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Chapter 15: Q15 E (page 871)

Assuming that no equilibria other than dissolution are involved, calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion. Show that changes in the initial concentrations of the common ions can be neglected.

\(\begin{array}{l}(a)AgCl(\;s\;)in 0.025MNaCl \\(b)Ca{F_2}(\;\;s\;)in 0.00133MKF \\(c)A{g_2}S{O_4}(\;\;s\;)in 0.500\;L of a solution containing 19.50\;g of {K_2}S{O_4}\\(d)Zn{(OH)_2}(\;s\;)in a solution buffere data pHof 11.45\end{array}\)

Short Answer

Expert verified

\(\begin{array}{l}{\rm{a)}}\left[ {{\rm{A}}{{\rm{g}}^{\rm{ + }}}} \right]{\rm{ = 7}}{\rm{.2 \times 1}}{{\rm{0}}^{{\rm{ - 9}}}}{\rm{M;}}\left[ {{\rm{C}}{{\rm{l}}^{\rm{ - }}}} \right]{\rm{ = 0}}{\rm{.025M}}\\{\rm{b)}}\left[ {{\rm{C}}{{\rm{a}}^{{\rm{2 + }}}}} \right]{\rm{ = 2}}{\rm{.2 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{M;}}\left[ {{{\rm{F}}^{\rm{ - }}}} \right]{\rm{ = 0}}{\rm{.0013M}}\\{\rm{c)}}\left[ {{\rm{A}}{{\rm{g}}^{\rm{ + }}}} \right]{\rm{ = 2}}{\rm{.3 \times 1}}{{\rm{0}}^{{\rm{ - 9}}}}{\rm{M;}}\left[ {{\rm{SO}}_{\rm{4}}^{{\rm{2 - }}}} \right]{\rm{ = 0}}{\rm{.2238M}}\\{\rm{d)}}\left[ {{\rm{Z}}{{\rm{n}}^{{\rm{2 + }}}}} \right]{\rm{ = 5}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 12}}}}{\rm{M;}}\left[ {{\rm{O}}{{\rm{H}}^{\rm{ - }}}} \right]{\rm{ = 2}}{\rm{.8 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}{\rm{M}}\end{array}\)

Step by step solution

01

Step 1: To calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion.

(a)

\({{\rm{K}}_{{\rm{sp}}}}{\rm{ = 1}}{\rm{.8 \times 1}}{{\rm{0}}^{{\rm{ - 10}}}}{\rm{ = }}\left[ {{\rm{A}}{{\rm{g}}^{\rm{ + }}}} \right]\left[ {{\rm{C}}{{\rm{l}}^{\rm{ - }}}} \right]{\rm{ = }}\;{\rm{x}}\; \times {\rm{(x}}\;{\rm{ + }}\;{\rm{0}}{\rm{.025)}}\)

If we assume that\(x\)is small comparing to\(0.025\), then

\(\begin{array}{l}\left[ {{\rm{C}}{{\rm{l}}^{\rm{ - }}}} \right]{\rm{ = 0}}{\rm{.025}}{{\rm{M}}^{\rm{ - }}}\\{{\rm{K}}_{{\rm{sp}}}}{\rm{ = 1}}{\rm{.8 \times 1}}{{\rm{0}}^{{\rm{ - 10}}}}{\rm{ = }}\;{\rm{x}}\;{\rm{ \times }}\;{\rm{0}}{\rm{.025}}\end{array}\)

\(\begin{array}{l}{\rm{x}}\;{\rm{ = }}\;\frac{{{\rm{1}}{\rm{.8 \times 1}}{{\rm{0}}^{{\rm{ - 10}}}}}}{{{\rm{0}}{\rm{.025}}}}\;{\rm{ = }}\;{\rm{7}}{\rm{.2 \times 1}}{{\rm{0}}^{{\rm{ - 9}}}}{\rm{M}}\;{\rm{ = }}\;\left[ {{\rm{A}}{{\rm{g}}^{\rm{ + }}}} \right]\\\frac{{{\rm{7}}{\rm{.2 \times 1}}{{\rm{0}}^{{\rm{ - 9}}}}{\rm{M}}}}{{{\rm{0}}{\rm{.025}}}}{\rm{ \times 100\% }}\;{\rm{ = }}\;{\rm{2}}{\rm{.9 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{\% }}\\{\rm{The change is not significant }}\end{array}\)

02

Step 2: To calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion.

