
A precipitate of $AgCl$ is formed when equal volumes of the following are mixed [${{10}^{-4}}{{10}^{-5}}{{10}^{-6}}{{10}^{-9}}MAgN{{O}_{3}}MHC{{l}^{-}}{{Q}_{sp}}{{K}_{sp}}A{{g}^{+}}\frac{{{10}^{-4}}}{2}M$${{K}_{sp}}$ for $AgCl$=${{10}^{-10}}$]
A. ${{10}^{-4}}$ $MAgN{{O}_{3}}$ and ${{10}^{-7}}$ $MHCl$
B. ${{10}^{-5}}$$MAgN{{O}_{3}}$and ${{10}^{-6}}$$MHCl$
C. ${{10}^{-5}}$$MAgN{{O}_{3}}$and ${{10}^{-4}}$$MHCl$
D. ${{10}^{-6}}$$MAgN{{O}_{3}}$and ${{10}^{-6}}$$MHCl$
Answer
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Hint: Precipitation process is a process in which a chemical reaction occurs in an aqueous medium where two ionic bonds combine , resulting in the formation of an insoluble salt which is called precipitate. The process of precipitation occurs for those reactions only if the ${{Q}_{sp}}$ > ${{K}_{sp}}$ condition is true.
Complete Step by Step Answer:
The solubility product quotient of a solution determines the process of precipitation will occur or not . The solubility product constant should be less than this value in order for precipitation. In an aqueous solution of $MAgN{{O}_{3}}$ there will be production of ions as $A{{g}^{+}}$and from $MHCl$the production of ion $C{{l}^{-}}$ is produced which ions are used in the formation of $AgCl$. Now in this case we need to check for the options whether the condition ${{Q}_{sp}}$>${{K}_{sp}}$holds true or not. For the concentration this holds true will be the correct option only .
A. ${{10}^{-4}}$ $MAgN{{O}_{3}}$ and ${{10}^{-7}}$ $MHCl$
Here,[ $A{{g}^{+}}$]=$\frac{{{10}^{-4}}}{2}M$ and [$C{{l}^{-}}$]=$\frac{{{10}^{-7}}}{2}M$
And so ${{Q}_{sp}}$=[ $A{{g}^{+}}$][$C{{l}^{-}}$]=2.5×${{10}^{-12}}$
Since here ${{Q}_{sp}}$>${{K}_{sp}}$ does not hold true . So it will not be the correct option.
B. ${{10}^{-5}}$$MAgN{{O}_{3}}$and ${{10}^{-6}}$$MHCl$
Here,[ $A{{g}^{+}}$]= $\frac{{{10}^{-5}}}{2}M$ and [$C{{l}^{-}}$]=$\frac{{{10}^{-6}}}{2}M$
And so ${{Q}_{sp}}$=[ $A{{g}^{+}}$][$C{{l}^{-}}$]=2.5×${{10}^{-12}}$
Since here ${{Q}_{sp}}$>${{K}_{sp}}$ does not hold true . So it will not be the correct option.
C. ${{10}^{-5}}$$MAgN{{O}_{3}}$and ${{10}^{-4}}$$MHCl$
Here,[ $A{{g}^{+}}$]= $\frac{{{10}^{-5}}}{2}M$and [$C{{l}^{-}}$]= $\frac{{{10}^{-4}}}{2}M$
And so ${{Q}_{sp}}$=[ $A{{g}^{+}}$][$C{{l}^{-}}$]=2.5× ${{10}^{-9}}$
Since here ${{Q}_{sp}}$>${{K}_{sp}}$ holds true . So it will be the correct option.
Thus, the correct option will be C.
Note: The concentration of the cation and anion from the given concentrations of the compounds will be half of the total concentrations this should be taken care of during the calculations.
Complete Step by Step Answer:
The solubility product quotient of a solution determines the process of precipitation will occur or not . The solubility product constant should be less than this value in order for precipitation. In an aqueous solution of $MAgN{{O}_{3}}$ there will be production of ions as $A{{g}^{+}}$and from $MHCl$the production of ion $C{{l}^{-}}$ is produced which ions are used in the formation of $AgCl$. Now in this case we need to check for the options whether the condition ${{Q}_{sp}}$>${{K}_{sp}}$holds true or not. For the concentration this holds true will be the correct option only .
A. ${{10}^{-4}}$ $MAgN{{O}_{3}}$ and ${{10}^{-7}}$ $MHCl$
Here,[ $A{{g}^{+}}$]=$\frac{{{10}^{-4}}}{2}M$ and [$C{{l}^{-}}$]=$\frac{{{10}^{-7}}}{2}M$
And so ${{Q}_{sp}}$=[ $A{{g}^{+}}$][$C{{l}^{-}}$]=2.5×${{10}^{-12}}$
Since here ${{Q}_{sp}}$>${{K}_{sp}}$ does not hold true . So it will not be the correct option.
B. ${{10}^{-5}}$$MAgN{{O}_{3}}$and ${{10}^{-6}}$$MHCl$
Here,[ $A{{g}^{+}}$]= $\frac{{{10}^{-5}}}{2}M$ and [$C{{l}^{-}}$]=$\frac{{{10}^{-6}}}{2}M$
And so ${{Q}_{sp}}$=[ $A{{g}^{+}}$][$C{{l}^{-}}$]=2.5×${{10}^{-12}}$
Since here ${{Q}_{sp}}$>${{K}_{sp}}$ does not hold true . So it will not be the correct option.
C. ${{10}^{-5}}$$MAgN{{O}_{3}}$and ${{10}^{-4}}$$MHCl$
Here,[ $A{{g}^{+}}$]= $\frac{{{10}^{-5}}}{2}M$and [$C{{l}^{-}}$]= $\frac{{{10}^{-4}}}{2}M$
And so ${{Q}_{sp}}$=[ $A{{g}^{+}}$][$C{{l}^{-}}$]=2.5× ${{10}^{-9}}$
Since here ${{Q}_{sp}}$>${{K}_{sp}}$ holds true . So it will be the correct option.
Thus, the correct option will be C.
Note: The concentration of the cation and anion from the given concentrations of the compounds will be half of the total concentrations this should be taken care of during the calculations.
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