Calculate the standard cell potential for each reaction...

Calculate the standard cell potential for each reaction below, and note whether the reaction is spontaneous under standard state conditions. (a) $\operatorname{Mg}(s)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Ni}(s)$ (b) $2 \mathrm{Ag}^{+}(a q)+\mathrm{Cu}(s) \longrightarrow \mathrm{Cu}^{2+}(a q)+2 \mathrm{Ag}(s)$ (c) $\operatorname{Mn}(s)+\operatorname{Sn}\left(\mathrm{NO}_{3}\right)_{2}(a q) \longrightarrow \mathrm{Mn}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\operatorname{Sn}(s)$ (d) $3 \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{Au}\left(\mathrm{NO}_{3}\right)_{3}(a q) \longrightarrow 3 \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}(a q)+\mathrm{Au}(s)$

Calculate the standard cell potential for each reaction below, and note whether the reaction is spontaneous
under standard state conditions.

(a) $\operatorname{Mg}(s)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Ni}(s)$
(b) $2 \mathrm{Ag}^{+}(a q)+\mathrm{Cu}(s) \longrightarrow \mathrm{Cu}^{2+}(a q)+2 \mathrm{Ag}(s)$
(c) $\operatorname{Mn}(s)+\operatorname{Sn}\left(\mathrm{NO}_{3}\right)_{2}(a q) \longrightarrow \mathrm{Mn}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\operatorname{Sn}(s)$
(d) $3 \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{Au}\left(\mathrm{NO}_{3}\right)_{3}(a q) \longrightarrow 3 \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}(a q)+\mathrm{Au}(s)$

Key Concepts

Standard Electrode Potentials

Standard electrode potentials are numerical values that indicate the tendency of a chemical species to be reduced, measured under standard conditions (usually 1 M concentration, 1 atm pressure, and 25 °C). These potentials are tabulated for reduction half-reactions and form the basis for determining the voltage of electrochemical cells.

Half-Reactions (Oxidation and Reduction)

Redox reactions involve both oxidation and reduction processes, which are conveniently separated into half-reactions. Each half-reaction represents either the loss or gain of electrons, and by examining these separately, one can determine the overall electron transfer and reaction feasibility.

Standard Cell Potential Calculation

The standard cell potential (E°cell) of an electrochemical cell is derived from the standard reduction potentials of the cathode and the anode. It is calculated using the formula E°cell = E°cathode - E°anode, where the cathode is where reduction occurs and the anode is where oxidation takes place. This calculation integrates the contributions of both half-reactions.

Reaction Spontaneity

The sign and magnitude of the standard cell potential are directly related to the spontaneity of the electrochemical reaction. A positive E°cell indicates that the reaction is spontaneous under standard state conditions, while a negative value suggests a non-spontaneous reaction, requiring an external energy input to proceed.

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