What happens to the bleach after mopping? At home, I clean the tiled floors by mopping with highly diluted bleach.  After mopping, I let the floor dry.  What happens to the acid in the bleach?  

Will it crystallize on the floor, stay there invisibly in solid form, and get solved again next time the floor gets wet?  Will it instead evaporate, or turn to fine dust that floats in the air and leaves through the window?  Will it decompose in some sort of chemical reaction?
Sodium hypochlorite decomposes by a couple of different pathways:

$\ce{NaOCl\leftrightharpoons Na^+ + OCl^-\\
2OCl^- \leftrightharpoons O_2 + 2 Cl^-}$

In that case, the oxygen escapes (if it didn't react with "things to bleach", which is of course how bleach works in the first place), and you are left with ordinary salt.

The other pathway is 

$\ce{3 OCl^- -&gt; ClO_3 + 2 Cl^-}$

In that case you get some sodium chlorate, and again some ordinary NaCl salt.

Both NaCl and NaClO3 are crystalline solids that may be blown around like fine dust; some NaOCl may also remain behind. Note that according to wikipedia most commercial bleach solutions contain a small amount of sodium hydroxide to slow down the decomposition along the pathways mentioned above.

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