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Chapter 19: Problem 46

Consider the electrolysis of molten barium chloride, \(\mathrm{BaCl}_{2}\). (a) Write the half-reactions. (b) How many grams of barium metal can be produced by supplying 0.50 A for 30 min?

Short Answer

Expert verified
The half-reactions for the electrolysis of molten barium chloride are: \( \mathrm{Ba^{2+}(l)+2e^{-}}\rightarrow \mathrm{Ba(s)} \) and \( \mathrm{2Cl^{-}(l)}\rightarrow \mathrm{Cl_{2}(g)+2e^{-}} \). The amount of barium produced when a current of 0.50 A is supplied for 30 minutes is approximately 0.64 g.

Step by step solution

01

Write half-reactions

Barium chloride (\(\mathrm{BaCl}_{2}\)) in molten state contains \(\mathrm{Ba}^{2+}\) and \(\mathrm{Cl}^{-}\) ions. During electrolysis, reduction and oxidation half-reactions happen. The barium ions are reduced to barium metal and chloride ions are oxidized to chlorine gas. The half-reactions are: \nFor Barium: \( \mathrm{Ba^{2+}(l)+2e^{-}}\rightarrow \mathrm{Ba(s)} \) \nFor Chlorine: \( \mathrm{2Cl^{-}(l)}\rightarrow \mathrm{Cl_{2}(g)+2e^{-}} \)
02

Calculate the quantity of electricity transferred

The quantity of electricity (charge) transferred can be calculated using the formula: \(Q = I \times t\), where \(I\) is current and \(t\) is time. Given that \(I = 0.50 \, A\) and \(t = 30 \, min = 1800 \, s\), we find \(Q = 0.50 \, A \times 1800 \, s = 900 \, C\)
03

Calculate the moles of electrons transferred

The number of moles of electrons (\(n\)) transferred can be found using Faraday鈥檚 law which states that each mole of electrons carries a charge equal to one Faraday. From this, we deduce that \(n = \frac{Q}{F}\), where \(F\) is Faraday鈥檚 constant, approximately \(96485 \, C \, mol^{-1}\). Therefore, \(n = \frac{900 \, C}{96485 \, C \, mol^{-1}} = 0.00933 \, mol\)
04

Calculate the grams of Barium produced

From the half-reaction for barium, it's seen that one mole of barium is produced for every two moles of electrons. Therefore, the moles of barium produced will be \(0.00933 \, mol / 2 = 0.00467 \, mol\). Considering that the molar mass of barium is \(137.3 \, g \, mol^{-1}\), the grams of barium produced can be calculated using the formula: \text{Mass} = \text{Molar mass} \times \text{Moles}. Therefore, the mass produced = \(0.00467 \, mol \times 137.3 \, g \, mol^{-1} = 0.64 \, g\)

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Most popular questions from this chapter

Tarnished silver contains \(\mathrm{Ag}_{2} \mathrm{~S}\). The tarnish can be removed by placing silverware in an aluminum pan containing an inert electrolyte solution, such as \(\mathrm{NaCl}\). Explain the electrochemical principle for this procedure. [The standard reduction potential for the half- cell reaction \(\mathrm{Ag}_{2} \mathrm{~S}(s)+2 e^{-} \rightarrow 2 \mathrm{Ag}(s)+\mathrm{S}^{2-}(a q)\) is \(-0.71 \mathrm{~V} .]\)

Industrially, copper is purified by electrolysis. The impure copper acts as the anode, and the cathode is made of pure copper. The electrodes are immersed in a \(\mathrm{CuSO}_{4}\) solution. During electrolysis, copper at the anode enters the solution as \(\mathrm{Cu}^{2+}\) while \(\mathrm{Cu}^{2+}\) ions are reduced at the cathode. (a) Write half-cell reactions and the overall reaction for the electrolytic process. (b) Suppose the anode was contaminated with \(\mathrm{Zn}\) and \(\mathrm{Ag} .\) Explain what happens to these impurities during electrolysis. (c) How many hours will it take to obtain \(1.00 \mathrm{~kg}\) of \(\mathrm{Cu}\) at a current of \(18.9 \mathrm{~A} ?\)

Consider a galvanic cell composed of the SHE and a half-cell using the reaction \(\mathrm{Ag}^{+}(a q)+e^{-} \rightarrow \operatorname{Ag}(s)\). (a) Calculate the standard cell potential. (b) What is the spontaneous cell reaction under standard-state conditions? (c) Calculate the cell potential when \(\left[\mathrm{H}^{+}\right]\) in the hydrogen electrode is changed to (i) \(1.0 \times\) \(10^{-2} M\) and (ii) \(1.0 \times 10^{-5} M,\) all other reagents being held at standard-state conditions. (d) Based on this cell arrangement, suggest a design for a pH meter.

A spoon was silver-plated electrolytically in a \(\mathrm{AgNO}_{3}\) solution. (a) Sketch a diagram for the process. (b) If \(0.884 \mathrm{~g}\) of \(\mathrm{Ag}\) was deposited on the spoon at a constant current of \(18.5 \mathrm{~mA},\) how long (in minutes) did the electrolysis take?

What is Faraday's contribution to quantitative electrolysis?
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