Ozone is a chemical mule.

It has bonds that are effectively 1 .5 bonds all the time.

The text also briefly mentions benzene C6H6 here as another famous resonance hybrid.

The classic hexagonal carbon ring.

We draw it with alternating double and single bonds around the hexagon.

But in reality, those pi electrons are completely delocalized, smeared evenly around the whole ring.

It is a perfect symmetrical hexagon.

Okay.

Section 10 -6, exceptions to the octet rule.

Because, of course, nature does not always care about our neat little human rules of eight.

Never.

There are three main categories of rule breakers here.

The first category is odd electron species.

Also known as free radicals.

Yes.

Molecules like nitrogen monoxide, NO.

Nitrogen brings five valence electrons.

Oxygen brings six.

The total is 11.

You literally cannot pair everyone up if you have an odd number.

It's mathematically impossible.

Someone is going to be left holding the bag with a single unpaired lonely electron.

And that makes them highly reactive, right?

Extremely reactive.

That one unpaired electron is absolutely desperate to find a partner to pair with.

That is exactly why free radicals are so dangerous in biological systems.

They will violently rip electrons off of your DNA or your cell walls just to satisfy themselves.

They are also paramagnetic, which means they are weakly attracted to external magnetic fields.

Exception category two is incomplete octets.

This is small club, mostly just boron and beryllium.

They are the chemical minimalists.

Boron is in group 13.

It only has three valence electrons to its name.

Even if it shares all three of them in three single bonds, it only ever gets to a total of six.

And it's just happy with that.

It tolerates it.

Boron trifluoride BF, three forms with just six electrons around the central boron.

It is stable enough to sit in a bottle.

However, the text notes it acts as a Lewis acid.

It is very open to accepting a donated pair of electrons from a richer molecule like ammonia to finally complete that octet.

But it doesn't strictly need it to survive.

And then we have exception three,

expanded valence shells.

This is a really big one.

This is by far the most common exception you will see.

Elements in period three of the table and beyond.

So we are talking phosphorus, sulfur, chlorine, xenon.

They can routinely handle more than eight electrons.

They can happily hold 10 or even 12.

Why them and not elements like carbon or nitrogen?

Because starting in period three, that third energy level, you finally have access to the d orbitals.

Think of the d orbitals as an empty dusty attic in the atom's house.

Carbon only has a one story house.

It has an s room and a p room.

No attic.

It physically cannot fit more than eight.

But phosphorus.

The phosphorus has a third floor attic.

It normally uses the s and p rooms.

But if it absolutely needs to, it can stash extra electrons up in the empty d orbitals.

The text gives examples like phosphorus pentachloride PCL5, which sources 10 electrons around the phosphorus.

And sulfur hexasolide SF6, which forces 12.

And this brings up a really interesting debate the text touches on with sulfuric acid H2SO4.

You can theoretically draw it perfectly obeying the octet rule for every atom.

But if you run the formal charge calculations, the charges are terrible.

Pluses and minuses everywhere.

But if you intentionally expand sulfur's octet to 12 by making double bonds to the top and bottom oxygens, the formal charges all magically drop to zero.

The expanded shell model is often preferred because it reflects that lower energy state.

Sulfur uses its attic specifically to lower the energy of the whole house.

Okay, so we have drawn the 2D molecules.

We have checked all the accounting with formal charges.

Now we finally need to pop them off the flat page and into 3D space.

Section 10 -7, VSEPR theory.

VSEPR, valence shell electron pair repulsion.

It is a terrible acronym, but the underlying concept is beautifully intuitive.

Electrons are entirely negative.

Negatives fundamentally repel each other.

They hate each other.

They want to be as far apart from each other as physically possible.

So if you are the central atom,

your surrounding electron groups are going to arrange themselves to maximize their personal space.

Correct.

And it is vital to note that groups means both bonding pairs and lone pairs.

They all count equally as regions of negative electron density that repel.

Let's walk through these geometry groups visually for the listener.

This is an audio medium, so we really need to paint a 3D picture.

Let's start with just two groups around the center.

Okay, imagine you are the central atom.

You have two balloons tied to your waist.

Where do they naturally go to avoid each other?

They push apart until they are sticking out on completely opposite sides of you.

That geometry is called linear.

The bond angle is a perfect 180 degrees.

An example is beryllium chloride, BECL2.

What if you have three groups?

You tie three balloons together.

They form a flat equal triangle.

Think of a classic Mercedes -Benz hood ornament.

That shape is called trigonal planar.

The angle between them is exactly 120 degrees.

Example is boron trifluoride BF3.

Four groups.

Now, this is the one everyone gets wrong on their first try if they only think in two dimensions.

Right.

If you draw four groups on a flat piece of paper, you draw a cross or a plus sign and you think, oh, it's a square.

The angles are 90 degrees.

But we live in a three -dimensional universe.

If you use the z -axis, the depth, you can actually spread them out much further than 90 degrees.

Right.

Think of a sturdy camera tripod with a stick pointing straight up out of the top.

One leg points up, three legs point down and away.

That beautiful 3D shape is a tetrahedron.

The geometry is called tetrahedral.

