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I know that $\ce{CO_2}$ and $\ce{O_2}$ are slightly soluble in water ($\ce{H_2O}$)

In my understanding, when carbon dioxide dissolves in water, it will react to form carbonic acid just like the equation below.

$\ce{H2O + CO2 -> H2CO3}$

So, my problem now is, I can't find the equation for oxygen.
Will they form hydroxide ions or something else?

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Carbon dioxide is not stable in water in its original form, so it undergoes an acid-base reaction to give the carbon dioxide.

On the other hand, oxygen is stable and soluble in water in its $\ce{O_2}$ form, so it will stay like that, no reaction other than solubilization. Besides, it could react with organic matter or other compounds in water, oxidizing them, and getting reduced to $\ce{OH^-}$

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    $\begingroup$ This is not correct - 99 % of the carbon dioxide dissolved in water appears in the form of CO2 and only 1 % as carbonic acid. Moreover, the hydration reaction is rather slow, rate is on the order of seconds. $\endgroup$ – Abel Friedman Nov 21 '14 at 17:29

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