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) $\operatorname{Mn}(s)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{Mn}^{2+}(a q)+\mathrm{Ni}(s)$ (b) $3 \mathrm{Cu}^{2+}(a q)+2 \mathrm{Al}(s) \longrightarrow 2 \mathrm{Al}^{3+}(a q)+3 \mathrm{Cu}(s)$ (c) $\mathrm{Na}(s)+\operatorname{LiNO}_{3}(a q) \longrightarrow \mathrm{NaNO}_{3}(a q)+\mathrm{Li}(s)$ (d) $\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{Ba}(s) \longrightarrow \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{Ca}(s)$

Calculate the standard cell potential for each reaction below, and note whether the reaction is spontaneous
under standard state conditions.
(a) $\operatorname{Mn}(s)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{Mn}^{2+}(a q)+\mathrm{Ni}(s)$
(b) $3 \mathrm{Cu}^{2+}(a q)+2 \mathrm{Al}(s) \longrightarrow 2 \mathrm{Al}^{3+}(a q)+3 \mathrm{Cu}(s)$
(c) $\mathrm{Na}(s)+\operatorname{LiNO}_{3}(a q) \longrightarrow \mathrm{NaNO}_{3}(a q)+\mathrm{Li}(s)$
(d) $\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{Ba}(s) \longrightarrow \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{Ca}(s)$

Key Concepts

Spontaneity Criterion in Electrochemistry

In electrochemistry, a reaction is considered spontaneous under standard state conditions if the standard cell potential is positive. This reflects a thermodynamically favorable process where the electrochemical cell can perform work, such as generating an electric current.

Standard State Conditions

Standard state conditions refer to a set of agreed-upon conditions for measurements and comparisons in chemistry, typically including a temperature of 25°C (298 K), a pressure of 1 atm for gases, and a concentration of 1 M for solutions. These conditions ensure consistency when using standard reduction potentials to calculate cell potentials.

Standard Reduction Potentials

Standard reduction potentials are tabulated values that indicate the tendency of a chemical species to gain electrons under standard state conditions. They serve as a reference to determine which half-reaction occurs at the cathode and which at the anode in an electrochemical cell, and they are crucial for calculating the overall cell potential.

Redox Reactions

Redox reactions involve the transfer of electrons between species. In these reactions, one species undergoes oxidation (losing electrons) while the other undergoes reduction (gaining electrons). Understanding redox processes is essential for identifying half-reactions and determining the flow of electrons in an electrochemical cell.

Standard Cell Potential

The standard cell potential is the voltage difference between the two electrodes of an electrochemical cell when all species are in their standard states. It is calculated using the equation E°cell = E°cathode - E°anode, and it provides information about the driving force of the electrochemical reaction.

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