Predict whether the following reactions would occur spontaneously in aqueous solution at \(25^{\circ} \mathrm{C}\). Assume that the initial concentrations of dissolved species are all \(1.0 M\) (a) \(\mathrm{Ca}(s)+\mathrm{Cd}^{2+}(a q) \longrightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{Cd}(s)\) (b) \(2 \mathrm{Br}^{-}(a q)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Br}_{2}(l)+\operatorname{Sn}(s)\) (c) \(2 \mathrm{Ag}(s)+\mathrm{Ni}^{2+}(a q) \longrightarrow 2 \mathrm{Ag}^{+}(a q)+\mathrm{Ni}(s)\) (d) \(\mathrm{Cu}^{+}(a q)+\mathrm{Fe}^{3+}(a q) \longrightarrow\) $$\mathrm{Cu}^{2+}(a q)+\mathrm{Fe}^{2+}(a q)$$

The Standard Reduction Potential (SRP) is an intrinsic property of a substance that measures its tendency to gain electrons and be reduced. It is defined with respect to a standard hydrogen electrode, which has an assigned potential of 0 volts. Chemical species with more positive SRP are better oxidizing agents, meaning they prefer to gain electrons, while species with more negative SRP are better reducing agents, willing to donate electrons.

When analyzing redox reactions, comparing SRP values helps determine the direction in which electrons will flow. The more positive the SRP of a reactant, the greater its ability to be reduced. If a reacting species has a higher SRP than another, it is more likely to be reduced, pulling electrons away from the other substance, which gets oxidized.

The Nernst equation is foundational in understanding electrochemical spontaneity. It quantifies the cell potential at any concentration, giving insight beyond the standard conditions considered by SRP. The Nernst equation is expressed as:

\( E = E^0 - \frac{RT}{nF} \ln(Q) \),

where \(E\) is the cell potential, \(E^0\) the standard cell potential, \(R\) the ideal gas constant, \(T\) the temperature in Kelvin, \(n\) the number of electrons transferred, \(F\) the Faraday's constant, and \(Q\) the reaction quotient. For spontaneous reactions at standard conditions, the cell potential calculated using the Nernst equation must be greater than zero. It allows predictions about reactions' behavior under varying concentrations, enhancing the understanding beyond what SRP alone can provide.

Electrochemical spontaneity refers to the natural tendency of a redox reaction to occur without the input of external energy. It is determined by the cell potential, which arises from the difference in SRP values of the reactant and product couples. A reaction is spontaneous if the overall cell potential is positive, as indicated by both the standard reduction potentials and the Nernst equation.

A positive cell potential indicates that the driving force for the transfer of electrons is favorable. In such cases, the reaction can release energy, usually as electrical work in a galvanic cell. Conversely, if the cell potential is negative, the reaction is non-spontaneous under standard conditions and would require external energy to proceed, such as in an electrolytic cell.

Oxidation-reduction (redox) reactions are chemical processes involving the transfer of electrons from one species to another. The species that loses electrons is oxidized, while the one that gains electrons is reduced. Working out whether these reactions are spontaneous requires an understanding of the involved species' redox potentials.

In a redox reaction context, such as the given exercises, it's crucial to identify the oxidizing and reducing agents. The reactant being oxidized must have a less positive, or more negative, SRP than the reactant being reduced. In other words, the oxidizing agent should have a greater tendency to gain electrons (higher SRP) compared with the reducing agent. When the oxidizing agent has a lower SRP value than the reducing agent, the reaction is not spontaneous and would not proceed under standard conditions.