Who loves geometry? I do :)
and offcourse Chemistry too! It's indeed a very challenging yet fun subject!
and offcourse Chemistry too! It's indeed a very challenging yet fun subject!
Who would have thought that our Chemistry has geometry in it!
Yes, it molecular geometry.
Do you have any idea what this is? If you are thinking it has something to do with obtuse and acute,proving and well , it's not! :) It's all about the molecular structure.
It is the three-dimensional arrangement of the atoms that constitute a molecule.
Like this! Looks cute right?
It seems like candies or connected lollipops! YUM!
Let's try something!!!
Imagine that you are in outer-space and there is no gravity. 
Now imagine that you have a big ball that can be attached to a bunch of little magnets with some string. 
These little magnets are really powerful. Ever try to push a magnet together the wrong way?
Same idea with the little magnets, they don't want to be anywhere near each other. So if we attach only one magnet to our ball, there's no problem, it can go anywhere around the ball it wants. But then we attach two magnets - all of a sudden they are on exact opposite sides because of how hard the magnetic forces are pushing on each other. What happens then, if we were to attach 3 magnets?
BAM!!!!!
They push each other into a triangle so they can stay as far away from each other as possible. Same thing happens when we add 4, 5, 6, 7, 8 or even more magnets to our ball. Their magnetic forces push them as far apart as they can be while still attached to our ball. This is the basic concept of molecular geometry, only an atoms nucleus is the ball in outer space, and electrons are our little magnets that don't like being close together. The angles between the electrons tell us how far apart they are, with larger angles meaning farther apart, and smaller angles meaning closer together.
Let's go to Electron Geometry
It is important to realize that electron-geometry and molecular-geometry are NOT the same thing, but are related. Keep that in mind as you read. The absolute simplest electron geometry is the one where we only have 2 magnets and they push each other to the opposite sides of the ball. If you measured the angle between the magnets, it would equal 180°. For all of my examples, X will stand for the central atom, and Y will stand for the electrons. I am also using the conventional wedges and dashed lines used in chemistry to indicate depth - if you don't understand them, go here.
This is known as a linear electron geometry.
When you have 3 magnets, they push each other into a triangle where the measured angle is equal to 120°.
This is known as trigonal planar electron geometry.
When you have 4 magnets, things get more complicated because the magnets push each other so that they form a strange shape called a tetrahedral, with angles measuring 109.5°
Some people can imagine a tetrahedral geometry better by pretending to look straight down one of the lines, this makes the other 3 lines appear to be in a triangle.
When you get up to 5 magnets, something interesting happens - you combine the linear and the trigonal planar geometries. The linear geometry goes up and down (vertical plane), while the trigonal planar geometry goes left, right, forward and back (horizontal plane). The angle between the magnets in the linear geometry is 180°. The angle between the magnets in the trigonal planar geometry is 120°. The angle between the magnets in the linear and the trigonal planar geometry is 90°.
This is known as trigonal bipyramidal. If you pretend the bottom magnet isn't there, you can see how everything else forms a pyramid shape. Then if you pretend the top magnet isn't there, you can see another pyramid. Two triangular pyramids = trigonal bipyramidal.
The last electron geometry we're going to talk about is actually one of the simplest. When you have 6 magnets, they actually push each other into a completely symmetrical shape, a combination of 3 linear geometries where the angle between any of the magnets is 90°.
This is known as an octahedral. You can see where the octa (8) part comes from if you imagine stacking 8 blocks together to make one big block - the middle of each side of that big block is where a magnet would be if our ball was in the middle.
Those are the 5 basic shapes that make up all of electron geometry. If you can remember those 5 shapes, you can figure out any shape in molecular geometry. You will probably have seen in class things like a "steric number" and "hybridization". For us, the steric number is just the number of magnets that we have and the hybridization is just a fancy way of writing the steric number so that it applies to a more advanced chemical theory called molecular orbital (or MO) theory.
Fellas! Let us explore the three dimensional structure of simple molecular (covalent) compounds and polyatomic ions. We will use a model called the Valence Shell Electron-Pair Repulsion (VSEPR) model that is based on the repulsive behavior of electron-pairs.
...for the mean time, let's talk about...
Bonding and non bonding electrons:
Bonding pairs of electrons are those electrons shared by the central atom and any atom to which it is bonded. Non-bonding pairs of electrons are those pairs of electrons on an individual atom that are not shared with another atom.
In simple molecules in which there are no nonbonding electrons, there are five basic shapes:
1. LINEAR - Bond angle = 180
o All diatomic molecules are linear.
o Molecules with two atoms around a central atom such as BF2 are linear because positioning the two attachments at opposite ends of the central atom minimizes electron repulsion.o Generic Formula: MX or MX2 (where M is the central atom and X is are the bonding atoms).