\(\begin{array}{l}{{\rm{K}}_{{\rm{sp}}}}{\rm{ = 3}}{\rm{.9 \times 1}}{{\rm{0}}^{{\rm{ - 11}}}}\\{\rm{ = }}\;\left[ {{\rm{C}}{{\rm{a}}^{{\rm{2 + }}}}} \right]{\left[ {{{\rm{F}}^{\rm{ - }}}} \right]^{\rm{2}}}\\{\rm{ = }}\;{\rm{x \times (2x + 0}}{\rm{.00133M}}{{\rm{)}}^{\rm{2}}}\end{array}\)

If we assume that x is small comparing to 0.0013 M, then:

\(\begin{array}{l}\left[ {{{\rm{F}}^{\rm{ - }}}} \right]{\rm{ = 0}}{\rm{.0013M;}}\\{\rm{x}}\;{\rm{ = }}\frac{{{\rm{3}}{\rm{.9 \times 1}}{{\rm{0}}^{{\rm{ - 11}}}}}}{{{\rm{0}}{\rm{.0013}}{{\rm{3}}^{\rm{2}}}}}{\rm{ = 2}}{\rm{.2 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{M}}\;{\rm{ = }}\;\left[ {{\rm{C}}{{\rm{a}}^{{\rm{2 + }}}}} \right]\\\frac{{{\rm{2}}{\rm{.25 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{M}}}}{{{\rm{0}}{\rm{.00133M}}}}{\rm{ \times 100\% }}\;{\rm{ = }}\;{\rm{1}}{\rm{.69\% }}\\{\rm{ The change is not significant}}\end{array}\)

03

Step 3: To calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion.

First we need the concentration of\({K_2}S{O_4}\):

\(\begin{array}{l}{\rm{ = }}\frac{{{\rm{19}}{\rm{.50\;g}}}}{{{\rm{174}}{\rm{.260\;g/mol}}}}{\rm{ = 0}}{\rm{.1119\;mol}}\\\frac{{{\rm{0}}{\rm{.1119\;mol}}}}{{{\rm{0}}{\rm{.5\;L}}}}\;{\rm{ = }}\;{\rm{0}}{\rm{.2238M}}\;{\rm{ = }}\;\left[ {{\rm{SO}}_{\rm{4}}^{{\rm{2 - }}}} \right]{{\rm{K}}_{{\rm{sp}}}}{\rm{ = 1}}{\rm{.18 \times 1}}{{\rm{0}}^{{\rm{ - 18}}}}{\rm{ = }}\left[ {{\rm{Ag}}{{\rm{g}}^{\rm{ + }}}} \right]\left[ {{\rm{SO}}_{\rm{4}}^{{\rm{2 - }}}} \right]\\{\rm{ = }}\;{\rm{4}}{{\rm{x}}^{\rm{2}}}{\rm{ \times (x + 0}}{\rm{.2238)}}\\{\rm{x}}\;{\rm{ = }}\sqrt {\frac{{{\rm{1}}{\rm{.18 \times 1}}{{\rm{0}}^{{\rm{ - 18}}}}}}{{{\rm{4 \times 0}}{\rm{.02238}}}}} {\rm{ = 1}}{\rm{.15 \times 1}}{{\rm{0}}^{{\rm{ - 9}}}}\\{\rm{ For A}}{{\rm{g}}_{\rm{2}}}{\rm{SO}}{{\rm{O}}_{\rm{4}}}{\rm{:1}}{\rm{.15 \times 1}}{{\rm{0}}^{{\rm{ - 9}}}}{\rm{ \times [Ag]}}\;{\rm{ = }}\;{\rm{2x}}\;{\rm{ = }}\;{\rm{2}}{\rm{.30 \times 1}}{{\rm{0}}^{{\rm{ - 9}}}}{\rm{M}}\\\frac{{{\rm{1}}{\rm{.15 \times 1}}{{\rm{0}}^{{\rm{ - 9}}}}}}{{{\rm{0}}{\rm{.2238}}}}{\rm{ \times 100\% }}\;{\rm{ = }}\;{\rm{5}}{\rm{.1 \times 1}}{{\rm{0}}^{{\rm{ - 7}}}}{\rm{\% }}\\{\rm{The change is insignificant }}\end{array}\)

