Question

If a piece of iron gains $10\%$ of its mass due to partial rusting into $F{e_2}{O_3}$ the percentage of total iron that has rusted is:
A.3
B.13
C.$23.2$
D.$25.67$

Answer 1

To answer this question, you should recall that rusting of iron refers to the formation of rust, a mixture of iron oxides, on the surface of iron objects or structures. This rust is formed from a redox reaction between oxygen and iron.

Complete step by step answer:
Rusting of iron is a chemical reaction which happens when iron comes in contact with air or water. The reaction behaves as an electrochemical cell reaction. In this reaction, iron loses electrons and gets converted to ferrous state thus behaving as the anode. The electrons lost from this atom of iron will move to the other side where they combine with protons released by exposed water. The reactions taking place are:
$F{e^{2 + }}\; + {\text{ }}3{O_2}\; \to {\text{ }}2F{e_2}{O_3}$
$F{e_2}{O_3}\; + {\text{ }}x{H_2}O{\text{ }} \to {\text{ }}F{e_2}{O_3}.{\text{ }}x{H_2}O{\text{ }}\left( {{\text{rust}}} \right)$.
The chemical reaction is: $4Fe{\text{ }} + {\text{ }}3{O_2}{\text{ }} \to {\text{ }}2F{e_2}{O_3}$.
Let Initial mass of iron $= {\text{ }}x$ and mole of iron be converted to rust $= {\text{ }}y$.
Then the mass of iron did not get rusted $= x - 56y$.
$\therefore$The mass of ${\text{ }}y$converted to rust $= {\text{ }}56y$.
4 moles of iron form 2 moles of rust.
This means that moles of rust formed $= \dfrac{y}{2}$ and mass of rust formed $= \dfrac{y}{2} \times 160 = 80y$.
The mass of iron not converted to rust and mass of rust has a total mass of $x{\text{ }}\& {\text{ }}10\% {\text{ }}x$ or $x + 0.1x = 1.1x$.
The final equation will be:
$x - 56y = 1.1x$.
Rearranging we will get:
$24y = 0.1x$.
Solving this equation we get:
$y = \dfrac{{0.1x}}{{24}}$.
By putting the value of y in the equation $56y$ we get $= 56 \times \dfrac{{0.1x}}{{24}}$. \% \;{\text{of iron converted to rust} = {\text{ mass of rust/initial mass } \times }}100$$$$ = 56 \times \dfrac{{0.1x}}{{24}} \times 100 = 23.3\% .

Hence, the correct option is option C.

Note:
You should know about tarnishing along with rusting of iron. We know that tarnish is a type of chemical reaction formed as a product when a metal and a nonmetal compound, especially oxygen and sulfur dioxide react and undergo oxidation. The reaction for tarnishing can be represented as: $8Ag + 4H{S^ - } \to {\text{ }}4A{g_2}S{\text{ }} + {\text{ }}2{H_2}\; + {\text{ }}4{e^ - }$and ${O_2}\; + {\text{ }}2{H_2}O{\text{ }} + {\text{ }}4{e^ - }\; \to {\text{ }}4O{H^ - }$. Silver tarnish can be considered as a type of corrosion, but unlike rust, the underlying metal remains undamaged. The process of tarnishing is fastened through tap water contact as it has the presence of chlorine), various food items, perfume and hair spray etc. For slowing down the process of tarnishing, silver ornaments should be cleaned regularly