which of these reactions (a) or (b) is spontaneous? Explain why. write the half cell equations for the spontaneous reaction. Identify which element is oxidized and which is reduced.
(a) Fe^0+Mg^+2 --> Mg^0 + Fe^+2
(b) Fe^+2 + Mg^0 --> Fe^0 + Mg^+2
Look up the reduction potentials and add the oxidation half cell to the reductin half cell to obtain the Eocell. If it is + the rxn is spontaneous; if Eocell is - it is not spontaneous.
To determine which of the reactions (a) or (b) is spontaneous, we can use the concept of standard reduction potentials. The more positive the reduction potential, the more likely a species is to be reduced (gain electrons) and the more negative the reduction potential, the more likely a species is to be oxidized (lose electrons).
Step 1: Write the half-cell reactions for each reaction:
(a) Fe^0 → Fe^+2 + 2e^-
Mg^+2 + 2e^- → Mg^0
(b) Fe^+2 + 2e^- → Fe^0
Mg^0 → Mg^+2 + 2e^-
Step 2: Look up the standard reduction potentials for each half-reaction. The more positive value indicates a higher tendency for reduction (gain of electrons).
Fe^+2 + 2e^- → Fe^0 : E° = +0.44V
Mg^+2 + 2e^- → Mg^0 : E° = -2.37V
Fe^0 → Fe^+2 + 2e^- : E° = -0.44V
Mg^0 → Mg^+2 + 2e^- : E° = +2.37V
Step 3: Calculate the total cell potential (E°cell) by subtracting the reduction potential of the anode (oxidation half-reaction) from the reduction potential of the cathode (reduction half-reaction).
For reaction (a):
E°cell = E°cathode - E°anode
= (-2.37V) - (-0.44V)
= -1.93V
For reaction (b):
E°cell = E°cathode - E°anode
= (+2.37V) - (+0.44V)
= +1.93V
Step 4: Analyze the sign of E°cell. A positive cell potential (E°cell > 0) indicates that the reaction is spontaneous, whereas a negative cell potential (E°cell < 0) indicates that the reaction is non-spontaneous.
In this case, reaction (b) has a positive cell potential (+1.93V) and so it is the spontaneous reaction. The reaction (a) has a negative cell potential (-1.93V), making it non-spontaneous.
Therefore, the spontaneous reaction is (b) Fe^+2 + Mg^0 → Fe^0 + Mg^+2.
In this reaction, Fe is being reduced (gaining electrons) from Fe^+2 to Fe^0, and Mg is being oxidized (losing electrons) from Mg^0 to Mg^+2.