Question

Consider a galvanic cell based upon the following half reactions: Ag+ + e- → Ag 0.80 V Cu2+ + 2 e- → Cu 0.34 V

How would the following changes alter the potential of the cell?

Adding Cu2+ ions to the copper half reaction (assuming no volume change).

Adding equal amounts of water to both half reactions.

Removing Cu2+ ions from solution by precipitating them out of the copper half reaction (assume no volume change).

Adding Ag+ ions to the silver half reaction (assume no volume change)

Answer 1

Nernst equation relates the reduction potential of an electrochemical reaction (half-cell or full cell reaction) to the standard electrode potential, temperature, and activities (often approximated by concentrations) of the chemical species undergoing reduction and oxidation.

Reaction under consideration:

Ag⁺ + e^- → Ag 0.80 V

Cu⁺² + 2 e^- → Cu 0.34 V

Clearly, Ag reduction potential is high and this indicates that it gets reduced readily which leaves Cu to oxidize. Cu⁺² ions are products of reaction and Ag⁺ ions are reactant ions.

Nernst equation : E_cell = E°_cell­ – (2.303 RT / n F) log Q   

where                              E_cell = actual cell potential

                                       E°_{cell­ ­}​ = standard cell potential

                                       R = the universal gas constant = 8.314472(15) J K−1 mol−1

                                       T = the temperature in kelvins

                                       n = the number of moles of electrons transferred                                     

                                       F = the Faraday constant, the number of coulombs per mole of electrons:

                                               (F = 9.64853399(24)×104 C mol−1)

                                      Q = [product ion]^y / [reactant ion] ^x

Accordingly when applied to above reaction one will get the following

= E°_cell­ – (2.303 x RT / 6 F) log [Cu⁺²] / [Ag⁺]

Now the given variables can be studied according to Le Chatelier's principle which states when any system at equilibrium is subjected to change in its concentration, temperature, volume, or pressure, then the system readjusts itself to (partially) counteract the effect of the applied change and a new equilibrium is established.

a)        Adding Cu²⁺ ions to the copper half reaction (assuming no volume change).

Addition of Cu⁺² ions increases its concentration and consequently increases the Q value which results in reduction of E_cell. In other words the addition of Cu⁺² ions favors the backward reaction to maintain the equilibrium of reaction and hence the forward reaction rate decreases.

b)       Adding equal amounts of water to both half reactions.

Addition of water increases the dilution of the electrochemical cell. For weak electrolytes such as Ag⁺/ Cu⁺² with increase in dilution, the degree of dissociation increases and as a result molar conductance increases.

c)        Removing Cu²⁺ ions from solution by precipitating them out of the copper half reaction (assume no volume change).

Based on Le Chatelier's principle when Cu⁺² ions amount is decreased by its continuous removal from                             the system the forward reaction is favored. As the Cu⁺² ions is removed the system attempts to generate more Cu⁺² ions to counter the affect of its removal.

d)       Adding Ag⁺ ions to the silver half reaction (assume no volume change)

Addition of reactant ions, i.e. Ag⁺ ions, will favour the forward reaction, which results in more product formation.