Determine whether the reaction given below would be spontaneous or not. JUSTIFY your answer.
Mg2+ (aq) + Ag (s) → Ag+ (aq) + Mg (s)
To determine whether the reaction is spontaneous or not, we need to consider two factors: the standard reduction potentials of the half-reactions and the concept of Gibbs free energy.
1. Identify the half-reactions:
The given reaction involves the following half-reactions:
Mg2+ (aq) + 2e- → Mg (s) (Reduction half-reaction)
Ag+ (aq) + e- → Ag (s) (Oxidation half-reaction)
2. Look up the standard reduction potentials:
The standard reduction potentials can be found in a table (such as the Standard Reduction Potentials table). The more positive the standard reduction potential is, the more likely the corresponding reduction half-reaction occurs spontaneously.
For the given half-reactions:
The standard reduction potential for the reduction of Mg2+ (aq) to Mg (s) is -2.37 V.
The standard reduction potential for the reduction of Ag+ (aq) to Ag (s) is +0.80 V.
3. Calculate the standard cell potential:
To calculate the standard cell potential (E°cell) of the reaction, subtract the oxidation half-reaction potential from the reduction half-reaction potential:
E°cell = E°red (cathode) - E°red (anode)
In this case, we have:
E°cell = (+0.80 V) - (-2.37 V) = +3.17 V
4. Determine if the reaction is spontaneous or not:
If the standard cell potential (E°cell) is positive, the reaction is spontaneous. If the standard cell potential is negative, the reaction is non-spontaneous.
In this case, since the calculated E°cell value is +3.17 V (which is greater than zero), the reaction is spontaneous. The transfer of electrons occurs spontaneously from the silver electrode (Ag) to the magnesium ion (Mg2+).
Therefore, the given reaction, Mg2+ (aq) + Ag (s) → Ag+ (aq) + Mg (s), is spontaneous based on the calculation of the standard cell potential.