Hybridization

VSEPR theory does a nice job of predicting the structure and shape of molecules in three-dimensional space. However, it does NOT explain how those shapes happen. In other words, it does a great job of predicting that CH₄ will be a tetrahedron, but NOT how the s and p orbitals found in an atom of carbon can justify the 109.5^o angles in that tetrahedron.

We'll use methane (CH₄) as our exemplar to understand this process.

Let's think about the C atom at the center of methane. The electron configuration for a carbon atom is 1s², 2s², 2p². So there are 4 valence electrons to make the 4 single bonds found in methane. That seems to make sense. However there is a problem. Two of those electrons are paired up in the 2s orbital and are not available to "partner" with an electron from a hydrogen atom.

A potential solution?

We could move one of the s electrons to the empty p orbital. That would give us 4 unpaired electrons.

Of course, there are several problems with this as a solution:

a) there is NO justification for this happening. (This is not a minor problem.)

b) It doesn't really solve the problem. Although we now have 4 electrons available for bonding, they aren't the same. 

There are two aspects to the problem. Here they are in detail. 

Problem 1: 

Three of those electrons are in p orbitals and one is in an s orbital. That means that they will interact with other electrons differently. We don't even need to worry about HOW they will be different (stronger/weaker, shorter/longer). It only matters that they will be different. Methane has 4 bonds that are all IDENTICAL. That tells us that this solution is wrong.

Problem 2: 

p orbitals exist at 90^o angles to each other. The s orbital is spherically symmetric around the nucleus. So, if we use these orbitals for bonding, we should have three  bonds at 90^o to each other and one that has no defined bond angle and which, as a result can move around. This is definitely not what we find in the (perfectly symmetric) molecule of methane.

A Better solution - hybridization

Rather than just shift an electron from one atomic orbital to another, hybridization suggests that the orbitals of an atom are changed by bonding. In other words the approach of 4 hydrogen nuclei and their electrons causes changes in the electron structure of the carbon atom.

In simple terms, hybridization is a blender for orbitals and we are going to make an orbital smoothie. When you put yogurt, bananas and strawberries into a blender, what comes out is no longer any ONE of those things, but rather something that combines the properties of all of them.

When we take the 4 orbitals of carbon and put them in the hybridization blender, we pour out orbitals that are neither s nor p orbitals, but rather some blend of the two.

Since we put four orbitals (s, p_x, p_y and p_z) into the blender, we will pour out four orbitals, but now all 4 are the same (same shape, same energy). That means that using Hund's rule, we can logically spread the 4 electrons out between them.

The label beneath the orbitals (sp³) is essentially the recipe. We put in a s orbital and 3 different p orbitals, so what came out of the blender were 4 sp³ orbitals.

In addition, since all four of these orbitals are identical, it makes sense for them to be spread evenly around the nucleus in 3-dimensional space - which just happens to be a tetrahedron.

Applying our "solution" beyond methane

Hybridization does an admirable job of explaining tetrahedrons in this way but, of course, there are other shapes and structures. If your goal is only to "get the right answer, go to the table at the bottom of the page, if you are curious where this goes...read on.

Covalent bonds can be classified as either sigma (σ) bonds or pi (π) bonds.

σ bonds form as an "overlap" along the line between the two nuclei (what you normally think of as a bond. The first bond formed between any two atoms is ALWAYS a σ bond.

pi bonds form in two pieces - above and below the line between the nuclei. Second and third bonds formed between atoms are π bonds. So, if two atoms have a triple bond between them, they have formed one σ bond and two π bonds.

π bonds can only be formed from orbitals that have two parts. In other words,a  π bond can only be made from p orbitals.

Because hybrid orbitals are so lopsided, they cannot form π bonds. That means that if an atom is making a π bond, it must have a p orbital that has NOT be hybridized. If the atom is making 2 pi bonds, it must have 2 un-hybridized orbitals.

Combining all of those ideas means that an atom making a double bond (perhaps oxygen, as seen here in this diagram from the earlier bonding pages)

each oxygen must keep 1 p orbital "out of the blender" to make the pi bond. That means that only 2 of the p orbitals went in the blender. The hybrids that are "poured" out of the blender are called sp² orbitals. The resulting three orbitals will then arrange themselves into a trigonal planar structure at 120^o.

