Question

Calculate the average oxidation number of the copper in ${\mathbf{YBa}}_2{\mathbf{Cu}}_3{\mathbf{O}}_{\mathbf{9}-\mathbf{x}}$ if $\mathbf{x}\mathbf{=}\mathbf{2}$ . Assume that the rare-earth element yttrium is in its usual +3 oxidation state.

Short answer

The average oxidation state of copper is 2.33.

Step-by-step solution

Oxidation number

The charge exhibited by an atom due to the loss or gain of electrons during the formation of its compound is called the oxidation number.

If an atom loses electrons then its oxidation number increases and it has positive sign.

If an atom gains electrons then its oxidation number decreases and it has negative sign.

Explanation

The molecular formula of the given compound is ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$.

The oxidation number of Y is +3.

The oxidation number of Ba is +2.

The oxidation number of O is -2.

The oxidation number of Cu be “x”.

The overall charge on the molecule is zero.

Hence, the average oxidation state of copper can be calculated as shown below:

$\begin{array}{c}{\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7\\ +3+2(+2)+3\left(\mathrm{x}\right)+7(-2)=0\\ +3+4+3\mathrm{x}-14=0\\ 3\mathrm{x}-7=0\\ \mathrm{x}=\frac{7}{3}\end{array}$

On simplification,

$\mathrm{x}=2.33$