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Math

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PROBLEM

A student proposes the following Lewis structure for the water (H2O)\left(\mathrm{H}_{2} \mathrm{O}\right) molecule.
HOH\mathrm{H}-\mathrm{O}-\mathrm{H} Assign a formal charge to each atom in the student's Lewis structure.
\begin{tabular}{|c|c|} \hline atom & formal charge \\ \hline left H & \square \\ \hlineOO & \square \\ \hline right H & \square \\ \hline \end{tabular}

STEP 1

1. The Lewis structure provided is for a water molecule, H2O\mathrm{H}_2\mathrm{O}.
2. The formal charge formula is: Formal Charge=(Valence Electrons)(Non-bonding Electrons)12(Bonding Electrons)\text{Formal Charge} = (\text{Valence Electrons}) - (\text{Non-bonding Electrons}) - \frac{1}{2}(\text{Bonding Electrons}).
3. Hydrogen typically has 1 valence electron, and oxygen typically has 6 valence electrons.

STEP 2

1. Identify the valence electrons for each atom.
2. Count the non-bonding and bonding electrons for each atom.
3. Calculate the formal charge for each atom using the formula.

STEP 3

Identify the valence electrons:
- Hydrogen (H) has 1 valence electron.
- Oxygen (O) has 6 valence electrons.

STEP 4

Count the non-bonding and bonding electrons:
- Each hydrogen atom is involved in 1 bond, contributing 2 bonding electrons.
- Oxygen is involved in 2 bonds (4 bonding electrons) and has 4 non-bonding electrons (2 lone pairs).

SOLUTION

Calculate the formal charge for each atom:
- Left H:
$$ \text{Formal Charge} = 1 - 0 - \frac{1}{2}(2) = 0
\] - O:
$$ \text{Formal Charge} = 6 - 4 - \frac{1}{2}(4) = 0
\] - Right H:
$$ \text{Formal Charge} = 1 - 0 - \frac{1}{2}(2) = 0
\] The formal charges for each atom are:
\begin{tabular}{|c|c|} \hline atom & formal charge \\ \hline left H & 00 \\ \hlineOO & 00 \\ \hline right H & 00 \\ \hline \end{tabular}

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