Question

For the following reaction, equilibrium constant${{K}_{c}}$ at 298 K is $1.96\times {{10}^{17}}$
\[F{{e}^{2+}}(aq)+{{S}^{2-}}(aq)\rightleftharpoons FeS(s)\]
When equal volume of 0.06 M $F{{e}^{2+}}(aq)$ and 0.2 M ${{S}^{2-}}(aq)$ solution are mixed, then equilibrium concentration of $F{{e}^{2+}}(aq)$ is found to be $Y\times {{10}^{-17}}M$.The value of Y is ⋯⋯.

Answer 1

Hint: The given reaction is about the formation of the compound ferrous sulphide or Iron (II) sulphide. They are often iron-deficient non-stoichiometric and also they are black, water-insoluble solids. They occur commonly in nature in the form of iron–sulfur proteins. Beside this iron (II) sulphide (FeS), there also exists ferric sesquisulfide and $Fe{{S}_{2}}$.

Complete step by step solution:
- The compound FeS can be obtained by the heating of sulfur and iron. In the question the equilibrium constant${{K}_{c}}$ for this reaction is given as$1.96\times {{10}^{17}}$. Also, when an equal volume of 0.06 M $F{{e}^{2+}}(aq)$ and 0.2 M ${{S}^{2-}}(aq)$ solution are mixed, then equilibrium concentration of $F{{e}^{2+}}(aq)$ is found to be $Y\times {{10}^{-17}}M$ and we are asked to find the value of Y.
- The given details can be written in a simpler form as follows
\[\begin{matrix}
 {} & F{{e}_{(aq)}}^{2+}+ & S_{(aq)}^{2-}\to & Fe{{S}_{(aq)}} \\
   Initial & 0.06M & 0.02M & {} \\
   After\text{ }mixing & 0.03M & 0.1M & {} \\
   At\text{ }equilibrium & x & 0.07M & {} \\
\end{matrix}\]
 We are supposed to find the value of x. As ${{K}_{c}}$ is very high, reaction proceed towards completion. And therefore the limiting reagent will be consumed almost completely. Hence we can write the relation as follows
\[{{K}_{c}}=\dfrac{1}{\left[ F{{e}^{2+}} \right]\left[ {{S}^{2-}} \right]}\]
\[x=\left[ F{{e}^{2+}} \right]=\dfrac{1}{\left[ {{K}_{c}} \right]\left[ {{S}^{2-}} \right]}\]
\[x=\dfrac{1}{\left( 1.6\times {{10}^{17}} \right)\times \left( 0.07 \right)}\]
\[x=\dfrac{100}{7\times 2.6}\times {{10}^{-17}}\]
\[x=8.93\times {{10}^{-17}}\]
\[Y=8.93\]

Therefore the value of Y is 8.93.

Note: Keep in mind that the iron (II) sulphide adopts the nickel arsenide structure, featuring trigonal prismatic sulfide sites and octahedral iron centers. Also, FeS reacts with hydrochloric acid, releasing hydrogen sulfide. In moist air, iron sulfides get oxidized to give ferrous sulfate. Also, do not confuse between sulfate, sulfite and sulfide ions. They are $SO_{4}^{2-},SO_{3}^{2-},{{S}^{2-}}$ respectively.