Draw a Lewis structure with lowest formal charges for \(\mathrm{MnO}_{4}^{-}\).

Understanding valence electrons is crucial for drawing the Lewis structure of \(\text{MnO}_4^-\). Valence electrons are the outermost electrons of an atom and participate in chemical bonding. Manganese (Mn) has 7 valence electrons, each oxygen (O) has 6, and since \(\text{MnO}_4^-\) carries a -1 charge, we add one more electron. This totals:
\(\text{7 (from Mn) + 4 \times 6 (from 4 oxygen atoms) + 1 (additional electron from the charge) = 32 electrons}\).
These valence electrons are distributed to form bonds and lone pairs around the atoms to satisfy their valence requirements.
Let's make sure we count and distribute them accurately to reflect the real molecular structure.

Formal charge calculations help us find the most stable Lewis structure by showing how the electron count differs from what's standard for each atom. The formula for formal charge is:
\(\text{FC} = \text{V} - (\text{N}_{\text{L.P.}} + \text{N}_{\text{B.P.}}/2)\)
where \(\text{V}\) is the number of valence electrons, \(\text{N}_{\text{L.P.}}\) is the number of lone pair electrons, and \(\text{N}_{\text{B.P.}}\) is the number of bonding electrons.
For oxygen in the original setup with 6 lone pairs and one single bond:
\(\text{FC} = 6 - (6+1) = -1\).
For manganese, changing single bonds to double bonds lowers formal charges, ideally, manganese should have formal charge close to zero, helping us spot the most stable structure.

The octet rule states that atoms tend to form bonds until they have 8 electrons in their valence shell, mimicking the electron configuration of noble gases. Each oxygen atom in \(\text{MnO}_4^-\) should follow this:
Connect Mn to each O with single bonds first, using up 8 electrons (2 per bond).
Then, complete each O's octet with 6 more electrons (3 lone pairs).
After distributing 24 more electrons among O atoms, check if each atom satisfies the octet rule. Manganese might exceed 8 electrons because it is in period 3, having access to 3d orbitals, allowing expanded octets necessary for correct formal charges.

Drawing the correct molecular structure requires balancing all these principles. The process is:

• Place Mn centrally and connect 4 Os around it.
• Use single bonds (8 electrons), then distribute remaining electrons to satisfy Os' octets (24 electrons).
• Check, correct formal charges by replacing single bonds with double bonds until charges are minimized (3 double bonds and 1 single ensures each atom follows the rules).
• This forms a valid Lewis structure: central Mn with double bonds to each O, maintaining overall –1 charge.

Each rule ensures stability and accuracy in the drawn structure. Properly applied, steps allow understanding of any compound's electron arrangement.