Question

What is the oxidation number of iron in goethite?

Answer 1

The oxidation number is +3.

Explanation:

Goethite is a dark and usually uninteresting mineral.

Its chemical formula is `"FeO(OH)"`, although it often contains small amounts of other metals such as manganese.

We can use the rules for oxidation numbers to determine the oxidation number
of `"Fe"`.

The essential rules for this problem are:

1. The oxidation number of oxygen in a compound is almost always -2.
2. The sum of the oxidation numbers of all atoms (or ions) in a neutral compound
   is 0.
3. The sum of the oxidation numbers of all atoms in an ion equals charge on the ion.

Per Rule 1, the oxidation number of `"O"` is -2.

Write the oxidation number above the `"O"` in the formula:

`"Fe"stackrelcolor(blue)("-2")("O")"(OH)"`

Per Rule 3, the sum of all the oxidation numbers in the hydroxide ion equals -1.

Put -1 above the `"OH"`.

`"Fe"stackrelcolor(blue)("-2")("O")stackrelcolor(blue)("-1")("(OH)")`

Per Rule 2, the sum of all the oxidation numbers in `"FeO(OH)"` (the blue numbers below the formula) must equal zero.

Let `x =` the oxidation number of `"Fe"`. Then

`x-2-1 = 0`

`x = 2+1 = 3`

There is only one `"Fe"` atom, so its oxidation number must be +3.

Write the oxidation number above the `"Fe"`.

`stackrelcolor(blue)("+3")("Fe")stackrelcolor(blue)("-2")("O")stackrelcolor(blue)("-1")("(OH)")`

The oxidation number of `"Fe"` is +3.