A full list of the possible hybridizations and structures is in the table below.

Why aBetterChemText?

What is aBetterChemtext?

aBetterChemText is intended to be a new way to look at Chemistry. It is written in plain English to make it accesible and is designed to be ever growing and expanding. As it grows, the Text is webbed, rather than strictly linear, to acknowledge the interconnections that link all aspects of chemistry and to allow students and teachers to move seamlessly through the material in any order that they deem appropriate.

You can find a list of the "Big Topics" (think chapters) on the right.

You can also find a google translate button there. The automatic translation may not be great...but it's a step in the right direction.

Tyndall Effect

The Tyndall Effect is the term used to describe the scattering of light by tiny particles.

(Note: light scattering is actually a quite complex idea and there are various types of scattering that occur based on several factors like the relative size of the light wavelength and the size of the particles. These issues are well beyond the scope of this text.)

Remember that light travels in waves.

When a particle gets in the way of that wave of light, the light may be deflected.

We see this in a movie theater when you look up and can see the movie going to the screen.

In order to see the movie on the screen, the projector shines light at the screen. The light bounces off of the screen and goes into your eye.

In order for you to see the "beam" of light traveling TO the screen, the light would have to change direction on the way.

Since we know that light travels in straight lines, the only way that this is possible, is if the light was re-directed by particles in the air. In a theater, those particles are generally dust.

This same effect is related to why the sky is blue.

Osmotic Pressure

Osmotic Pressure is a (not-so-great) name for the process that shrivels slugs when they encounter salt and prevents honey from rotting.

To understand this idea, we need to start with osmosis. In biology class, osmosis is defined this way:
Osmosis is the movement of water through a semi-permeable membrane from an area of high concentration to low concentration.
Let's pull that apart.

Permeable means that things can go through. So, a permeable membrane is one that allows things to move through it. Essentially, a permeable membrane is a membrane with holes.

SEMI-permeable would mean a membrane with holes that are large enough for some things to go through, but small enough to block other things.

Specifically, the holes are large enough for water to go through.

Remember that when something (like table salt) dissolves, the pieces of the solute are surrounded by water molecules.

Because those solute particles and water molecules move together, these "clumps" area too large to move through the membrane.

It is important to realize that there is no "need" for water particles to go through. The molecules are moving randomly. Some of those particles will go through the membrane simply because they can.

So, if the only thing present on one side of the membrane is water, then (effectively) 100% of the particles "can" go through the membrane.

At the same time, if the other side of the membrane has some water and some solute, less than 100% of the particles "can" go through that membrane.

The result is that water will go faster in one direction than it will in the other.

We can see this happen, if we set up the equipment below.

In this diagram, we have taken special tube, called a thistle tube (sort of like a funnel with a REALLY long tube) and sealed the top with a semi-permeable membrane.

That tube was then flipped upside down and submerged into a beaker of water.

The tube was then filled with a sugar solution so that the level of the solution matches the level of water in the beaker.

In this set-up, 100% of the water in the beaker "can" move up through the membrane. At the same time, only some of the water in the tube can move out.

Then, because the water can move INTO the tube faster than the water can move OUT of the tube, the level of liquid in the tube will rise.

The final result of this process is a tube sticking into a beaker of water with liquids at different heights. The lat time we looked at this, we were discussing gas pressure. (Think about straws and barometers.) Since this set-up allows osmosis and results in something that looks like pressure, we call this process osmotic pressure.

Slugs

This same process is the reason that salt kills slugs. The skin of a slug is a semi-permeable membrane. Inside that membrane is some water (and other stuff -- but that's bio!). Outside the membrane is the mucus coating (which is water and other stuff -- also bio). As a result some water can move in and some water can move out. Slugs "work" because the rate at which water moves in matches the rate at which water moves out.


If however, you put salt on the slug, the water on the outside will stick to the salt and that water will NOT be able to move in through the membrane. Suddenly, water will be going out (as it always did...not because it is being pulled) but it is not being replaced.

Honey

Osmotic pressure is also the reason that honey (and other thick things like syrup and ketchup) doesn't rot.