04

Step 4: To calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion.

First, we need the concentration of hydroxide ion

\(\begin{array}{l}{\rm{O}}{{\rm{H}}^{\rm{ - }}}{\rm{:pOH = 14 - 11}}{\rm{.45}}\\{\rm{ = }}\;{\rm{2}}{\rm{.55;}}\left[ {{\rm{O}}{{\rm{H}}^{\rm{ - }}}} \right]\\{\rm{ = }}\;{\rm{2}}{\rm{.8 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}{\rm{M}}\end{array}\)

\(\begin{array}{l}{{\rm{K}}_{{\rm{sp}}}}{\rm{ = 4}}{\rm{.5 \times 1}}{{\rm{0}}^{{\rm{ - 17}}}}{\rm{ = }}\left[ {{\rm{Z}}{{\rm{n}}^{{\rm{2 + }}}}} \right]{\left[ {{\rm{O}}{{\rm{H}}^{\rm{ - }}}} \right]^{\rm{2}}}{\rm{ = x \times }}{\left( {{\rm{2x + 2}}{\rm{.8 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}} \right)^{\rm{2}}}\\{\rm{If we assume that x is small comparing to 2}}{\rm{.8 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}{\rm{:x = }}\frac{{{\rm{4}}{\rm{.5 \times 1}}{{\rm{0}}^{{\rm{ - 17}}}}}}{{{{\left( {{\rm{2}}{\rm{.8 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}} \right)}^{\rm{2}}}}}\\{\rm{ = 5}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 12}}}}{\rm{M = }}\left[ {{\rm{Z}}{{\rm{n}}^{{\rm{2 + }}}}} \right]\\{\rm{ = }}\frac{{{\rm{5}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 12}}}}}}{{{\rm{2}}{\rm{.8 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}}}{\rm{ \times 100\% = 2 \times 1}}{{\rm{0}}^{{\rm{ - 7}}}}{\rm{\% }}\\{\rm{The change is insignificant}}\end{array}\)

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Most popular questions from this chapter

A solution is 0.010 M in both Cu2+and Cd2+. What percentage ofCd2+remains in the solution when 99.9% of the Cu2+ has been precipitated as CuS by adding sulfide?

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Question: A roll of \(35 - mm\) black and white photographic film contains about \(0.27g\) of unexposed \(AgBr\) before developing. What mass of \(N{a_2}{S_2}{O_3} \cdot 5{H_2}O\) (sodium thiosulfate penta hydrate or hypo) in \(1.0L\)of developer is required to dissolve the \(AgBr\)as \(Ag\left( {{S_2}{O_3}} \right)_2^{3 - }\left( {{K_f} = 4.7 \times 1{0^{13}}} \right)?\)

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\(\begin{array}{*{20}{c}}{CoS(s) \rightleftharpoons C{o^{2 + }}(aq) + {S^{2 - }}(aq)\quad \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{K_{sp}} = 4.5 \times 1{0^{ - 27}}} \\ {{H_2}S(aq) + 2{H_2}O(l) \rightleftharpoons 2{H_3}{O^ + }(aq) + {S^{2 - }}(aq)\quad \;\;\;\;\;\;\;\;\;K = 1.0 \times 1{0^{ - 26}}} \end{array}\;\;\)
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