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Homework 2: Electrochemistry

There are select solutions to these problems here.

For these problems the Standard Reduction Potential table may be useful.

Q2.1

From the observations listed, estimate the value of \(\mathrm{E^\circ}\) for the imaginary half reaction \(\mathrm{M^{2+} + 2e^- \rightarrow M(s)}\), where \(\mathrm{M}\) is an unknown metal to be determined under the following conditions:

  1. The metal \(\mathrm{M}\) reacts with \(\ce{HCl (aq)}\).
  2. The metal displaces \(\ce{Fe^3+}\) but does not displace \(\ce{Sn^4+}\).
  3. The metal reacts with \(\ce{HNO3 (aq)}\).
  4. The metal can displace \(\ce{K+ (aq)}\).

Q2.2

You may assume that the reactants and products in the equations are in their standard states. Use the information from Table 19.1 to predict if a spontaneous reaction will occur in the forward direction for the following cases.

  1. \(\mathrm{ Zn (s) + Cu^{2+} \rightarrow Zn^{2+} + Cu (s)}\)
  2. \(\mathrm{2Hg^{2+} (aq) + 2Br^- (aq) \rightarrow Hg_2^{2+}(aq) + Br_2 (l)}\)
  3. \(\mathrm{2Fe^{2+} (aq) + Cl_2 (g) \rightarrow 2Fe^{3+}(aq) + 2Cl^-(aq)}\)

Q2.3

Determine \(\mathrm{\Delta G^\circ}\)​ for the following voltaic cell reactions:

  1. \(\mathrm{Pb^{2+}(aq) +Sn(s) \rightarrow Pb(s) +Sn^{2+}(aq)}\)
  2. \(\mathrm{O_2(g) +2H^+(aq) + 2F^-(aq) \rightarrow H_2O_2(aq) + F_2(g)}\)
  3. \(\mathrm{Br_2(l) +2Fe^{2+}(aq) \rightarrow 2Br^-(aq) + 2Fe^{3+}(aq)}\)

Q2.4

Find the values of \(\mathrm{\Delta G^\circ}\)​ for the following reactions in the voltaic cells

  1. \(\mathrm{2V^{3+}(aq) + Ni(s) \rightarrow 2V^{2+}(aq) + Ni^{2+}(aq)}\)
  2. \(\mathrm{2Al (s) +3Br_2(l) \rightarrow 2Al^{3+}(aq) + 6Br^-}\)
  3. \(\mathrm{2Cu^{2+}(aq) + Sn^{4+} (aq) \rightarrow 2Cu^{+} + Sn^{2+}}\)

Q2.5

Determine if these reactions are Endoenergonic or Exoenergonic under standard conditions.

  1. \(\mathrm{Na^+(aq)+K(s)\rightarrow Na(s)+K^+(aq)}\)
  2. \(\begin{align}\mathrm{2IO_3(aq)} &\mathrm{+12H^+(aq)+2Mn^{2+}(aq)+8H_2O(l)}  \rightarrow\mathrm{I_2(g)+6H_2O(l)+2MnO_4^-(aq)+16H^+(aq)}\end{align}\)
  3. \(\mathrm{Mg^{2+}(aq)+Pb^{2+}(aq)+2H_2O(l) \rightarrow PbO_2(s)+4H^+(aq)+Mg(s)}\)
  4. \(\mathrm{O_2(g)+2H_2O(l)+2Mn^{2+}(aq)\rightarrow 2MnO_2(s)+4H^+(aq)}\)

Q2.6

Identify where each reaction will take place (on the cathode or anode), balance the equation if necessary, and calculate the \(\mathrm{E^\circ_{cell}}\).

