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Chapter 21: Problem 105

Will 0.10 mol of AgBr completely dissolve in 1.0 \(\mathrm{L}\) of 3.0 \(\mathrm{M} \mathrm{NH}_{3} ?\) The \(K_{\mathrm{sp}}\) value for \(\mathrm{AgBr}(s)\) is \(5.0 \times 10^{-13},\) and the overall formation constant for the complex ion \(\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}+\) is \(1.7 \times 10^{7}\) , that is, $$\mathrm{Ag}^{+}(a q)+2 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}(a q) \quad K=1.7 \times 10^{7}$$

Short Answer

Expert verified
The solubility of AgBr in the presence of 3.0 M NH₃ is calculated to be approximately \(7.1 \times 10^{-7}\ \mathrm{M}\). Given the maximum amount of AgBr that can dissolve is about \(7.1 \times 10^{-7}\ \mathrm{mol}\) in 1.0 L of NH₃ solution, which is much smaller than the given amount of AgBr (0.10 mol), it will not completely dissolve.

Step by step solution

01

Write the Ksp expression for AgBr

The solubility product (Ksp) expression for AgBr can be written as follows: \[K_{sp} = [\mathrm{Ag}^+][\mathrm{Br}^-]\] We are given the value of Ksp as \(5.0 \times 10^{-13}\).
02

Write the complex formation reaction and its equilibrium expression

The formation of the complex ion Ag(NH3)2+ can be represented as: \[\mathrm{Ag}^+ + 2 \mathrm{NH}_3 \rightleftharpoons \mathrm{Ag}(\mathrm{NH}_3)_2^+\] The equilibrium expression for this reaction is: \[K = \frac{[\mathrm{Ag}(\mathrm{NH}_3)_2^+]}{[\mathrm{Ag}^+][\mathrm{NH}_3]^2}\] We are given the value of K as \(1.7 \times 10^{7}\).
03

Relate the equilibrium expressions with the solubility of AgBr

Let the solubility of AgBr in moles per liter (molar solubility) be represented by S. The concentration of Ag+ will be equal to S, and the concentration of Br- will also be equal to S. The concentration of NH3 is given as 3.0 M. Using the equilibrium expression for the complex formation, we can write: \[1.7 \times 10^7 = \frac{[\mathrm{Ag}(\mathrm{NH}_3)_2^+]}{[\mathrm{Ag}^+][\mathrm{NH}_3]^2}\] We can relate this to the solubility of AgBr: \[1.7 \times 10^7 = \frac{[\mathrm{Ag}(\mathrm{NH}_3)_2^+]}{(S)(3)^2}\] Solve for the concentration of Ag(NH3)2+: \[[\mathrm{Ag}(\mathrm{NH}_3)_2^+] = (1.7 \times 10^7)(S)(3)^2\]
04

Use the Ksp expression to find the solubility of AgBr

Using the Ksp expression and the relationship in Step 3, we can write: \(5.0 \times 10^{-13} = S (S + (1.7 \times 10^7)(S)(3)^2)\) Simplify the equation and solve for S: \(5.0 \times 10^{-13} = S^2 + (1.53 \times 10^8)S^3\) Since the Ksp value is very small, we can make the approximation that S^3 is much smaller compared to the S^2 term. Therefore, we can ignore the S^3 term and solve for S: \(5.0 \times 10^{-13} \approx S^2\) Solving for S, we get: \[S = \sqrt{5.0 \times 10^{-13}} \approx 7.1 \times 10^{-7}\ \mathrm{M}\]
05

Calculate the maximum amount of AgBr that can dissolve in 1.0 L solution

Now that we have the solubility of AgBr, we can calculate the maximum amount of AgBr that can dissolve in 1.0 L of the NH3 solution: \[7.1 \times 10^{-7}\ \mathrm{M} \times 1.0\ \mathrm{L} \approx 7.1 \times 10^{-7}\ \mathrm{mol}\]
06

Compare the maximum amount with the given amount of AgBr

We found that the maximum amount of AgBr that can dissolve in 1.0 L of 3.0 M NH3 solution is approximately 7.1 x 10^-7 mol. Since this value is much smaller than the given amount of AgBr (0.10 mol), the given amount of AgBr will not completely dissolve in the solution.

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Most popular questions from this chapter

Draw geometrical isomers of each of the following complex ions. a. $\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}-$ b. \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{I}_{2}^{2+}\) c. \(\operatorname{Ir}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\) d. $\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{I}_{2}^{+}$

Which of the following statement(s) is(are) true? a. The coordination number of a metal ion in an octahedral complex ion is 8. b. All tetrahedral complex ions are low-spin. c. The formula for triaquatriamminechromium(III) sulfate is $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]_{2}\left(\mathrm{SO}_{4}\right)_{3}$ d. The electron configuration of \(\mathrm{Hf}^{2+}\) is $[\mathrm{Xe}] 4 f^{12} 6 s^{2}$ e. Hemoglobin contains \(\mathrm{Fe}^{3+}\)

How many unpaired electrons are present in the tetrahedral ion \(\mathrm{FeCl}_{4}^{-} ?\)

The following statements discuss some coordination compounds. For each coordination compound, give the complex ion and the counterions, the electron configuration of the transition metal, and the geometry of the complex ion. a. \(\mathrm{CoCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) is a compound used in novelty devices that predict rain. b. During the developing process of black-and-white film, silver bromide is removed from photographic film by the fixer. The major component of the fixer is sodium thiosul-fate. The equation for the reaction is: $$\operatorname{AgBr}(s)+2 \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(a q) \longrightarrow \\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \mathrm{Na}_{3}\left[\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}\right](a q)+\mathrm{NaBr}(a q)$$ c. In the production of printed circuit boards for the electronics industry, a thin layer of copper is laminated onto an insulating plastic board. Next, a circuit pattern made of a chemically resistant polymer is printed on the board. The unwanted copper is removed by chemical etching, and the protective polymer is finally removed by solvents. One etching reaction is: $$\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}(a q)+4 \mathrm{NH}_{3}(a q)+\mathrm{Cu}(s) \longrightarrow \\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad 2 \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}(a q)$$ Assume these copper complex ions have tetrahedral geometry.

Name the following coordination compounds. a. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{2}\) b. $\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{I}_{3}$ c. \(\mathrm{K}_{2}\left[\mathrm{PtC}_{4}\right]\) d. \(\mathrm{K}_{4}\left[\mathrm{Pt} \mathrm{C}_{6}\right]\) e. $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2}$ f. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{NO}_{2}\right)_{3}\right]\)
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