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My teacher wrote the reaction for heating of borax like this: $$\ce{Na2B4(OH)4 .8H2O->Na2B4O7 + 10H2O}$$ $$\ce{Na2B4O7->B2O3 +Na2B2O4}$$ And told us that $\ce{Na2B2O4}$ can be written as $\ce{2NaBO2}$,is this correct? If yes then why?

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No, $\ce{Na2B2O4}$ can not be written as $\ce{2NaBO2}$. $\ce{Na2B2O4}$ means 1 mole of $\ce{Na2B2O4}$ and $\ce{2NaBO2}$ means there are 2 moles of $\ce{NaBO2}$. Both are different compounds and have different molar mass.

Actually in real $\ce{2NaBO2}$ should be written as $\ce{(NaBO2)2}$. Now, both $\ce{Na2B2O4}$ and $\ce{(NaBO2)2}$ are same.

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