What is the formal charge on carbon atom in $\text{CO}_3^{2-}$ ion ?
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A highly reliable shortcut: If carbon forms exactly four chemical bonds (e.g., four singles, two doubles, or one triple and one single) and possesses no lone pairs, its formal charge will absolutely always be zero!
Step 1: Recall the formal charge rule.
$$\text{FC} = V - N - \tfrac{B}{2}$$ where $V$ is valence electrons, $N$ is lone pair electrons, and $B$ is shared bonding electrons.
Step 2: Fill in for carbon in $\text{CO}_3^{2-}$.
Carbon has 4 valence electrons. In the ion it makes one double and two single bonds, so it has no lone pairs and shares 8 bonding electrons.