CHE 323 Electrochemisty Problem Set 3-16-17.pdf

CHE 323

Electrochemisty Problem Set

March 16, 2017

Engr. May V. Tampus

Instructions: Write your answers in a long-size bondpaper. Submit your answers on or before March 23, 2017. I.

Conceptual Questions:

1. 2. 3.

What is the difference between a galvanic cell and an electrolytic cell? What are the laws governing migration of ions. What are the limitations of these laws? Sketch a typical galvanic cell. Show direction of electron flow, the direction of ion migration through the porous disk, and identify the cathode and anode. Indicate in which electrode oxidation and reduction occur. Will there be migration of ions in the absence of the porous disk? Next, sketch a galvanic cell with a salt bridge showing the required features as in a typical galvanic cell. Is there a change in the direction of ion migration when a salt bridge is present? Explain. 4. Discuss the relationship between ionic mobility, molar conductivity, and transport number to ionic conduction. Does electronic conduction also involve the measurement of these quantities? Explain. 5. Explain the following relationships: ΔG and W, cell potential and W, cell potential and ΔG, cell potential and Q (reaction quotient). Using these relationships, explain how you could make a cell in which both electrodes are the same metal and both solutions contain the same compound, but at different concentrations. How could this cell run spontaneously? 6. What is standard cell potential? Describe the significance of the standard cell potential. 7. What is the difference between ξ and ξo? When is ξ equal to zero? When is ξo equal to zero? (Consider “regular” galvanic cells as well as concentration cells.) 8. Explain why cell potentials are not multiplied by the coefficients in the balanced equation. 9. Describe how Faraday’s laws are used in order to quantify the amount of substance that participates in a chemical reaction. 10. Why do dry cells and lead-acid cells “run down” during use? Do you think a fuel cell runs down? Explain. II. 1.

Problem-Solving: Every year, oral rehydration therapy (ORT) – the feeding of an electrolyte solution – saves the lives of countless children worldwide who become severely dehydrated as a result of diarrhea. One requirement of the solution used is that it be isotonic with human blood. a) One definition of an isotonic solution given in the text is that it have the same osmotic pressure as 0.92% NaCl(aq) (mass/volume). Another definition is that the solution has a freezing point of -0.52oC. Show that these two definitions are in reasonably close agreement given that we are using solution concentrations rather than activities. b) Use the freezing-point definition from part (a) to show that an ORT solution containing 3.5 g NaCl, 1.5 g KCl, 2.9 g Na 3C6H5O7 (sodium citrate), and 20.0 g C6H12O6 (glucose) per liter meets the requirements of being isotonic. (Hint: Which of the solutes are nonelectrolytes, and which are strong electrolytes?)

2.

A AgNO3 solution containing 0.00739 g of AgNO3 per g of H2O is electrolyzed between silver electrodes. During the experiment 0.078 g of Ag plate out at the cathode. At the end of the experiment the anode portion contains 23.14 g of H2O and 0.236 g of AgNO3. What is the transference number of Ag+? [ANSWER: 0.47] A fuel cell designed to react grain alcohol with oxygen has the following net reaction:

3.

C2H5OH(l) + 3O2(g)  2CO2(g) + 3H2O(l)

4.

5.

The maximum work one mole of alcohol can yield by this process is 1320 kJ. What is the theoretical maximum voltage this cell can achieve? [ANSWER:1.14 V] A hydrogen electrode can, in principle, be used to monitor changes in the molar concentration of weak acids in biologically active solutions. Consider a hydrogen electrode in a solution of lactic acid (CH3CHOCOOH) as part of an overall galvanic cell at 25oC and 1 bar. Estimate the change in the electrode potential when the solution is charged from 5.0 mmol/L to 25.0 mmol/L. [ANSWER: 20.6 mV] Show that for a combination of half-cell reactions that produce a standard reduction potential for a half-cell that is not directly observable, the standard reduction potential is ∑ 𝑛𝑖 𝐸𝑖𝑜 ∑ 𝑛𝑖 Where ni is the number of electrons in each half-reaction of potential 𝐸𝑖𝑜 . Use the following half-reactions: 𝐸𝑜 =

