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Chapter 17: Q12P (page 428)

What cathode potential (versus S.H.E.) is required to reduce 99.99%of cd(II) from a solution containing 0.10Mcd (II) in 1,0M ammonia if there is negligible current? Consider the following reactions and assume that nearly all (II) is in the form $Cd {({NH}_{3})}_{4}^{2 +}$
localid="1663647104121" $C d^{2 +} + 4 N H_{3} 鈬� C d {(N H_{3})}_{4}^{2 +} 尾_{4} = 3.6 脳 10^{6} C d^{2 +} + 2 e^{-} 鈬� C d (s) E 掳 = - . 402 V$

Short Answer

Expert verified

The potential of cathode is E=-0.744 V

Step by step solution

01

Electrogravimetric Analysis

Separation along with the quantification of metals are mainly observed in electrogravimetric analysis.
Electrolysis of the analyte solution is done during this procedure.

02

Determine the lead lactate

Given data:

$[C d (I I)] = 0.10 M [N H_{3}] = 1 M 尾_{4} = 3.6 脳 10^{6} E 掳 = - 0.402 V E = ?$

First we need to calculate $[C d^{2 +}]$

$尾_{4} = \frac{[C d {(N H_{3})}_{4}^{2 +}]}{[C d^{2 +}] {[N H_{3}]}^{4}}$

99.99% Of Cd is reduced, so the concentration of $C d {(N H_{3})}_{4}^{2 +}$ is then:

$[C d {(N H_{3})}_{4}^{2 +}] = [C d (I I)] - ([C d (l l)] . 0.9999) [C d {(N H_{3})}_{4}^{2 +}] = 0.10 M - (0.10 M . 0.9999) [C d {(N H_{3})}_{4}^{2 +}] = 1 脳 10^{- 5} M$

The concentration of $C d^{2 +}$ is:

$[C d^{2 +}] = \frac{[C d {(N H_{3})}_{4}^{2 +}]}{{[N H_{3}]}^{4} . 尾} [C d^{2 +}] = \frac{1 脳 10^{- 5} M}{1^{4} M 脳 3.6 脳 10^{6}} [C d^{2 +}] = 2.78 脳 10^{- 12} M$

The potential of cathode is

$E (c a t h o d) = E 掳 - \frac{0.05916}{2} . \log (\frac{1}{[C d^{2 +}]}) E (c a t h o d) = - 0.402 V - \frac{0.05916}{2} . \log (\frac{1}{[2.78 . 10^{- 12}]}) E (c a t h o d) = - 0.744 V$

The potential of cathode is E = -0.744V

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Most popular questions from this chapter

Chlorine has been used for decades to disinfect drinking water. An undesirable side effect of this treatment is reaction with organic impurities to create organochlorine compounds, some of which could be toxic. Monitoring total organic halide (designated TOX) is required for many water providers. A standard procedure for TOX is to pass water through activated charcoal, which adsorbs organic compounds. Then the charcoal is combusted to liberate hydrogen halides:

$Organic halide (RX) \overset{o_{2} / 800 掳 C}{鈫�} {CO}_{2} + H_{2} O + HX$

HX is absorbed into aqueous solution and measured by coulometric titration with a silver anode:

$X^{-} (aq) + Ag (s) 鈫� AgX (s) + e^{-}$

When 1.00 L of drinking water was analyzed, a current of 4.23 mA was required for 387 s. A blank prepared by oxidizing charcoal required 6 s at 4.23 mA. Express the TOX of the drinking water as $渭$ mol halogen/L. If all halogen is chlorine, express the TOX as $渭 g CI / L$ .

${cd}^{2 +}$ was used as an internal standard in the analysis of ${Pb}^{2 +}$ by square wave polarography. ${Cd}^{2 +}$ gives a reduction wave at -0.60 V and ${Pb}^{2 +}$ gives a reduction wave at 鈥�0.40 V. It was first verified that the ratio of peak heights is proportional to the ratio of concentrations over the whole range employed in the experiment. Here are results for known and unknown mixtures:

The unknown mixture was prepared by mixing $25.00 (卤 0.05) mL$ of unknown (containing only ${Pb}^{2 +}$ ) plus $10.00 (卤 0.05) mL$ of $3.23 (卤 0.01) 脳 10^{- 4} {MCd}^{2 +}$ and diluting to $50.00 (卤 0.05) mL$ .

(a) Disregarding uncertainties, find $[{Pb}^{2 +}]$ in the undiluted unknown.

(b) Find the absolute uncertainty for the answer to part (a).

Fundamentals of Electrolysis

17-9. A lead-acid battery in a car has six cells in series, each delivering close to2.0Vfor a total of 12V when the battery is discharging. Recharging requires $~ 2.4 V$ per cell, or $~ 14 V$ for the entire battery. ⁵⁵Explain these observations in terms of Equation 17-6.

(a) which voltage, $V_{1}$ or $V_{2}$ in the diagram is constant in controlled-potential electrolysis? Which are the working, auxiliary, and reference electrodes in the diagram?

(b) Explain how the Luggin capillary in Figure 17-4 measures the electric potential at the opening of the capillary.

Measuring the size of a microelectrode by cyclic voltammetry.

(a) Redox chemistry for ferrocyanide in Figure 17-32 was given at the beginning of Section 17-5. Write the analyte half-reaction that occurs at the upper plateau near 0.4 Vand at the lower plateau near 0 V(versus S.C.E.).

(b) The limiting current $I_{l i m i t}$ , which is the difference between the upper and lower plateaus, is related to the radius of the disk-shaped electrode (r)and the diffusion coefficient (D)and bulk concentration (C)of the analyte:

$I_{l i m i t} 4 n F D C r$

Where nis the number of electrons in the half-reaction and F is the Faraday constant. In this equation, the units of concentration should be $mol / m^{3}$ to be consistent with the other quantities in SI units. The diffusion coefficient for ferrocyanide cited in the reference for Figure 17 - 32is $9.2 脳 10^{- 10} m / s$ in water at $25^{掳} C$ . Calculate the radius of the microelectrode.

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