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Chapter 15: Q24 E (page 872)

Perform the following calculations:

(a) Calculate \(\left[ {A{g^ + }} \right]\)in a saturated aqueous solution of\(AgBr\).

(b) What will \(\left[ {A{g^ + }} \right]\)be when enough \(KBr\)has been added to make \(\left[ {B{r^ - }} \right] = 0.050M\) ?

(c) What will \(\left[ {B{r^ - }} \right]\)be when enough \(AgN{O_3}\)has been added to make\(\left[ {A{g^ + }} \right] = 0.020M\)?

Short Answer

Expert verified

The solubility product constant represented as Ksp can be defined as state in which a solid and its respective ions in given solution are in equilibrium. Its value indicates the extent to which a compound can undergo dissociation in water.

a) \(\left[ {{\rm{A}}{{\rm{g}}^ + }} \right] = 7.07 \cdot {10^{ - 7}}\)

b) \(\left[ {{\rm{A}}{{\rm{g}}^ + }} \right] = {1.10^{ - 11}}\)

c) \(\left[ {{\rm{B}}{{\rm{r}}^ - }} \right] = 2.5 \cdot {10^{ - 11}}\)

Step by step solution

01

To calculate \(\left[ {A{g^ + }} \right]\)in a saturated aqueous solution of \(AgBr\) Step 2: To calculate \(\left[ {A{g^ + }} \right]\) when enough \(KBr\) has been added to make\(\left[ {B{r^ - }} \right] = 0.050M\)?

\({{\rm{K}}_{{\rm{sp}}}} = \left[ {{\rm{A}}{{\rm{g}}^ + }} \right]\left[ {{\rm{B}}{{\rm{r}}^ - }} \right]\)

Expression for\(\left[ {{\rm{B}}{{\rm{r}}^ - }} \right]\)is\(({\rm{x}} + 0.05)\)- here\(0.05\)is coming from\({\rm{KBr}}\). However,\(x\)here is very, very small number, so we can neglect it to simplify the equation. If we substitute\({{\rm{K}}_{{\rm{sp}}}}\)for its value, we get:

\(5 \cdot {10^{ - 13}} = {\rm{x}} \cdot 0.05\)

\({\rm{x}} = \frac{{5 \cdot {{10}^{ - 13}}}}{{0.05}}\)

\({\rm{x}} = 1 \cdot {10^{ - 11}}\)

\(\left[ {{\rm{A}}{{\rm{g}}^ + }} \right] = 1 \cdot {10^{ - 11}}\)

02

To calculate \(\left[ {B{r^ - }} \right]\) when enough \(AgN{O_3}\) has been added to make\(\left[ {A{g^ + }} \right] = 0.020M\)?

Dissociation of

\({{\rm{K}}_{{\rm{sp}}}} = \left[ {{\rm{A}}{{\rm{g}}^ + }} \right]\left[ {{\rm{B}}{{\rm{r}}^ - }} \right]\)

Expression for\(\left[ {{\rm{A}}{{\rm{g}}^ + }} \right]\)is\(({\rm{x}} + 0.02)\)- here\(0.02\)is coming from\({\rm{AgN}}{{\rm{O}}_3}\). However,\({\rm{x}}\)here is very, very small number, so we can neglect it to simplify the equation. If we substitute\({{\rm{K}}_{{\rm{sp}}}}\)for its value, we get:

\(\begin{array}{l}5 \cdot {10^{ - 13}} = 0.02 \cdot {\rm{x}}\\{\rm{x}} = \frac{{5 \cdot {{10}^{ - 13}}}}{{0.02}}\\{\rm{x}} = 1 \cdot {10^{ - 11}}\end{array}\)

\(\left[ {{\rm{B}}{{\rm{r}}^ - }} \right] = 2.5 \cdot {10^{ - 11}}\)

Finally we get,

a) \(\left[ {{\rm{A}}{{\rm{g}}^ + }} \right] = 7.07 \cdot {10^{ - 7}}\)

b) \(\left[ {{\rm{A}}{{\rm{g}}^ + }} \right] = {1.10^{ - 11}}\)

c) \(\left[ {{\rm{B}}{{\rm{r}}^ - }} \right] = 2.5 \cdot {10^{ - 11}}\)

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Most popular questions from this chapter

Question: 30. Which of the following compounds precipitates from a solution that has the concentrations indicated? (See Appendix J for \({K_{sp}}\) values.)

(a) \(KCl{O_4}:\left( {{K^ + }} \right) = 0.01{M^ - }\left( {ClO_4^ - } \right) = 0.01M\)

(b) \({K_2}PtC{l_6}:\left( {{K^ + }} \right) = 0.01M,\left( {PtC{l_6}^{2 - }} \right) = 0.01M\) \(\)

(c) \(Pb{I_2}:\left( {P{b^{2 + }}} \right) = 0.003M,\left( {{I^ - }} \right) = 1.3 \times 1{0^{ - 3}}M\)

(d) \(A{g_2}\;S:\left( {A{g^ + }} \right) = 1 \times 1{0^{ - 10}}M,\left( {{S^{2 - }}} \right) = 1 \times 1{0^{ - 13}}M\)

Magnesium hydroxide and magnesium citrate function as mild laxatives when they reach the small intestine. Why do magnesium hydroxide and magnesium citrate, two very different substances, have the same effect in your small intestine. (Hint: The contents of the small intestine are basic.)

Question: A solution contains \(1.0 \times 1{0^{ - 2}}\)mol of KI and 0.10 mol of KCl per liter. \(AgN{O_3}\)is gradually added to this solution. Which forms first, solid AgI or solid AgCl?

Question: Perform the following calculations involving concentrations of iodate ions:

(a) The iodate ion concentration of a saturated solution of \(La{\left( {I{O_3}} \right)_3}\)was found to be\(3.1 \times 1{0^{ - 3}}mol/L\). Find the\({K_{sp}}\).

(b) Find the concentration of iodate ions in a saturated solution of \(Cu{\left( {I{O_3}} \right)_2}\left( {{K_{5p}} = 7.4 \times 1{0^{ - 8}}} \right)\).

Question: 28. The following concentrations are found in mixtures of ions in equilibrium with slightly soluble solids. From the concentrations given, calculate \({K_{sp}}\)for each of the slightly soluble solids indicated:

(a) \(AgBr:\left( {A{g^ + }} \right) = 5.7 \times 1{0^{ - 7}}M,\left( {B{r^ - }} \right) = 5.7 \times 1{0^{ - 7}}M\)

(b) \(CaC{O_3}:\left( {C{a^{2 + }}} \right) = 5.3 \times 1{0^{ - 3}}M,\left( {C{O_3}^{2 - }} \right) = 9.0 \times 1{0^{ - 7}}M\)

(c) \(Pb{F_2}:\left( {P{b^{2 + }}} \right) = 2.1 \times 1{0^{ - 3}}M,\left( {{F^ - }} \right) = 4.2 \times 1{0^{ - 3}}M\)

(d) \(A{g_2}Cr{O_4}:\left( {A{g^ + }} \right) = 5.3 \times 1{0^{ - 5}}M,3.2 \times 1{0^{ - 3}}M\)

(e) \(In{F_3}:\left( {I{n^{3 + }}} \right) = 2.3 \times 1{0^{ - 3}}M,\left( {{F^ - }} \right) = 7.0 \times 1{0^{ - 3}}M\)
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