Question

The precipitate of ${\mathrm{Ag}}_2{\mathrm{CrO}}_4({\mathrm{K}}_{\mathrm{sp}}=1.9\mathrm{x}{10}^{-12})$ is obtained when equal volumes of the following are mixed:

• A. ${10}^{-4}{\mathrm{MAg}}^{+}+{10}^{-4}{{\mathrm{MCrO}}_4}^{2-}$
• B. ${10}^{-2}{\mathrm{MAg}}^{+}+{10}^{-5}{{\mathrm{MCrO}}_4}^{2-}$
• C. ${10}^{-5}{\mathrm{MAg}}^{+}+{10}^{-3}{{\mathrm{MCrO}}_4}^{2-}$
• D. ${10}^{-4}{\mathrm{MAg}}^{+}+{10}^{-5}{{\mathrm{MCrO}}_4}^{2-}$

Answer 1

The correct option is B

${10}^{-2}{\mathrm{MAg}}^{+}+{10}^{-5}{{\mathrm{MCrO}}_4}^{2-}$

Explanation for correct option:

(B) ${10}^{-2}{\mathrm{MAg}}^{+}+{10}^{-5}{{\mathrm{MCrO}}_4}^{2-}$

Step 1: Condition for precipitation:

• When the product of the ions present i.e ionic product ${\mathrm{Q}}_{\mathrm{sp}}$should be greater than the solubility product ${\mathrm{K}}_{\mathrm{sp}}$.

Step 2: Check the option for the ionic products:

• The dissociation of silver chromate will be as,

${\mathrm{Ag}}_2{\mathrm{CrO}}_4\left(\mathrm{aq}\right)\rightleftharpoons 2{\mathrm{Ag}}^{+}\left(\mathrm{aq}\right)+{{\mathrm{CrO}}_4}^{2-}\left(\mathrm{aq}\right)$

$$\begin{gathered} {\mathrm{Q}}_{\mathrm{sp}}={\left[{\mathrm{Ag}}^{+}\right]}^2\left[{{\mathrm{CrO}}_4}^{2-}\right](\mathrm{When}\mathrm{equal}\mathrm{volumes}\mathrm{of}\mathrm{two}\mathrm{solutions}\mathrm{are}\mathrm{mixed}\mathrm{the}\mathrm{concentration}\mathrm{is}\mathrm{reduced}\mathrm{to}\mathrm{half}\mathrm{for}\mathrm{each}) \\ ={\left(\frac{{10}^{-2}}{2}\right)}^2\left(\frac{{10}^{-5}}{2}\right) \\ =\frac{1}{8}\mathrm{x}{10}^{-11} \\ =1.25\mathrm{x}{10}^{-11}>1.9\mathrm{x}{10}^{-12} \\ {\mathrm{Q}}_{\mathrm{sp}}>{\mathrm{K}}_{\mathrm{sp}} \end{gathered}$$

Hence precipitation occurs, this is the correct option

Explanation for incorrect option:

(A)${10}^{-4}{\mathrm{MAg}}^{+}+{10}^{-4}{{\mathrm{MCrO}}_4}^{2-}$

• The value ${\mathrm{Q}}_{\mathrm{sp}}-1.25\mathrm{x}{10}^{-12}$is less than ${\mathrm{K}}_{\mathrm{sp}}$ value, so this is an incorrect option.

(C)${10}^{-5}{\mathrm{MAg}}^{+}+{10}^{-3}{{\mathrm{MCrO}}_4}^{2-}$

• The value ${\mathrm{Q}}_{\mathrm{sp}}-1.25\mathrm{x}{10}^{-13}$is less than ${\mathrm{K}}_{\mathrm{sp}}$ value, so this is an incorrect option.

(D) ${10}^{-4}{\mathrm{MAg}}^{+}+{10}^{-5}{{\mathrm{MCrO}}_4}^{2-}$

• The value ${\mathrm{Q}}_{\mathrm{sp}}-1.25\mathrm{x}{10}^{-13}$is less than ${\mathrm{K}}_{\mathrm{sp}}$ value, so this is an incorrect option.

Hence, the correct option is (B) ${10}^{-2}{\mathrm{MAg}}^{+}+{10}^{-5}{{\mathrm{MCrO}}_4}^{2-}$