The angle widens out to 109 .5 degrees.

Methane CH4 is the classic textbook example.

Stepping up to five groups.

Now it gets a little weird.

You basically combine the shapes.

You have a flat triangle of three atoms spinning around the equator.

They are 120 degrees apart.

And then you have one atom pointing straight up like the North Pole and one pointing straight down like the South Pole.

Those are the axial positions.

This whole geometry is called trigonal bipyramidal.

It uniquely has two different internal angles.

90 degrees between the poles in the equator and 120 degrees around the equator itself.

Phosphorus pentachloride PCL5 takes the ship.

And finally, six groups.

This is octahedral geometry.

Everything is perfectly symmetric again.

Top, bottom, left, right, front, back.

Everything is exactly 90 degrees apart.

It looks exactly like a metal jack.

You know the little toy you step on in the dark and completely ruin your foot.

Sulfur hexafluoride SF6 is a perfect octahedron.

Now here is a really critical distinction the text makes that trips up so many students.

Electron group geometry versus molecular geometry.

This is the ultimate trap.

You have to read the question carefully.

Electron geometry counts absolutely everything.

It counts the visible bonds and the invisible lone pairs.

It tells you where all the electron clouds are pointing.

But molecular geometry.

Molecular geometry describes only the physical positions of the atoms themselves.

We cannot literally see the lone pairs with our instruments in the final shape, but they act as these invisible ghosts that shove the actual atoms around.

And the text makes a very specific point that these invisible lone pairs are physically fat.

They absolutely are.

Think about a bonding pair of electrons.

It is stretched tight between two positive nuclei.

It's pulled thin like a taut rubber band.

But a lone pair is only anchored by one single nucleus.

So the other end just balloons out into space.

It takes significantly more volume and therefore it repels its neighbors much harder.

So let's look at how this changes ammonia NH3.

Right.

So count the groups on nitrogen.

It has three single bonds to hydrogen and one lone pair sitting on top.

That is four total groups.

So the underlying electron geometry is tetrahedral.

The ghosts and the atoms are arranged in a tetrahedron.

But what is the actual molecular geometry?

What do we see?

We ignore the invisible lone pair at the top when naming the shape.

What is left over?

It looks like a camera tripod with the top camera removed.

A pyramid with a triangle base.

So we call it trigonal pyramidal.

And what about that tetrahedral 109 .5 degree angle?

Because that lone pair sitting on top is so fat, it pushes down hard on the three hydrogen legs and squishes them closer together.

It physically squeezes the angle down from 109 .5 to about 107 degrees.

And water H2O is even more extreme.

Water's oxygen has four groups.

Two bonds to hydrogen and two lone pairs.

So the electron geometry is still tetrahedral.

But the molecular geometry.

We erase the two lone pairs from our vision and we are left with a V shape.

We literally just call it bent geometry.

And the angle gets squeezed even more right.

Yes, those two fat lone pairs are fighting for space at the top and they brutally squeeze the hydrogen atoms together at the bottom.

The angle drops all the way down to 104 .5 degrees.

So water is bent specifically because of these invisible electron ghosts pushing down on the hydrogen atoms.

Exactly.

The text also walks through some really complex geometries for the five group category.

Things called seesaw or T shaped.

This happens when you start replacing atoms with lone pairs in that trigonal bipyramidal structure.

The golden rule here is that lone pairs will always always take the equatorial positions first.

Why do they prefer the equator?

It is entirely about legroom.

The equatorial seats are spaced 120 degrees apart.

The axial north and south seats are incredibly cramped at only 90 degrees.

Fat lone pairs absolutely demand the bigger seats.

So if you have five groups but one is a lone pair like an SF4.

The lone pair takes an equatorial seat.

If you look at the remaining four atoms and turn it on its side, it looks exactly like a playground seesaw.

If you have two lone pairs like CLF3.

They take two equatorial seats.

The remaining atoms form a rigid T shape.

And if you have three lone pairs like the triadide ion I3 -.

All three lone pairs take the entire equator.

The three remaining atoms are just the north pole, the center, and the south pole.

They are left in a perfectly straight line So the molecular geometry is just linear again.

It is basically just the 3D logic puzzle.

You place the fat invisible ghosts in the biggest available rooms.

And then you just name the shape that the actual atoms are forced into.

Exactly.

One last note on VSPR before we move on.

Multiple bonds?

Right.

For the strict purposes of VSPR counting a double bond or a triple bond only counts as one single electron group.

We call it a super group.

It is physically larger and contains more electrons but it only occupies one directional slot in the overall geometry.

Okay, moving on to the homestretch.

Section 10 -8.

Bond order and bond lengths.

Very simple intuitive definitions here.

Bond order is just the sheer number of bonds between two atoms.

A single bond has a bond order of one, a double bond is two, a triple bond is three.

And the physical trend associated with that.

The higher the bond order, the shorter the physical distance between the atoms.

A triple bond pulls the two nuclei together much tighter than a single bond does.

It's like using three heavy -duty rubber bands to connect two blocks of wood instead of just one.

The blocks are going to get pulled closer together.

The text actually mentions estimating these lengths in example 10 -14.

