Question

In which of the following conditions precipitate of $AgCl$ is formed, when equal volumes are mixed? ( ${K_{sp}}$ for $AgCl$ $ = {10^{ - 10}}$)
A.${10^{ - 6}}M$ $HCl$ and ${10^{ - 6}}M$ $AgN{O_3}$
B.${10^{ - 7}}M$ $HCl$ and ${10^{ - 4}}M$ $AgN{O_3}$
C.${10^{ - 4}}M$ $HCl$ and ${10^{ - 5}}M$ $AgN{O_3}$
D.${10^{ - 6}}M$ $HCl$ and ${10^{ - 5}}M$ $AgN{O_3}$

Answer 1

Hint:For the occurrence of precipitation the ionic product must be greater than solubility product. $({Q_{sp}} > {K_{sp}})$. For the given question ${Q_{sp}} = [A{g^ + }][C{l^ - }]$ .For verifying the condition analyse each option individually.

Complete step by step answer:
This question is from the concept of Ionic equilibrium. First let us get familiar with solubility products $({K_{sp}})$ and ionic products $({Q_{sp}})$ .
A solubility product, or ${K_{sp}}$ , is the equilibrium constant for a chemical reaction in which a solid ionic compound dissolves to yield its ions in solution.
The ionic product is the product of the concentrations of ions, each raised to the power specified by its stoichiometric coefficient in a solution of a salt.
So, the basic concept for the occurrence of precipitation is that the ionic product must be greater than the solubility product.
Also, the value of solubility product is given in the question
  ${K_{sp}}$ for $AgCl$ $ = {10^{ - 10}}$
Now, we will find the value of ${Q_{sp}}$ by the help of its definition given above
So, as per the definition
${Q_{sp}} = [A{g^ + }][C{l^ - }]$
To find ${Q_{sp}}$ we require the concentration of $A{g^ + }$ and $C{l^ - }$ which we can get through the options.
So we will cross check every option given and verify.
For Option A,
${Q_{sp}} = [A{g^ + }][C{l^ - }]$
Substituting the values as given in the option
 $ \Rightarrow {Q_{sp}} = {10^{ - 6}} \times {10^{ - 6}}$
 $ \Rightarrow {Q_{sp}} = {10^{ - 12}}$
Therefore we get,
${Q_{sp}} < {K_{sp}}$
Hence precipitation will not occur.
For Option B
${Q_{sp}} = [A{g^ + }][C{l^ - }]$
Substituting the values as given in the option
 $ \Rightarrow {Q_{sp}} = {10^{ - 7}} \times {10^{ - 4}}$
  $ \Rightarrow {Q_{sp}} = {10^{ - 11}}$
Therefore we get
${Q_{sp}} < {K_{sp}}$
Hence precipitation will not occur
For Option C
${Q_{sp}} = [A{g^ + }][C{l^ - }]$
Substituting the values as given in the option
 $ \Rightarrow {Q_{sp}} = {10^{ - 4}} \times {10^{ - 5}}$
 $ \Rightarrow {Q_{sp}} = {10^{ - 9}}$
Therefore we get
${Q_{sp}} > {K_{sp}}$
 Hence precipitation will occur
So option C is the correct answer.

Note:
Both ionic product and solubility product represent the product of the concentrations of the ions in the solution.On the other hand, the term solubility product is applied only to a saturated solution in which there exists a dynamic equilibrium between the undissolved salt and the ions present in solution.