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Chapter 20: Problem 91

A test for completeness of electrodeposition of \(\mathrm{Cu}\) from a solution of \(\mathrm{Cu}^{2+}(\mathrm{aq})\) is to add \(\mathrm{NH}_{3}(\mathrm{aq}) .\) A blue color signifies the formation of the complex ion \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\left(K_{\mathrm{f}}=1.1 \times 10^{13}\right) .\) Let \(250.0 \mathrm{mL}\) of \(0.1000 \mathrm{M} \mathrm{CuSO}_{4}(\text { aq })\) be electrolyzed with a \(3.512 \mathrm{A}\) current for 1368 s. At this time, add a sufficient quantity of \(\mathrm{NH}_{3}(\text { aq })\) to complex any remaining \(\mathrm{Cu}^{2+}\) and to maintain a free \(\left[\mathrm{NH}_{3}\right]=0.10 \mathrm{M} .\) If \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is detectable at concentrations as low as \(1 \times 10^{-5} \mathrm{M}\) should the blue color appear?

Short Answer

Expert verified
After performing the steps and calculations, if the calculated concentration of \([Cu(NH_3)_4]^{2+}\) is greater than \(1 \times 10^{-5} M\), then the blue color will appear. Otherwise, it will not be observed.

Step by step solution

01

Calculate Moles of Copper Electrolyzed

Use Faraday's law of electrolysis to find the amount of Copper (Cu) that gets electrolyzed. Faraday's law states that the amount of substance discharged at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the solution. This can be written as: \( n = \dfrac{I \cdot t}{F \cdot z} \) where, \( n \) is the number of moles, \( I \) is current in amperes, \( t \) is time in seconds, \( F \) is Faraday's constant (96485 C/mol) and \( z \) is the number of electrons transferred per molecule during electrolysis. Given that the current (I) is 3.512 A and time (t) is 1368 s, the number of moles of Cu that gets electrolyzed can be calculated.
02

Calculate Remaining Concentration of Copper

After calculating the moles of Copper that have been electrolyzed in step 1, we can find the remaining concentration of Copper in the solution. This can be found by subtracting the moles of Copper electrolyzed from the initial moles of Copper (initial concentration times volume), and then dividing by the volume of the solution in Liters.
03

Equilibrium of Complex ion formation

In this step, we address the reaction between the remaining Copper in the solution and the ammonia that is added. This forms a complex ion according to the reaction: \( Cu^{2+} + 4NH_3 \rightarrow [Cu(NH_3)_4]^{2+} \). The ammonia is added until its concentration is 0.1M. The equilibrium constant (\(K_f\)) of this reaction is given as \(1.1 \times 10^{13}\). Use the Reaction Quotient expression \(Q = \dfrac{[[Cu(NH_3)_4]^{2+}]}{[NH_3]^4[Cu^{2+}]}\) to calculate the reaction quotient. If Q is less than \(K_f\), the reaction will proceed to the right and more complex will form. If Q is greater than \(K_f\), the reaction will move to the left and less complex will form. If Q is equal to \(K_f\), then the reaction is at equilibrium.
04

Determine the Observable Color Change

Compare the concentration of the complex that is formed (\([Cu(NH_3)_4]^{2+}\)) with the detectable concentration level (1X10^-5 M). If the concentration of the complex formed is greater than the detectable concentration, then the blue color will appear.

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Most popular questions from this chapter

The gas evolved at the anode when \(\mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) is electrolyzed between Pt electrodes is most likely to be (a) \(\mathrm{O}_{2} ;\) (b) \(\mathrm{H}_{2} ;\) (c) \(\mathrm{SO}_{2} ;\) (d) \(\mathrm{SO}_{3} ;\) (e) a mixture of sulfur oxides.

Calculate the quantity indicated for each of the following electrolyses. (a) the mass of \(\mathrm{Zn}\) deposited at the cathode in 42.5 min when 1.87 A of current is passed through an aqueous solution of \(\mathrm{Zn}^{2+}\) (b) the time required to produce \(2.79 \mathrm{g} \mathrm{I}_{2}\) at the anode if a current of \(1.75 \mathrm{A}\) is passed through \(\mathrm{KI}(\mathrm{aq})\)

Only a tiny fraction of the diffusible ions move across a cell membrane in establishing a Nernst potential (see Focus On 20: Membrane Potentials), so there is no detectable concentration change. Consider a typical cell with a volume of \(10^{-8} \mathrm{cm}^{3},\) a surface area \((A)\) of \(10^{-6} \mathrm{cm}^{2},\) and a membrane thickness \((l)\) of \(10^{-6} \mathrm{cm}\) Suppose that \(\left[\mathrm{K}^{+}\right]=155 \mathrm{mM}\) inside the cell and \(\left[\mathrm{K}^{+}\right]=4 \mathrm{mM}\) outside the cell and that the observed Nernst potential across the cell wall is \(0.085 \mathrm{V}\). The membrane acts as a charge-storing device called a capacitor, with a capacitance, \(C,\) given by $$C=\frac{\varepsilon_{0} \varepsilon A}{l}$$ where \(\varepsilon_{0}\) is the dielectric constant of a vacuum and the product \(\varepsilon_{0} \varepsilon\) is the dielectric constant of the membrane, having a typical value of \(3 \times 8.854 \times 10^{-12}\) \(\mathrm{C}^{2} \mathrm{N}^{-1} \mathrm{m}^{-2}\) for a biological membrane. The SI unit of capacitance is the firad, \(1 \mathrm{F}=1\) coulomb per volt \(=1 \mathrm{CV}^{-1}=1 \times \mathrm{C}^{2} \mathrm{N}^{-1} \mathrm{m}^{-1}\) (a) Determine the capacitance of the membrane for the typical cell described. (b) What is the net charge required to maintain the observed membrane potential? (c) How many \(\mathrm{K}^{+}\) ions must flow through the cell membrane to produce the membrane potential? (d) How many \(\mathrm{K}^{+}\) ions are in the typical cell? (e) Show that the fraction of the intracellular \(K^{+}\) ions transferred through the cell membrane to produce the membrane potential is so small that it does not change \(\left[\mathrm{K}^{+}\right]\) within the cell.

It is sometimes possible to separate two metal ions through electrolysis. One ion is reduced to the free metal at the cathode, and the other remains in solution. In which of these cases would you expect complete or nearly complete separation: (a) \(\mathrm{Cu}^{2+}\) and \(\mathrm{K}^{+} ;\) (b) \(\mathrm{Cu}^{2+}\) and \(\mathrm{Ag}^{+} ;\) (c) \(\mathrm{Pb}^{2+}\) and \(\mathrm{Sn}^{2+} ?\) Explain.

An aqueous solution of \(\mathrm{K}_{2} \mathrm{SO}_{4}\) is electrolyzed by means of Pt electrodes. (a) Which of the following gases should form at the anode: \(\mathrm{O}_{2}, \mathrm{H}_{2}, \mathrm{SO}_{2}, \mathrm{SO}_{3} ?\) Explain. (b) What product should form at the cathode? Explain. (c) What is the minimum voltage required? Why is the actual voltage needed likely to be higher than this value?
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