Question

What are the oxidation states of manganese in the following series of oxides? MnO, ${\mathbf{MnO}}_{\mathbf{2}}$, ${\mathbf{Mn}}_2{\mathbf{O}}_3$, ${\mathbf{Mn}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}$,${\mathbf{Mn}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{4}}$, and ${\left[{\mathbf{MnO}}_{\mathbf{4}}\right]}^{\mathbf{-}}$. Recall that you must include the total charge on the ion for ionic species.

Short answer

The oxidation state of Mn in MnO is +2.

The oxidation state of Mn in${\text{MnO}}_{\text{2}}$is +4.

The oxidation state of Mn in${\text{Mn}}_2{\text{O}}_3$is +3.

The oxidation state of Mn in${\text{Mn}}_2{\text{O}}_7$is +7.

The oxidation state of Mn in ${\text{Mn}}_3{\text{O}}_4$is +8/3 .

The oxidation state of Mn in ${\left[{\text{MnO}}_{\text{4}}\right]}^{\text{-}}$is +7.

Step-by-step solution

Oxidation state

Thecount of electrons lost or gained by an atom can be understood using the termoxidation state. The atoms possess a positive oxidation state if the atom loses electrons. The atoms possess a negative oxidation state if the atom receives electrons.

The oxidation state of manganese in the given series of oxides

To find the oxidation state of Mn in MnO, let us take the value of Mn as x, and the oxygen will have an oxidation state of -2.

Hence, the oxidation state of Mn is:

$\begin{array}{rcl}x-2& =& 0\\ x& =& 2\\ & & \end{array}$

Hence, the oxidation state of Mn in MnO is +2.

To find the oxidation state of Mn in ${\text{MnO}}_{\text{2}}$, let us take the value of Mn as x, and there are two oxygen atoms with an oxidation state of -2. The oxidation state of Mn is:

$\begin{array}{rcl}x-2\times 2& =& 0\\ x-4& =& 0\\ x& =& 4\\ & & \end{array}$

Hence, the oxidation state of Mn in role="math" localid="1663704910611" ${\mathbf{\text{MnO}}}_{\mathbf{\text{2}}}$ is +4.

To find the oxidation state of Mn in ${\text{Mn}}_{\text{2}}{\text{O}}_{\text{3}}$, the value of Mn will be 2x as there are two manganese atoms. There are three oxygen atoms with an oxidation state of -2. The oxidation state of Mn is:

$\begin{array}{rcl}2x-2\times 3& =& 0\\ 2x-6& =& 0\\ 2x& =& 6\\ x& =& 3\end{array}$

Hence, the oxidation state of Mn in ${\mathbf{\text{Mn}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{3}}}$is +3.

To find the oxidation state of Mn in ${\text{Mn}}_{\text{2}}{\text{O}}_7$, the value of Mn will be 2x as there are two manganese atoms. There are seven oxygen atoms with an oxidation state of -2. The oxidation state of Mn is:

Hence, the oxidation state of Mn in ${\mathbf{\text{Mn}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{7}}$ is +7.

To find the oxidation state of Mn in ${\text{Mn}}_3{\text{O}}_4$, the value of Mn will be 3x as there are three manganese atoms. There are four oxygen atoms with an oxidation state of -2. The oxidation state of Mn is:

$\begin{array}{rcl}3x-2\times 4& =& 0\\ 3x-8& =& 0\\ 3x& =& 8\\ x& =& \frac{8}{3}\end{array}$

Hence, the oxidation state of Mn in ${\mathbf{\text{Mn}}}_{\mathbf{3}}{\mathbf{\text{O}}}_{\mathbf{4}}$is +8/3 .

To find the oxidation state of Mn in${\left[{\text{MnO}}_{\text{4}}\right]}^{\text{-}}$ , the value of Mn is taken as x, and there are four oxygen atoms. The overall charge of the compound is -1. The oxidation state of Mn can be found as:

$\begin{array}{rcl}x+-2\times 4& =& -1\\ x-8& =& -1\\ x& =& -1+8\\ & =& 7\\ & & \end{array}$

The oxidation state of Mn in ${\left[{\text{MnO}}_{\text{4}}\right]}^{\mathbf{\text{-}}}$is +7.