Remember (from biology) that rotting is just what happens when bacteria grows on (and eats) something.

Honey is a solution made with a HUGE amount of sugar and a very a small amount of water.

Bacteria can be thought of as little bags of water with a semi-permeable membrane as "the bag." Bacteria thrive when they find themselves in a warm wet environment. Warmth helps them function, but the "wet" part is really important part. For a bacteria to live, it needs to be in a place where water can move in and out  at equal rates.

When a bacteria lands on honey, the water inside the bacteria can move out, but there is so much sugar and so little water in the honey that essentially "no" water moves back in. As a result, the bacteria lose all of their water, dehydrate and die.

The math:

Osmotic pressure can be measured just like gas pressure, in terms of the height of the liquid. Just like the other colligative properties, osmotic pressure depends on the concentration of the solution and can be calculated using the formula:

Where Π is the osmotic pressure, M is the molarity, R is the universal gas constant, and T is the temperature.

Freezing Point Depression

Freezing point depression means that a solution will freeze at a lower temperature than a pure liquid.

For instance, ocean water freezes at a lower temperature than pure water.

The reasons behind this have to do with the structure of ice and the arrangement of water molecules and solute particles in a solution.

Looking at the molecules of water in an ice crystal we see that they are arranged in a very specific 3 dimensional arrangement.

When a solute is dissolved in water, the molecules are arranged very differently - specifically they are arranged around the solute particles.

This means that in a solution, the waters are not arranged "correctly" to form ice. As a result, the waters must be pulled away from the solute particles, so that they can join the forming ice crystal.

To make that happen, the water-water attraction needs to be strong enough to pull molecules away from the solute particles. To make that attraction stronger, we need to slow the particles down (South Street Effect). That means we need to make it colder.

This same effect helps us understand why we put salt on icy sidewalks and streets.

When a crystal of salt falls onto ice, the attraction between the ions and the molecules of water can pull molecules out of the ice crystal, melting it.

The math:

The more solute that is added to a solution, the lower the freezing point goes. In other words, the change in the freezing point is proportional to the concentration of the solution. Specifically, the change in the freezing point can be calculated with the formula:

where &Delta: T is the change in the freezing point, k_f is the freezing point depression constant (which depends on the solvent), m is the molality, and i is the vant Hoff factor.

Temperature (T)

The temperature of a gas is a measure of the average kinetic energy that the particles have. For a complete discussion of this idea and the difference between temperature and heat, go here.

For most of the unit, we just need to understand that the hotter a gas is, the faster the particles move.

If you want to understand Graham's Law, you will need to know a little more. Specifically, you need to know the formula for kinetic energy.

In this equation, the m stands for the mass and v is the velocity of the particle.

This formula means that the when the velocity doubles, the KE (and therefore the T) quadruples. Or, in a more useful form, if the temperature is quadrupled the molecules are moving twice as fast.

In chemistry, temperature is generally measured in degrees Celsius (occasionally called degrees centigrade), symbolized ^oC. This is the unit that most thermometers found in science classrooms and labs measure. However, we cannot use ^oC in mathematical calculations.

For that reason we also use the kelvin scale, measured in kelvins, K. (Note: the Kelvin scale does NOT use a degree symbol.)

Converting between ^oC and K is done according to the equation:

You can understand the relationship between Celsius and Kelvin by imagining a thermometer that records both temperature scales as seen below.

Absolute zero (on the diagram) will be discussed later in the unit.

Suction Cups

Suction cups are, of course, mis-named, since there is no such thing as suction.

A suction cup is simply a flexible piece of material that has wide edges. If this is placed (very gently) against a wall, the pressure pushing out and the pressure pushing in will be equal and the unmatched force of gravity will “win” causing the suction cup to fall.

If, on the other hand, the suction cup is pressed against the wall the situation changes. Pressing the suction cup against the wall flattens it. So, the volume of the space behind the suction cup decreases, thus increasing the pressure of that small amount of air. This high pressure air can then force the edges of the suction cup away from the wall and escape. The net result is that much of the air behind the suction cup is removed.

