Without performing detailed calculations, indicate whether either of the following compounds is appreciably soluble in \(\mathrm{NH}_{3}(\mathrm{aq}):(\mathrm{a}) \mathrm{CuS}, K_{\mathrm{sp}}=6.3 \times 10^{-36},\)(b) \(\mathrm{CuCO}_{3}, K_{\mathrm{sp}}=1.4 \times 10^{-10} .\) Also use the fact that \(K_{\mathrm{f}}\) for \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is \(1.1 \times 10^{13}\).

Short Answer

Expert verified
Both CuS and CuCO3 are appreciably soluble in NH3(aq), given the fact that their Kf for [Cu(NH3)4]2+ complex formation is significantly greater than their Ksp.

Step by step solution

01

Understand the Problem

When the compound containing copper, either CuS or CuCO3, is dissolved in an aqueous solution of ammonia, the copper ions react with the NH3 to form a complex ion, [Cu(NH3)4]2+. This process is accompanied by a significant increase in solubility if the equilibrium constant for the formation of the complex ion (Kf) is much greater than the solubility constant (Ksp) of the compound.
02

Solubility of CuS in NH3(aq)

First, for CuS, the Ksp given is \(6.3 \times 10^{-36}\). This value is very small, indicating that the compound is barely soluble. However, the Kf for formation of the complex ion is \(1.1 \times 10^{13}\), a very large number. If the Kf is much greater than the Ksp, it indicates that CuS is appreciably soluble in an aqueous solution of ammonia as the reaction will be pushed towards the formation of the complex ion.
03

Solubility of CuCO3 in NH3(aq)

Next, for CuCO3, the Ksp given is \(1.4 \times 10^{-10}\), also very small, indicating the compound is barely soluble. However, similarly to CuS, the large Kf value suggests that CuCO3 may also be appreciably soluble in NH3(aq) since the formation of the complex ion is favored.

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Most popular questions from this chapter

Pure water is saturated with slightly soluble \(\mathrm{PbI}_{2}\) Which of the following is a correct statement concerning the lead ion concentration in the solution, and what is wrong with the others? (a) \(\left[\mathrm{Pb}^{2+}\right]=\left[\mathrm{I}^{-}\right]\); (b) \(\left[\mathrm{Pb}^{2+}\right]=K_{\mathrm{sp}}\) of \(\mathrm{PbI}_{2} ;(\mathrm{c})\left[\mathrm{Pb}^{2+}\right]=\sqrt{K_{\mathrm{sp}}}\) of \(\mathrm{PbI}_{2}\); (d) \(\left[\mathrm{Pb}^{2+}\right]=0.5\left[\mathrm{I}^{-}\right]\)

Determine whether \(1.50 \mathrm{g} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) (oxalic acid: \(K_{\mathrm{a}_{1}}=\) \(\left.5.2 \times 10^{-2}, K_{\mathrm{a}_{2}}=5.4 \times 10^{-5}\right)\) can be dissolved in \(0.200 \mathrm{L}\) of \(0.150 \mathrm{M} \mathrm{CaCl}_{2}\) without the formation of \(\mathrm{CaC}_{2} \mathrm{O}_{4}(\mathrm{s})\left(K_{\mathrm{sp}}=1.3 \times 10^{-9}\right)\).

In your own words, define the following terms or symbols: (a) \(K_{\mathrm{sp}} ;\) (b) \(K_{f} ;\) (c) \(Q_{\mathrm{sp}} ;\) (d) complex ion.

All but two of the following solutions yield a precipitate when the solution is also made \(2.00 \mathrm{M}\) in \(\mathrm{NH}_{3}\). Those two are (a) \(\mathrm{MgCl}_{2}(\mathrm{aq}) ;\) (b) \(\mathrm{FeCl}_{3}(\mathrm{aq})\); (c) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(\mathrm{aq}) ;(\mathrm{d}) \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})\); (e) \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(\mathrm{aq})\).

Assume that, to be visible to the unaided eye, a precipitate must weigh more than \(1 \mathrm{mg}\). If you add \(1.0 \mathrm{mL}\) of \(1.0 \mathrm{M} \mathrm{NaCl}(\mathrm{aq})\) to \(100.0 \mathrm{mL}\) of a clear saturated aqueous AgCl solution, will you be able to see \(\mathrm{AgCl}(\mathrm{s})\) precipitated as a result of the common-ion effect? Explain.

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