More Metal Complexation Poetry

Do you remember the poem that I wrote about ligands and brigands. Well here's some more about ligands.
Ligands are like people they like to be complex. 
They are like goth kids. They like metal. They have negative or neutral attitudes.

Coordination Numbers
When a person coordinates they bond around a central goal or if you are ligand, you bond to a central molecule because your attitudes are negative or neutral and you're too cool for goals. Your coordination number is the number of bonds you've formed to your metal.

Free metal ions
It's a ruse. Nothing is really free. Cations in water naturally exist as complexes with water molecules. They're just called free metal ions as a sales pitch.

Inner-Sphere Complexes: (coordinate complexes)
The bonding is covalent. (I can't really think of any puns or analogies for covalent bonding.) Nothing is free. the ligand must replace water. Poor water.
Stability of a complex increases with charge and or radius. That makes sense. Just think about religion. Neutral religions don't last very long. The bigger they are the harder it is to change anything-stable.

Outer-Sphere Complexes
No water is replaced. You, the ligand, are just hanging out like a groupy hoping for an autograph. The forces that hold you to the metal are electrostactic. You know like crazy fans with their hair standing on end. No wait that's static electricity. That's totally different, but they sound the same so I'm going to use the idea anyway. So not surprisingly. These bonds are weaker. "Man you are totally not covalent. That metal is totally hydrated. " Poor ligand.

Formation Constants
10^4  increase with increaseing change.

Chelation
a ligand that coordinates at several positions with the "donor" atom, the metal. Sounds kinky. That's all I have to say.

Polydentate
That's right ligand. You a tooth. Polydentate means a complex with multiple teeth.

Polynuclear
A complex with more than one central metal ion. Now that is complex.

Why do we care?
We probably don't. We're to cool for that. We're complex. Complexation only effect solubility, chemical behavior, bioavailability and toxicity.

Oh look we can do some math. Complexation solubility constants work like any other solubility constant. The solid goes on the bottom. the activity of the disolved components go on top

Metal + Ligand = Metal_Ligand complex  K1 (that's your stability or formation constant that how you find out where you reach equilibrium and become a stoner)

Metal_Ligand complex + Ligand = Metal _Ligand_Ligand complex K2 (that's right you not the only ligand. Deal with it)

If you want to write thing thing all in one step:
Metal +Ligand+ Ligand = Metal _Ligand_Ligand complex     B2 (it's actually beta in my book but I don't want to try to find the symbol for that.)
B2=K1*K2

If you want to use math language to generalize it you say:
M+iL=MLi
Bi = (funny symbol)Ki means multiply all the k's together. It's like the summation symbol very intimidating thing that looks like greek cuz it is. The i is math language for put what ever number you want here. Well any positive whole number. Fractions of ligands are like fractions of people. It doesn't work out well.

Alright listen up you ligands! Which one of you is a hydroxide. Ah yes there you are. Yes I see you are negative because you are a ligand.
OH-
Well you're special.
Side story: Even though he is negative, the hydroxide always knew that he was special. Nobody understood his pain. He was an unappreciated poet and infinitly complex.
end side story

Well sometimes we don't want to deal with the hydroxide because he will start reading his poetry.
instead of writing
M+OH =MOH  K1
we combine this reaction with the reation for water and use a *K1 to keep from getting confused, but we really want you to be confused because it makes us feel smart so we don't explicitly tell you why we are using K*. It's cuz we don't like poetry ok. Well also it's useful to write things in terms of released H's instead of added OH's.
H2O = OH-  +  H +   Kw (formation constant for water)
If you are reading this, Dad, you may be interested to recall that you can add chemical equations together just like algebraic ones. The OH's cancel and you get.

M + H2O = MOH + H+   You've added equations so you multiply the formation constants and call them something new for the sake of lazy writing.


What you need to solve a problem involving a metal and some ligands.
1. you need equilibrium constants. Think of these as an (I don't care attitude. You can't touch me. I got equilibrium constants. You know where everything lines up.)
2. Mass balance on your metal. Everybody is obsessed with mass. Just look at the weight loss commercials. The nice the about mass is the whole really is the sum of it's parts (unless you're doing nuclear chemistry.)

Now it's just algebra. Alphabet soup. Put the equilibrium constants into the mass balance.