Question

What percentage of $F{e^{3 + }}$ is present in $F{e_{0.93}}O$.
A. $15\%$
B. $12\%$
C. $9\%$
D. $13\%$

Answer 1

We know that the electronic configuration of iron is $[Ar]3{d^6}4{s^2}$ that means it has a tendency to exist in its two oxidation states i.e., $+ 3$ and $+ 2$. For the given question, first find the number of molecules of each ion using the charge conservation method for a compound and then the percentage of each ion can be evaluated by using the percentage formula.

Complete answer:
For the given sample of iron oxide, let us assume that there are x molecules of $F{e^{2 + }}$ and y molecules of $F{e^{3 + }}$ are present. Thus, the formula of the sample can be represented as ${\left( {F{e^{2 + }}} \right)_x}{\left( {F{e^{3 + }}} \right)_y}O$.
As per given in question, the formula of iron oxide is $F{e_{0.93}}O$. So, we can say that the ions of iron metal cannot exceed $0.93$. Therefore, x and y can relate to each other by the following expression:
$x + y = 0.93\;\;\;\;\;...(1)$
Also, we know that according to charge conservation of a compound, for a neutral molecule the charge on electropositive ions counterbalances the charge on electronegative ions. Thus, in the given formula the total positive charge of ferric and ferrous ions must be equal to the two units of negative charge on the oxygen atom. Hence, another expression relating x and y will be as follows:
$2x + 3y = 2$
$\Rightarrow x + \dfrac{3}{2}y = 1\;\;\;\;\;\;...(2)$
On subtracting equation (1) from equation (2), the value of y can be calculated as follows:
$\dfrac{3}{2}y - y = 1 - 0.93$
$\Rightarrow y = 0.14$
This means the number of molecules of $F{e^{3 + }}$ ions in the given formula of iron oxide $= 0.14$
Therefore, the percentage of $F{e^{3 + }}$ ions $= \dfrac{{0.14}}{{0.93}} \times 100 \Rightarrow 15\%$
Thus, we can conclude that the percentage of $F{e^{3 + }}$ is present in $F{e_{0.93}}O$ is $15\%$. So, option (A) is the correct answer.

Note:
It is important to note that the percentage of $F{e^{2 + }}$ ions can also be calculated by determining the value of x using equation (1). Also, this question can alternatively be solved without involving second variable y and considering it as $0.93 - x$ and directly substituting the value in charge conservation formula of the given oxide.