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# If excess of $AgC{{O}_{3}}$ solution is added to $100mL$ of a $0.024M$ solution of dichlorobis (ethylenediamine) cobalt $(III)$ chloride. How many moles of $AgCl$ be precipitated?A. $0.0012$B. $0.0016$C. $0.0024$D. $0.0048$

Last updated date: 12th Aug 2024
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Hint: The question given is just a regular limiting reactant problem. The only thing is to figure out the charge of the complex given i.e. dichlorobis (ethylenediamine) cobalt $(III)$ chloride.

Complete step by step solution:
Given that, Excess of $AgC{{O}_{3}}$ solution is added to $100mL$ ($0.1L$) of a $0.024M$ solution of dichlorobis (ethylenediamine) cobalt $(III)$ chloride. We have to find out the number of moles of $AgCl$ is precipitated.
Dichlorobis (ethylenediamine) cobalt $(III)$ chloride (with chemical formula $[CoC{{l}_{2}}{{(en)}_{2}}]Cl$ is a complex which has two -chloro ligands ($C{{l}^{-}}$), having an oxidation state of $-1$ in the inner coordination sphere, two ethylenediamine ligands (${{H}_{2}}N-C{{H}_{2}}-C{{H}_{2}}-N{{H}_{2}}$), having an oxidation state of $0$ in the inner coordination sphere, a chloride ($C{{l}^{-}}$) ligand which is coordinated on the outer coordination sphere and cobalt $(III)$, having oxidation state of $3$.
In short, we can say that the coordination sphere of a complex contains, $C{{o}^{3+}}+2C{{l}^{-}}+2(en)$ .
So, the net oxidation charge of the coordination sphere adds up as $2\times (-1)+2\times 0+(+3)=+1$.
Thus the complex has an oxidation state of $+1$.
The reaction between $[CoC{{l}_{2}}{{(en)}_{2}}]Cl$ and $AgC{{O}_{3}}$ is an outer sphere, double replacement reaction. The reaction is shown as follows:
$AgC{{O}_{3}}_{(aq)}+[CoC{{l}_{2}}{{(en)}_{2}}]C{{l}_{(aq)}}\to AgC{{l}_{(s)}}+[CoC{{l}_{2}}{{(en)}_{2}}]C{{O}_{3}}_{(aq)}$
We can see that the complex is clearly the limiting reactant so the number of moles will be the product of molarity and the volume in litres.
Thus, the number of moles will be $0.024\times 0.1=0.0024$.
We can see that the complex is $1:1$ with $AgCl$. So, $0.0024$moles of $AgCl$ will be precipitated.

Hence, the correct option is C.

Note: It is important to keep in mind that; ethylenediamine ligands are bidentate, sigma donor and are strong field ligands. The complexes having these ligands will behave as a low-spin complex where the inner coordination sphere will be inert.