Yeah, you can roughly estimate the length of a mixed bond like bromine bonded to chlorine by just mathematically averaging the measured covalent radii of the pure elements.

You average the length of a Br -Br bond and a Cl -Cl bond.

It is a simplification, but it works surprisingly well for estimates.

Which brings us to our final major section.

10 -9.

Bond energies.

This is where we actually pay the bills.

Thermodynamics.

Energy is all about the breaking and forming of bonds.

Here is the golden unbreakable rule you must memorize.

Breaking a bond always, always costs energy.

It is always an endothermic process.

Yes, you always have to put physical energy into the system to snap the stick in half.

So the bond dissociation, energy variable D, is always listed as a positive number.

And forming a chemical bond.

The exact opposite.

Forming a bond always releases energy out into the universe.

It is exothermic.

Atoms fundamentally want to bond.

They fall into a much lower, more stable energy state when they finally click together.

So we can actually use these individual bond energies to calculate the total enthalpy of reaction for a whole chemical equation.

The delta H.

This is a fantastic alternative method if you don't happen to have the standard enthalpies of formation tables handy.

The formula is given as equation 10 .26.

Delta H equals the sum of the bond energies broken minus the sum of the bond energies formed.

So it's essentially the total cost to break everything apart minus the total payoff from making the new stuff.

Exactly.

Let's walk through example 10 -15 to prove it.

The reaction of methane CH, four gas plus chlorine Cl, two gas reacting to form chloramethane CH, three Cl, and hydrogen chloride HCl.

Okay, so first we have to visualize the structures.

On the reactant side, methane has four individual C to H single bonds.

Chlorine has one Cl to Cl single bond.

And on the product side, chloramethane has three C to H bonds and one new C to Cl bond.

And the HCl molecule has one new H to Cl bond.

So looking at that, we don't actually need to break every single bond in the molecule.

We just need to see what actually changed.

Right.

Be smart about your math.

Three of the C to H bonds survived perfectly intact.

We only actually broke one C to H bond and one Cl to Cl bond.

That is our total cost.

So looking at table 10 .3 in the text, breaking one C to H bond costs positive 414 kilojoules.

Breaking the Cl to Cl bond costs positive 243 kilojoules.

So 414 plus 243 gives us a total energy cost of positive 657 kilojoules to break the reactants.

And then we calculate the payoff on the other side.

We formed one entirely new carbon -chlorine bond and one new hydrogen -chlorine bond.

Forming a C to Cl bond pays out 339 kilojoules.

Forming an H to Cl bond pays out a massive 431 kilojoules.

So the total payoff is 339 plus 431, which equals 770 kilojoules.

So to find the net delta H, you take the cost of 657 and you subtract the payoff of 770.

Which gives a net change of negative 113 kilojoules.

That negative sign is everything.

It means the overall reaction is exothermic.

It releases 113 kilojoules of heat out into the environment.

And structurally this makes perfect sense because the new bonds we formed were mathematically stronger than the old bonds we broke.

That new HCl bond at 431 is vastly stronger than the weak Cl bond at 243 that we broke.

That raw difference in stability is the engine that drives the reaction forward.

Nature always prefers to form strong, stable bonds.

Well, we have covered a truly massive amount of ground today.

From simple Lewis dots on a page to 3D octagons to calculating the thermodynamic heat of a reaction.

It's quite a structural journey.

We literally started with counting simple dots and ended up being able to predict the energy release of chemical explosions.

But as we wrap up this deep dive,

we do have to drop a little bit of a reality check.

The text explicitly mentions a provocative thought for the end of the chapter.

We have spent an entire hour heaping praise on Lewis theory.

It is brilliant.

It explains 90 % of what you will ever need to know for general chemistry.

But, and it is a big dump, but it does fail sometimes.

Where exactly does it fall apart?

The absolute classic failure is with pure oxygen gas O2.

If you draw the Lewis structure for O2, you get a neat little double bond and every single electron is perfectly paired up.

Right.

Everything has an octagon.

Now in physics, if all electrons in a substance are perfectly paired up, the substance should be diamagnetic, meaning it should be very slightly repelled by a magnetic field.

But if you physically pour liquid oxygen gas directly through a powerful magnet, like they actually show in a photograph in figure 10 -3, it sticks.

The liquid oxygen literally hangs in midair, completely trapped between the magnetic poles.

It is strongly paramagnetic, which proves unequivocally that it acts like it has unpaired electrons.

But our perfect Lewis structure clearly says it doesn't have any unpaired electrons.

Exactly.

Lewis theory simply cannot explain why oxygen is magnetic.

The model is fundamentally incomplete when it comes to oxygen.

To truly understand that bizarre magnetic behavior, you have to abandon the docks and move to a much deeper, more advanced theory called molecular orbital theory, which coincidentally just happens to be the primary subject of chapter 11.

There's always a bigger fish in chemistry, isn't there?

Always.

Every model is just an approximation.

But for today, for this test, just master the dots, master the 3D shapes, and always respect the power of the lone pair.

A very warm thank you for listening from the Last Minute Lecture team.

Go ace that chemistry test.

Good luck, everyone.

See you next time on the Deep Dive.