I'm not really sure, and I'll bet it depends on
the form of the sodium. Pure sodium normally
reacts with chlorine (in bleach) to make sodium
chloride (table salt), but sodium reacts even
more strongly with oxygen, which is in the water
that the bleach is dissolved in, to make sodium
oxide. I doubt you would get anything different
for this reason than if you dropped sodium
directly into water.
Warning: DON'T try this experiment unless you
are wearing protective gear and know what you're
doing. The reaction between sodium and water
releases a lot of energy. You could be
splattered with boiling water, set on fire,
breathing sodium oxide vapor, or even blown to
bits if you used enough sodium.
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