Matter & Motion: Electrochemistry Worksheet

A galvanic cell is constructed from the following electrodes: Cr (s) | Cr2+ and Pt | Cr2O72- (aq), Cr3+ (aq). The solutions at both electrodes are acidic with pH = 0.

a) What is the overall redox reaction taking place in the cell? What reaction is taking place at the anode?
 

The two electrochemical couples (written as reductions) present are:

Cr2+ (aq) + 2 e- ® Cr (s)                                                 E°red = -0.92 V

14 H+ + Cr2O72- + 6 e- ® 2 Cr3+ + 7 H2O (l)             E°red = 1.33 V

Since one of these half-reactions must be an oxidation, we need to reverse the direction of one of them - which one to reverse, you ask? Aaah, good question. The sum of E°ox and E°red must be positive to have a negative DG° . Since this is a galvanic cell, DG° must be negative, so the actual half- reactions are:

oxidation (at the anode): Cr (s) ® Cr2+ + 2e-             E°ox = +0.92 V

reduction (at the cathode):

14 H+ (aq) + Cr2O72- (aq) + 6 e- ®
                 3 Cr2+ (aq) + 2 Cr3+ (aq) + 7 H2O (l)        E°red = 1.33 V

  net reaction:

14 H+ (aq) + Cr2O72- (aq) + 3 Cr (s) ® 3 Cr2+ (aq) + 2 Cr3+ (aq) + 7 H2O (l)
 

 b) Draw a sketch of the cell and clearly indicate the direction of the electron flow, the identity of the anode and cathode as well as the direction of ion flow through the salt bridge. Would it be possible to use this cell for the electroplating of chromium? Instead of drawing a picture, I'll describe the important bits of information. The electrons always flow from the anode to the cathode, so in this case, they flow from the chromium to the platinum strips. Anions flow in the salt bridge toward the anode compartment to maintain charge balance.

It would be impossible to use this cell to plate chromium on an electrode, since metallic chromium is not a product of the reaction. However, if a voltage were applied to the cell, electrical work could be done to get the above reaction to run in reverse. The cell would then be operating as an electrolytic cell and chromium would be electroplated on the cathode.

 c) What is DEo for the above cell?
  D E°= E°red + E°ox = 1.33 V + 0.92 V = 2.25 V
  d) Calculate the change in free energy if 1.00 g of the reactant at the anode material is consumed and all species remain in their standard states.
  DG = -nFE


 

 e) If a current of 0.50 A runs through the cell for 45 minutes, what would be the change in mass at the anode? at the cathode?
 

There is no change in mass of the cathode since it is an inert metal; it does not directly participate in the redox reaction.
 

 f) If pH = 0 in both compartments, [Cr2+] = 0.15 M, [Cr3+] = 0.001 M and [Cr2O72-] = 0.05 M, what is the actual potential of the cell?
 
 


 


 

 g) What is the equilibrium constant of the above balanced equation?
 
 

log K = 228

K ~ 10228