  1. \(\mathrm{Fe^{3+} (aq) + Ag(s) \rightarrow Fe^{2+}(aq) + Ag^+(aq)}\)
  2. \(\mathrm{Cu^{2+}(aq) + Zn(s) \rightarrow Cu(s) + Zn^{2+}(aq)}\)
  3. \(\mathrm{Cd(s) + Cu^{2+}(aq) \rightarrow Cd^{2+} + Cu(s)}\)
  4. \(\mathrm{Fe^{2+}(aq) + Cl_2(g) \rightarrow Fe^{3+}(aq) + 2Cl^-(aq)}\)

Q2.7

In the reaction given, calculate the

  1. \(\mathrm{E^\circ_{cell}}\)
  2. \(\mathrm{\Delta G^\circ}\)​
  3. \(\mathrm{K}\)
  4. and if the reaction goes towards completion when the reactants and products are in their standard states:

\[\mathrm{O_2(g) + 4I^-(aq) + 4H^+(aq) \rightarrow 2H_2O (l) +2I_2(s)}\]

Q2.8

The voltaic cell in the following diagram has an \(\mathrm{E_{cell}= 0.5464\: V}\). Solve for the \(\mathrm{[Cl^-]}\) in the cell

\[\mathrm{Ag (s)|Ag^+(0.40\:M)||Cl_2 (0.60\:atm),\, Cl^- (x\:M),|Pt(s)}\]

Q2.9

Using the Nernst equation and a list of \(\mathrm{E^\circ_{cell}}\) values, calculate the \(\mathrm{E_{cell}}\) for the following cells:

  1. \(\mathrm{Al(s)| Al^{3+}(0.36\:M)||Sn^{4+}(0.086\:M),\,Sn^{2+}(0.54\:M)|Pt}\)
  2. \(\mathrm{Sn(s)|Sn^{2+}(0.01\:M)||Pb^{2+}(0.700\:M)|Pb(s)}\)

Q2.10

If \(\ce{[Cu^2+]}\) is maintained at 2.0 M. What is the minimum \(\ce{[Ag+]}\) must be at to push the forward direction spontaneously. Use equation \(\mathrm{Cu(s) + 2Ag^+(aq) \rightarrow Cu^{2+}(aq) + 2Ag(s)}\).

Q2.11

For following voltaic (concentration) cell is constructed:

\[\mathrm{Pb(s)|Pb^{2+}(satd\:PbI_2)||Pb^{2+}(0.100\:M)|Pb(s)}\]

Given that the \(\mathrm{E_{cell} = 0.0567\: V}\), find the \(\mathrm{K_{sp}}\) for Pb in water.

Q2.12

For each of the following reactions: 1) identify the oxidation and reduction half-equations, and 2) balance the equation (adding H+ and H2O as needed), 3) find Eo (in volts) and 4) determine whether the reaction is spontaneous under standard conditions.

  1. \(\ce{Ag(s) + Cu^2+(aq) \rightarrow Ag+(aq) + Cu(s)}\)
  2. \(\ce{Ni(s) + MnO_4- (aq) \rightarrow Ni^2+(aq) + Mn^2+(aq)}\)
  3. \(\ce{Mn^2+(aq) + NO3- (aq) \rightarrow MnO2(s) + NO(g)}\)

Q2.13

For each of the following reactions: 1) find Eo (in volts) and 2) determine whether the reaction is spontaneous under standard conditions.

  1. the reaction between iron and iron(III) ions to give iron(II) ions.
  2. the following cell:   I- | I2 || Zn2+ | Zn

Q2.14

Which of the following ions will oxidize Br- ion to Br2?

  1. Pb2+
  2. H+   
  3. Au3+ 
  4. MnO4-

Q2.15

A voltaic cell has an aluminum electrode in Al2(SO4)3 solution in one compartment and the other compartment has a lead electrode in PbSO4 solution.

  1. Which has a greater tendency to be oxidized, Al or Pb?  Write a balanced equation for the spontaneous reaction.
  2. Draw a picture of the voltaic cell, including
    1. the anode and cathode
    2. the direction of flow of electrons, positive ions and negative ions
  3. Which electrode will increase in mass?

Q2.16

The following table contains data obtained by measuring the voltage between two metals:

Voltaic Cell Anode (-) Cathode (+) Cell Voltage (v)
Pb/Ni Ni Pb 0.10 volts
Pb/Au Pb Au 0.80 volts
Pb/Fe Fe Pb 0.25 volts
Ni/Au Ni Au 0.90 volts
Ni/Fe Fe Ni 0.15 volts
Fe/Au Fe Au 1.05 volts
  1. From the data in the table above, which metal is the strongest reducing agent?
  2. From the data in the table above, which metal is the weakest reducing agent?
  3. Using the reduction of lead (Pb) as a reference, construct a half-cell voltage table from the experimental data above.