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equation

I need to figure out the equation of an experiment

I added carbonated water; h2co3
and naoh
and found out the solubility of the carbon dioxide in the h2o by figuring out the acidity but what is the equation?

$CO_2 + H_2O \rightleftharpoons H_2CO_3$

$H_2CO_3 + 2NaOH \rightleftharpoons Na_2CO_3 + 2H_2O$

Remember that the following occurs

$H_2CO_3\, \rightleftharpoons\, 2H^+ + CO_3^{-2}$

and

$NaOH \rightleftharpoons Na^+ + OH^-$

$H^+ + OH^- \rightarrow H_2O$

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