Question

Given, $F{e_x}O$ contains one $Fe(III)$ for every three $Fe(II)$. What is $x$?
A. $\dfrac{2}{3}$
B. $\dfrac{8}{9}$
C. $\dfrac{3}{4}$
D. $\dfrac{5}{3}$

Answer 1

We know that the iron metal can exist in its two possible oxidation states i.e., +2 and +3 and for the given question, just use the concept of oxidation states to find the value of x i.e., summation of oxidation number of individual ions or atoms in a compound is equal to the overall charge present on the molecule (zero if the molecule is neutral).

Complete answer:
As per question, it is given that the $F{e^{2 + }}$ and $F{e^{3 + }}$ ions are present in the ratio $3:1$. So, we can say that the number of moles of $F{e^{2 + }}$ and $F{e^{3 + }}$ in the given iron oxide will be $\dfrac{3}{4}x$ and $\dfrac{1}{4}x$ respectively.
Now, we know that for a neutral molecule, the charge on the electronegative ions counterbalances the charge present on the electropositive elements. So, in the given formula the total positive charge on ferrous and ferric ions should balance the two units negative charge on electronegative oxygen atoms. Thus, mathematically it can be represented as follows:
$2 \times \left( {\dfrac{3}{4}x} \right) + 3 \times \left( {\dfrac{1}{4}x} \right) - 2 = 0$
On simplifying the expression:
$\Rightarrow \dfrac{9}{4}x = 2$
$\Rightarrow x = \dfrac{8}{9}$
Hence, the value of x for the given iron oxide is $\dfrac{8}{9}$.
Hence, option (B) is the correct answer.

Note:
Always remember that while converting the ratios into fractions, the actual value is represented in the numerator while the total value of the ratio is represented in the denominator along with a variable which indicates the number of possible values. For example if $x:y = 2:3$ , then the value of $x$can be represented as $\dfrac{2}{5}k$ and the value of $y$ can be represented as $\dfrac{3}{5}k$, where k is any variable.