Which of the following about \(Fe_3O_4\) is true?

It has both divalent and trivalent iron.

The correct answer is option 4. It has both divalent and trivalent iron.

\(Fe_3O_4\), known as magnetite, is a mixed-valence compound containing iron in two different oxidation states: \(Fe(II)\) and \(Fe(III)\). Here's a detailed explanation:

Composition and Oxidation States

Chemical Formula: The chemical formula of magnetite is \(Fe_3O_4\).

Oxidation States:

It can be viewed as a combination of ferrous oxide (\(FeO\)) and ferric oxide (\(Fe_2O_3\)).

\(FeO\) contains iron in the +2 oxidation state (Fe(II)).

\(Fe_2O_3\) contains iron in the +3 oxidation state (Fe(III)).

Therefore, \(Fe_3O_4\) = \(FeO \cdot Fe_2O_3\).

Iron Valency in \(Fe_3O_4\)

To understand the valency and charge balance in \(Fe_3O_4\):

There are a total of 3 iron atoms and 4 oxygen atoms in the formula unit.

Oxygen has a -2 oxidation state, so four oxygen atoms contribute a total of \(-8\) charge.

To balance this \(-8\) charge, the total positive charge from iron must be \(+8\).

Since \(Fe_3O_4\) contains both Fe(II) and Fe(III):

Let's denote the number of Fe(II) atoms as \(x\) and Fe(III) atoms as \(y\).

We know that \(x + y = 3\) (total number of iron atoms).

The total positive charge must be \(+8\), so \(2x + 3y = 8\) (accounting for the charges of Fe(II) and Fe(III)).

By solving these equations:

\(x + y = 3\)

\(2x + 3y = 8\)

We can solve for \(x\) and \(y\):

From the first equation, \(y = 3 - x\).

Substitute \(y\) into the second equation:

\(2x + 3(3 - x) = 8\)

\(2x + 9 - 3x = 8\)

\(-x + 9 = 8\)

\(-x = -1\)

\(x = 1\)

Substituting \(x = 1\) into \(y = 3 - x\):

\(y = 3 - 1 = 2\)

So, \(Fe_3O_4\) contains:

1 atom of Fe(II) (divalent iron).

2 atoms of Fe(III) (trivalent iron).

Therefore, \(Fe_3O_4\) has both divalent (Fe(II)) and trivalent (Fe(III)) iron, making statement (4) true. The presence of both Fe(II) and Fe(III) gives rise to the unique electronic and magnetic properties of magnetite.