𝐻5 𝐼𝑂6 (𝑎𝑞) + 𝐻 + (𝑎𝑞) + 2𝑒 − → 𝐼𝑂3− (𝑎𝑞) + 3𝐻2 𝑂(𝑙) 𝐸 𝑜 = 1.60𝑉 𝐼𝑂3− (𝑎𝑞) + 6𝐻 + (𝑎𝑞) + 5𝑒 − → 1⁄2 𝐼2 (𝑠) + 3𝐻2 𝑂(𝑙) 𝐸 𝑜 = 1.19𝑉 2𝐻𝐼𝑂(𝑎𝑞) + 2𝐻 + (𝑎𝑞) + 2𝑒 − → 𝐼2 (𝑠) + 2𝐻2 𝑂(𝑙) 𝐸 𝑜 = 1.45𝑉 𝐼2 (𝑠) + 2𝑒 − → 2𝐼 − (𝑎𝑞) 𝐸 𝑜 = 0.535𝑉 Calculate the standard reduction potential for 𝐻6 𝐼𝑂6 + 5𝐻 + + 2𝐼 − + 3𝑒 − → 1⁄2 𝐼2 + 4𝐻2 𝑂 + 2𝐻𝐼𝑂

6.

For the oxidation-reduction reaction S4O62-(aq) + Cr2+(aq)  Cr3+(aq) + S2O32-(aq) The appropriate half reactions are

7.

S4O62- + 2e-  2S2O32-

o = 0.17 V

Cr3+ + e-

o = -0.50 V

 Cr2+

What is the value of the equilibrium constant K at 25oC? [ANSWER: 4.32 x 1022] In a common car battery, six identical cells each carry out the reaction: Pb + PbO2 + 2HSO4- + 2H+ 2PbSO4 + 2H2O

8.

For such a cell Eo is 2.04 V. Calculate ΔGo at 25oC. [ANSWER:-394 kJ] A fuel cell designed to react grain alcohol with oxygen has the following net reaction: C2H5OH(l) + 3O2(g)  2CO2(g) + 3H2O(l)

The maximum work one mole of alcohol can yield by this process is 1320 kJ. What is the theoretical maximum voltage this cell can achieve? [ANSWER:1.14 V] 9. A 4 molal solution of FeCl3 is electrolyzed between platinum electrodes. After the electrolysis the cathode portion, weighing 30 g, is 3.15 molal in FeCl3 and 1.00 molal in FeCl2. What are the transport numbers of Fe3+ and Cl- ions, respectively? [ANSWER: 0.647; 0.353] 10. Given the reactions: Fe2+ + 2e-  Fe(s) Eo = -0.440 V 2H+ + 2e-  H2(g) Eo = 0.000 V In a galvanic cell, the iron compartment contains an iron electrode and [Fe 2+] =1.00 x 10-3 M. The hydrogen compartment contains a platinum electrode (PH2 = 1.00 atm) and a weak acid HA at an initial concentration of 1.00 M. If the observed cell potential is 0.333 V at 25 oC, calculate Ka for the weak acid HA at 25oC. [ANSWER:2.43 x 10-7] 11. The calomel electrode, Hg(l) l Hg2Cl2(s) l Cl-(aq), is a component of instruments used to measure pH. What is the half reaction of this electrode? What is the reaction quotient? [ANSWER: Hg2Cl2(s) + 2e-  2 Hg(l) + 2 Cl- (aq);

Q  aCl2  ]

12. A hydrogen electrode can, in principle, be used to monitor changes in the molar concentration of weak acids in biologically active solutions. Consider a hydrogen electrode in a solution of lactic acid (CH3CHOCOOH) as part of an overall galvanic cell at 25oC and 1 bar. Estimate the change in the electrode potential when the solution is charged from 5.0 mmol/L to 25.0 mmol/L. [ANSWER:64.2 mV] 13. What fraction of the total current is carried by Cl- when current flows through an aqueous solution of NaCl at 25oC? Limiting conductivities in water of Na+ and Cl- in mS.m2.mol-1 are 5.01 and 7.63, respectively. [ANSWER:0.396] 14. An antique automobile bumper is to be chrome plated. The bumper, which is dipped into an acidic Cr 2O72- solution, serves as a cathode of an electrolytic cell. If oxidation of H2O occurs at the anode, how many moles of oxygen will evolve for every 1.00 x 10 2 grams of Cr(s) deposited? MCr = 51.996 g/mol [ANSWER:2.88 moles] 15. Refer to #14. If the current is 10.0 amperes, how long will it take to deposit 100 x 102 grams of Cr(s) onto the bumper? [ANSWER: 1.29 d]