When the suction cup is released, the material (rubber, silicone, plastic, etc.) returns to its original shape (this is why we don't make suction cups out of steel or wood). When that happens the volume of space behind the suction cup goes up and the pressure goes down. This pressure is now much less that the pressure of the atmosphere. (Remember that the two pressures were the same, but we have lost much of the air that was originally trapped.

As a result, the atmosphere presses the suction cup against the wall much harder than the air behind the suction cup pushed out and the cup is held against the wall with enough force to fight gravity.

Why the Width of a Straw Doesn't Matter

Assuming that you already understand how a straw works, you know that a straw uses the difference between the pressure inside the straw and the pressure outside the straw.

To understand how this relates to the width of a straw, let's look at the pressure down exerted by the water in the straw.

We know (from physics) that

The force in this case is the force of gravity acting on the water. The force of gravity is

where m is the mass of the water and g is the gravitational constant (how hard the Earth is pulling on the water).

We know that

and therefore

Substituting in, we get

The water in the straw is in the shape of a cylinder. The volume of that cylinder (or any cylinder) is

Substituting that formula in gives us

Since area appears on both the top and the bottom of the equation, they cancel and, thus, don't affect the pressure. The width of the straw (which determines the area) is irrelevant.

How we use a straw – the rest of the story

We have already explained how decreasing the pressure in the straw allows the atmosphere to push the liquid up the straw.

What was not discussed, was how the pressure in the straw is decreased in the first place.

It is tempting to say that we reduce the pressure in the straw by inhaling, but that is not correct. Take a moment or two to prove this to yourself. If you have a straw available, use it to drink, but while you are bringing the liquid up the straw, notice that you can inhale and exhale through your nose while you are drinking (obviously not while you are swallowing, though).

If you don't have a straw, or if you have trouble breathing while drinking, try putting a single fingertip in your mouth and sucking on it like a straw. Then, with your cheeks “sucked” in, breathe through your nose. You should be able to breathe both in and out without affecting the “suction” on your finger at all.

Once you are convinced that the “suction” you create with your mouth is not about breathing (if you aren't convinced yet, go back and prove it to yourself – seriously, if you don't, you'll never really get the truth) pay attention to how you create that “suction.” Most people do it by lowering their jaw, although it can be done by lowering your tongue inside your mouth.

What matters most is that, no matter how you do it, you are making the volume of your mouth bigger. We know (Boyle's Law) that when volume goes up, the pressure goes down. So, as a result of dropping your jaw the pressure in your mouth is decreased.

Now, assuming that you have a straw in your mouth, rather than your finger, the pressure of the air in the straw will be more than the pressure of the air in your mouth, so air will be pushed into your mouth.

As a result of that air movement, there will be less air in the straw. We know (the Un-Named Law) that a decrease in amount means a decrease in pressure, so as the air leaves the straw and goes into your mouth, the pressure in the straw will decrease – allowing the atmosphere to push the water up into your mouth.

A last thought... if you are wondering how the width of the straws plays in here, it doesn't.

A Mechanism analogy:

Imagine that you open a doll factory. You rent the factory space, hire the workers and buy all the raw materials for your “Hand-Painted Dolls of famous chemists.”

On the opening day of your business, you give your workers a brief pep talk and then go up to your office and put your feet up on the desk. At the end of the day, you go down to the factory floor and discover that only 6 dolls have been made.

The next morning, you give your workers a stern talking to and then retire to your office and put your feet up on the desk, sure that things will go better today. However, at the end of the day, you discover that only 6 more dolls have been produced.

Pondering the failure of your pep talks to make your workers productive, you decide to sneak down to the factory floor and watch the process.

What you see is this:

• Doll torsos are moving into the main room on a conveyor belt. 
• A woman standing beside the belt sticks two legs onto the torso. 
• Next to her, is a man sticking arms onto the torso. 
• Just down the belt is a college student sticking on a head, 
• and at the end of the line is…
• an old man…
• dipping his paint brush into the paint… 
• and carefully… 
• very carefully...
• painting… 
• each… 
• separate… 
• feature… 
• of the face.

So, you hire more arm stickers, right?

Of course not.

