How does the saponification process actually create soap?

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By what process does this actually happen?

On wikipedia they show this reaction?

2 NaOH + CO2 → Na2CO3 + H2O

My chemistry teacher described it as a process
where

Process 2
NaOH + CO2 → NaHCO3 + (something else to balance equation not sure)

then

NaHCO3 + CO2 → Na2CO3 + H2O

How would I finish balancing that equation and which is the actual process?
 
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http://en.wikipedia.org/wiki/Saponification

The process you have described will not create soap. It will create sodium carbonate, which is not soap.

Soap is an amphipathic molecule which consists of a nonpolar chain (hydrophobic) bonded to a polar (hydrophilic) functional group (carboxylate anion). These are created by treating animal fats (which contain ester bonds) with NaOH. The mechanism is described in the wikipedia article.

You can probably use carbon dioxide to make soap but you would need to use a hydrocarbon base (something like a grignard/gilman or organolithium) however you would then need to use an organic solvent because water will kill these reagents (they are some of the strongest bases known and will deprotonate any type of acidic hydrogen).

Soaps form micelles and 'solvate' or trap any particles that are hydrophobic while exposing the charged/hydrophilic head to the outside allowing for water to solvate the whole thing and wash everything away. Carbonates have no such hydrophobic regions and are not stable in solution anyway. They spontaneously decompose to carbon dioxide and water although I believe you need a bit of acid (don't quote me on the last part though, it may be the same situation with base).

http://en.wikipedia.org/wiki/Micelle