2. TRIGONAL PLANAR - Bond angle = 120
o Molecules with three atoms around a central atom such as BF3 are trigonal planar because electron repulsion is minimized by positioning the three attachments toward the corners of an equilateral triangle.
o Generic Formula: MX3 (where M is the central atom and X is are the bonding atoms).
3. TETRAHEDRAL - Bond angle = 109.5
o Molecules with four atoms around a central atom such as CH4 are tetrahedral because electron repulsion is minimized by position the four attachments toward the corners of a tetrahedron.
o Generic Formula: MX4 (where M is the central atom and X is are the bonding atoms).
4. TRIGONAL BIPYRAMIDAL
o Bond angle within the equatorial plane = 120
o Bond angle between equatorial and axial plane = 90
o Molecules with five atoms around a central atom such as PF5 are trigonal bipyramidal. Three of the attachments are positioned in a trigonal plane with 120 bond angles. The remaining two attachments are positioned perpendicular (90) to the trigonal plane at opposite ends of the central atom. This arrangement of atoms minimizes electron repulsion.
o Generic Formula: MX5 (where M is the central atom and X is are the bonding atoms).
5. OCTAHEDRAL - Bond angle = 90
o Molecules with six atoms around a central atom such as SF6 are octahedral. Four of the attachments are positioned in a square plane with 90 bond angles. The remaining two attachments are positioned perpendicular (90) to the square plane at opposite ends of the central atom. This arrangement of atoms minimizes repulsion.
o Generic Formula: MX6 (where M is the central atom and X is are the bonding atoms).
To summarize it all, we made a table. We also included other shapes ... Take a LOOK!
# of lone pair electrons on 'central' atom | # of bonding groups (pair electrons) on 'central' atom | Electron-pair Geometry | Molecular Geometry | Bond Angle |
0 | 2 | linear | 180 | |
0 | 3 | trigonal planar | 120 | |
1 | 2 | trigonal planar | less than 120 | |
0 | 4 | tetrahedral | 109.5 | |
1 | 3 | tetrahedral | less than 109.5 | |
2 | 2 | tetrahedral | less than 109.5 | |
0 | 5 | trigonal bipyramidal | 90, 120 and 180 | |
1 | 4 | trigonal bipyramidal | 90, 120 and 180 | |
2 | 3 | trigonal bipyramidal | 90 and 180 | |
3 | 2 | trigonal bipyramidal | 180 | |
0 | 6 | octahedral | 90 and 180 | |
1 | 5 | octahedral | 90 and 180 | |
2 | 4 | octahedral | 90 and 180 |
In this table the term bonding groups (second from the left column) is used in the column for the bonding pair of electrons. Groups is a more generic term. Group is used when a central atom has two terminal atoms bonded by single bonds and a terminal atom bonded with two pairs of electrons (a double bond). In this case there are three groups of electrons around the central atom and the molecualr geometry of the molecule is defined accordingly. The term electron-pair geometry is the name of the geometry of the electron-pairs on the central atom, whether they are bonding or non-bonding.
Molecular geometry is the name of the geometry used to describe the shape of a molecule. The electron-pair geometry provides a guide to the bond angles of between a terminal-central-terminal atom in a compound. The molecular geometry is the shape of the molecule. So when asked to describe the shape of a molecule we must respond with a molecular geometry. If asked for the electron-pair geometry on the central atom we must respond with the electron-pair geometry. Notice that there are several examples with the same electron-pair geometry, but different molecular geometries. You should note that to determine the shape (molecular geometry) of a molecule you must write the Lewis structure and determine the number of bonding groups of electrons and the number of non-bonding pairs of electrons on the central atom, then use the associated name for that shape.
NOTICE!!! for bent molecular geometry when the electron-pair geometry is trigonal planar the bond angle is slightly less than 120 degrees, around 118 degrees. For trigonal pyramidal geometry the bond angle is slightly less than 109.5 degrees, around 107 degrees. For bent molecular geometry when the electron-pair geometry is tetrahedral the bond angle is around 105 degrees.
dot dot dot
I'm sure you guys are bonding with your friends, family and love ones through many ways... Hanging out together, going on a trip, lolling together, having cofee, or just by simply chillin' and such. How do you bond with your them?
Did you know that molecules bond as well?
Bonding
Molecules, by definition, are most often held together with covalent bonds involving single, double, and/or triple bonds, where a "bond" is a shared pair of electrons (the other method of bonding between atoms is called ionic bonding and involves a positive cation and a negativeanion).
Molecular geometries can be specified in terms of bond lengths, bond angles and torsional angles. The bond length is defined to be the average distance between the centers of two atoms bonded together in any given molecule. A bond angle is the angle formed between three atoms across at least two bonds. For four atoms bonded together in a chain, the torsional angle is the angle between the plane formed by the first three atoms and the plane formed by the last three atoms.
