Why is $\ce{Ba(OH)2}$ Barium hydroxide not Barium dihydroxide?
Why is Lithium carbonate $\ce{Li2CO3}$ instead of $\ce{LiCO3}$?
Is there a formula or is just the case for these two?
Answer
There is no other Ba(OH)x so there is no need to note a difference between several forms.
This happens with any metal ion that only attains precisely one positive charge, whether it is +1 or +10.
Lithium ions have +1 charge. Carbonate ions have -2 charge. Therefore to balance the charge in the formula we need 2 lithium to 1 carbonate.
This happens with all formulae, and it is a simple mathematical check to decide what the correct ratios should be.
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