You can probably imagine that at this point, after three days of work, there is a pile of finished, but unpainted dolls piled up at the painter’s feet. The issue is not the production of the dolls (arm, leg and head sticking), but the painting of the faces. The only way to speed up the process is to speed up that step.

What you need to do, of course, is to hire more face painters.

Arm stickers, leg stickers and head stickers have no effect on the rate at all.

Only the face painter affects the rate, because he is SOOOOO much slower than any of the other steps. In fact, those steps could get faster (or even slower) and there would be no change in the rate of doll production.

We could write out a “formula” for the process of doll making, which would look like this:

However, it would be more helpful to look at the steps that occur:

The overall process (similar to a chemical reaction) takes place through a series of steps (together called a mechanism) and only by changing the rate of the slowest step (called the rate-determining-step) can we change the overall rate.

There are two ways that this process can be sped up. By changing the concentration (this has to do with order) and by changing the mechanism (this has to do with catalysts)


Understanding Order - the analogy continues...
Since the last step of the process is clearly the slowest, then anything that can be done to make that step faster will increase the overall rate. For instance if we doubled the number of workers painting faces we could double the rate of doll production, even if both painters were still slow and meticulous.

So, how does this explain 0^th order? How can the concentration of a reactant have NO impact on the rate of the reaction? the answer is rather simple - only those things that are in the slow step can influence the overall rate of the reaction. Hiring more "arm-stickers" will have no effect on the rate of doll production. In the same way, the concentration of anything that does not appear in the slow step will not affect the rate of the reaction, and will therefore be zeroth order.

Understanding "get-involved" catalysts - The analogy continues...
It might be possible to speed up the process by changing it. Perhaps you could find a face stamp, with which a worker could quickly stamp the face onto the doll. In this way the process would be the same (torso + legs + arms + head + paint) but the slow step would be much faster, and thus the whole process would be faster. In this analogy, the face “stamp” would be a catalyst – providing a faster way for the slow step to occur.

How a Straw Works

When water is in a glass it experiences a downward force (gravity) which keeps it in the glass. In order to drink the water through a straw there must be a force up that is stronger than the force of gravity downwards. That means that we must either pull the water up the straw or it must be pushed up the straw.

Before we see which of those possibilities is the correct one, let's make sure we understand the difference between pulling and pushing. Quite simply, pushing is when the force is applied behind the direction of motion and pulling is when the force is applied in front of the direction of motion. The diagram below may help to make that more clear.

So, in order to pull something you need to be able to apply a force from the front.

There are only a few ways to do this. Magnets can apply such a force to each other, as can charged particles (when they are VERY close), but water is not magnetic and no charge is used to drink from a straw.

So, the only way left to pull something is to grab it from the front. However, in this case, this is impossible. You cannot grab water – it has no hooks or handles.

That means that you cannot pull the water up the straw. Really. Can't be done. Don't even try to argue your way out of it. When you drink from a straw, you are NOT pulling the water up the straw.

That leaves only one possibility. The water is pushed up the straw. The obvious question is “by what?” Let's take a look at what is going on in and around that straw. When the straw is just placed into the water the water fills the straw up to the height of the water outside the straw. In this situation, the air above the glass is pushing down on the water both in the straw and around the straw. Since the forces are the same (it's the same atmosphere) the forces are balanced, the water levels are balanced and nothing moves.

It is easiest to imagine this if you picture a see-saw at the bottom edge of the straw. Inside the straw (on that side of the see-saw) the water in the straw pushes down, as does the air in the straw. Outside the straw (on the other side of the see-saw) the water pushed down as does the air outside the straw. Since the height of the water is the same, the pressure from the water is the same in and out of the straw and the air pressure is the same.

When you drink from the straw, you reduce the pressure in the straw. (How you do that will be explained later in the unit.) Suddenly, the forces are unbalanced.

In this case the force down on the inside part of the see-saw is weaker than the push on the outside side of the see-saw. As a result of the unbalanced forces, the water (the see-saw) will move. In this case the water outside of the straw will be pushed down and the water in the straw will be pushed up.

When you drink from a straw, you are actually allowing the water to be pushed up the straw by the atmosphere.

Of course, this doesn't explain HOW you make the pressure in the straw go down. That explanation is here...