Molecular geometry is determined by the quantum mechanical behavior of the electrons. Using the valence bond approximation this can be understood by the type of bonds between the atoms that make up the molecule. When atoms interact to form a chemical bond, the atomic orbitals are said to mix in a process called orbital hybridisation. The two most common types of bonds are Sigma bonds and Pi bonds. The geometry can also be understood by molecular orbital theory where the electrons are delocalised.
An understanding of the wavelike behavior of electrons in atoms and molecules is the subject of quantum chemistry.
This is the easy part!
We got all the grunt work out of the way learning electron geometry, now we just need to apply our knowledge. You just need to know a couple of things to do this.
1 - In all those pictures, we referred to Y as a magnet. It is actually either a bond between atoms, or a lone pair of electrons.
2 - When we name molecular geometries, we ignore lone pairs of electrons, even though they are still there and still push away other electrons like the little magnets that they are.
3 - Lone pairs of electrons are stronger magnets than bonds are, so they will push harder.
4 - When every Y stands for a bond, the molecular geometry is the same as the electron geometry.
Like before we will start with the linear electron geometry. Good news, it does not matter if Y is a bond or a lone pair - they still both from a linear molecular geometry. Even though lone pairs push harder than bonds, its impossible to get farther away then 180°. All of these pictures were created using ACD Chemsketch and Chem3D - free chemistry drawing programs.
Linear
Next up!... we have the trigonal planar electron geometry. If all of our Y's are bonds, the molecular geometry will again be trigonal planar. However in this case, we can replace one Y with a lone pair of electrons to get a "bent" molecular geometry. Just imagine in your head removing one of the bonds and replacing it with the lone pair. Like rule #3 says, lone pairs push harder than bonds do, so while the angle between bonds is 120° for a trigonal planar molecule, it is actually <120° for a bent molecule, all because that lone pair is pushing the bonds farther away.
Trigonal Planar Bent
It starts to get fun here!!!
... with the tetrahedral electron geometry. Again, if all the Y's are bonds, the molecular geometry is just tetrahedral again with angles equal to 109.5°. Now if we replace just one of the bonds with a lone pair, we get what is called trigonal pyramidal - it looks like a pyramid with 3 sides - and because the lone pair is pushing harder than the bonds, the angle is <109.5°. Finally, with a tetrahedral, we can replace 2 of the Y's with lone pairs (i.e. water - 2 bonds and 2 lone pairs) and we get a familiar looking "bent" shape, only the angle between the bonds is now <109.5°.
... with the tetrahedral electron geometry. Again, if all the Y's are bonds, the molecular geometry is just tetrahedral again with angles equal to 109.5°. Now if we replace just one of the bonds with a lone pair, we get what is called trigonal pyramidal - it looks like a pyramid with 3 sides - and because the lone pair is pushing harder than the bonds, the angle is <109.5°. Finally, with a tetrahedral, we can replace 2 of the Y's with lone pairs (i.e. water - 2 bonds and 2 lone pairs) and we get a familiar looking "bent" shape, only the angle between the bonds is now <109.5°.
Tetrahedral
Trigonal Pyramidal Bent
Now we have to look at the trigonal bipyramidal electron geometry!
Remember how this was a combination of linear and trigonal planar geometries?
This becomes important when we start adding lone pairs. Since the lone pairs push harder than bonds do, they want to be farther away from everything. That means that when we add them, they MUST be added to the horizontal plane (trigonal planar geometry). This puts the lone pairs as far away as possible (120° angle is farther away than a 90° angle).
So we begin, as always, when all Y's are bonds, the molecular geometry is the same as always - trigonal bipyramidal - with angles equal to 120° and 90°. When we replace one bond with a lone pair (in the horizontal plane) we get what looks like a see saw if we turn it sideways so we call that a seesaw molecular geometry with angles <120° and <90°. Replacing two bonds (in the horizontal plane) with lone pairs of electrons gives us what looks like a T if we turn it sideways, so naturally we call that T-shaped molecular geometry, with angles <90°. Finally, we can replace all three of the bonds in the horizontal plane with lone pairs, and we're just left with our linear geometry (vertical plane) so naturally we call that a linear molecular geometry with an angle of 180°.
Trigonal Bipyramidal Seesaw
T-shaped Linear
Last, but not least!...
... we have the octahedral electron geometry. As always, if all Y's are bonds, than the molecular geometry will be octahedral with angles of 90°. When we replace one bond with a lone pair of electrons, we get another pyramid shape, but this time with 4 sides. We call this molecular geometry square pyramidal with angles <90°. Finally, if we replace two bonds with lone pairs of electrons, the lone pairs must be added on opposite sides because of their more powerful magnetic force - they push harder. This gives us a molecular geometry where we have 4 bonds in a single plane, so we call it square planar where the angles all equal 90°.
Octahedral
Square Pyramidal Square Planar
Interesting isn't it? Geometry in molecules!!
no evaluation part...
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