APChemistryCollege BoardTopic QuestionsUnit 9: Applications of Thermodynamics9.8 Cell Potential & Free Energy

Cell Potential & Free Energy (College Board AP Chemistry)

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1a2 marks

q1-june-2015---ap-chemistry

Metal-air cells are a relatively new type of portable energy source consisting of a metal anode, an alkaline electrolyte paste that contains water, and a porous cathode membrane that lets in oxygen from the air. A schematic of the cell is shown above. Reduction potentials for the cathode and three possible metal anodes are given in the table below.

Half Reaction

E at pH 11 and 298 K (V)

O2(g) + 2 H2O(l) + 4 e−  → 4 OH−(aq)

+ 0.34

ZnO(s) + H2O(l) + 2 e−  → Zn(s) + 2 OH−(aq)

– 1.31

Na2O(s) + H2O(l) + 2 e−  → 2 Na(s) + 2 OH−(aq)

–1.60

CaO(s) + H2O(l) + 2 e−  → Ca(s) + 2 OH−(aq)

– 2.78

Early forms of metal-air cells used zinc as the Zinc oxide is produced as the cell operates according to the overall equation below.

2 Zn(s) + O2(g) → 2 ZnO(s)

 

i)
Using the data in the table above, calculate the cell potential for the zinc-air

 

ii)
The electrolyte paste contains OH− On the diagram of the cell above, draw an arrow to indicate the direction of migration of OH− ions through the electrolyte as the cell operates.

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1b2 marks

A fresh zinc-air cell is weighed on an analytical balance before being placed in a hearing aid for

i)
As the cell operates, does the mass of the cell increase, decrease, or remain the same?

ii)
Justify your answer to part (b)(i) in terms of the equation for the overall cell

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1c2 marks

The zinc-air cell is taken to the top of a mountain where the air pressure is lower

i)
Will the cell potential be higher, lower, or the same as the cell potential at the lower elevation?

ii)
Justify your answer to part (c)(i) based on the equation for the overall cell reaction and the information

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1d2 marks

Metal-air cells need to be lightweight for many In order to transfer more electrons with a smaller mass, Na and Ca are investigated as potential anodes. A 1.0 g anode of which of these metals would transfer more electrons, assuming that the anode is totally consumed during the lifetime of a cell? Justify your answer with calculations.

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1e2 marks

The only common oxide of zinc has the formula ZnO.

i)
Write the electron configuration for a Zn atom in the ground

ii)
From which sublevel are electrons removed when a Zn atom in the ground state is oxidized?

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2a1 mark

M + I2  →  MI2

To determine the molar mass of an unknown metal, M, a student reacts iodine with an excess of the metal to form the water-soluble compound Ml2 , as represented by the equation The reaction proceeds until all of the I2  is consumed . The Ml2(aq) solution is quantitatively collected and heated to remove the water , and the product is dried and weighed to constant mass. The experimental steps are represented below , followed by a data table.

q3-june-2016---ap-chemistry

Data for Unknown Metal Lab

Mass of beaker

125.457 g

Mass of beaker  + metal M

126.549 g

Mass of beaker  + metal M + I2

127.570 g

Mass of Ml2 , first weighing

1.284 g

Mass of Ml2 , second weighing

1.284 g

Given that the metal M is in excess, calculate the number of moles of I2 that reacted.

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2b2 marks

Calculate the molar mass of the unknown metal M .

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2c2 marks

The student hypothesizes that the compound formed in the synthesis reaction is ionic.

Propose an experimental test the student could perform that could be used to support the hypothesis. Explain how the results of the test would support the hypothesis if the substance was ionic.

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2d2 marks

The student hypothesizes that Br2  will react with metal M more vigorously than I2  did because  Br2  is a liquid at room temperature.

Explain why I2  is a solid at room temperature whereas Br2  is a liquid. Your explanation should clearly reference the types and relative strengths of the intermolecular forces present in each substance.

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2e2 marks

While cleaning up after the experiment, the student wishes to dispose of the unused solid I2  in a responsible manner. The student decides to convert the solid  I2  to I−(aq) anion. The student has access to three solutions, H2O2(aq), Na2S2O3(aq) ,  and  Na2S4O6(aq) ,  and the standard reduction table shown below.

Half reaction

E° (V)

S4O62−(aq) + 2 e−   →   2 S2O32−(aq)

0.08

l2(s) + 2 e−   →    2 I−(aq)

0.54

O2(g) + 2 H+(aq) + 2 e−  →  H2O2(aq)

0.68

Which solution should the student add to l2(s) to reduce it to I−(aq)? Circle your answer Justify your answer, including a calculation of E°  for the overall reaction.

H2O2(aq) 

Na2S2O3(aq)

Na2S4O6(aq) 

                            

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2f1 mark

Write the balanced net-ionic equation for the reaction between  I2  and the solution you selected in part (e).

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3a2 marks

A student wants to determine the concentration of H2O2 in a solution of H2O2(aq). The student can use one of two titrants, either dichromate ion, Cr2O72−(aq), or cobalt(II) ion,  Co2+(aq). The balanced  chemical equations for the two titration reactions are shown below.

Dichromate as titrant:         Cr2O72−(aq)  + 3 H2O2(aq) + 8 H+(aq)    →    2 Cr3+(aq) + 3 O2(g) + 7 H20(l)

Cobalt(II) as titrant:             2CO2+(aq) + H2O2(aq) + 2 H+(aq)    →    2 CO3+(aq) + 2 H2O(l)

The half-reactions and the E° values for the systems related to the titrations above are given in the following table.

Half-Reaction

E°  (V)

at 298 K

CO3+(aq) + e−     →    CO2+(aq)

1.84

H2O2(aq) + 2 H+(aq) + 2 e−    →      2 H2O (l)

1.77

Cr2O72−(aq) + 14 H+(aq) + 6 e−    →     2 Cr3+(aq) + 7 H2O(l)

1.33

O2(g) + 2 H+(aq) + 2 e−    →     H2O2(aq)

0.70

Use the information in the table to calculate the following.

i)
E° for the reaction between Cr2O72−(aq) and H2O2(aq) at 298 K

ii)
E° for the reaction between CO2+(aq) and H2O2(aq) at 298 K

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3b2 marks

Based on the calculated values of E° , the student must choose the titrant for which the titration reaction is thermodynamically favorable at 298 K.

i)
Which titrant should the student choose? Explain your reasoning.

ii)
Calculate the value of ΔG° in kJ/molrxn , for the reaction between the chosen titrant and H2O2(aq).

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4a1 mark

q6-june-2018---ap-chemistry

A student sets up a galvanic cell at 298 K that has an electrode of Ag(s) immersed in a 1.0 M solution of Ag+(aq) and an electrode of Cr(s) immersed in a 1.0 M solution of Cr3+(aq), as shown in the diagram above.

The student measures the voltage of the cell shown above and discovers that it is zero. Identify the missing component of the cell, and explain its importance for obtaining a nonzero voltage.

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4b3 marks

Half-Reaction

E° (V)

Ag+(aq) + e−   →  Ag(s)

+ 0.80

Cr3+(aq) + 3 e−   →  Cr(s)

?

The student adds the missing component to the cell and measures E°cell  to be +1.54 V. As the cell operates, Ag+ ions are reduced. Use this information and the information in the table above to do the following.

i)
Calculate the value of E° for the half-reaction Cr3+(aq) + 3 e−   →  Cr(s).

ii)
Write the balanced net-ionic equation for the overall reaction that occurs as the cell operates.

iii)
Calculate the value of ΔG° for the overall cell reaction in J/molrxn.

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