Question

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 \(1.0 \mathrm{M}\). (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) \(\mathrm{Cu}^{+}(a q)+\mathrm{Fe}^{3+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+\mathrm{Fe}^{2+}(a q)\)

Short answer

(a) Yes, (b) Yes, (c) No, (d) Yes.

Step-by-step solution

Understanding Reaction Potentials

The spontaneity of each reaction is determined using the electromotive force (EMF) calculated from standard reduction potentials. A reaction is spontaneous if the calculated EMF (or potential difference, \( \Delta E^0 \)) is positive. The reaction series involves comparing the given half-reactions with known standard reduction potentials.

Processing Reaction (a)

For the reaction \( \mathrm{Ca}(s) + \mathrm{Cd}^{2+}(aq) \rightarrow \mathrm{Ca}^{2+}(aq) + \mathrm{Cd}(s) \), find the standard reduction potentials: Ca: \( E^0 \) for \( \mathrm{Ca}^{2+} + 2e^- \rightarrow \mathrm{Ca}(s) \) is \(-2.87 \, \mathrm{V}\).Cd: \( E^0 \) for \( \mathrm{Cd}^{2+} + 2e^- \rightarrow \mathrm{Cd}(s) \) is \(-0.40 \, \mathrm{V}\).Calculate \( \Delta E^0 \): \(-0.40 - (-2.87) = 2.47 \, \mathrm{V}\). This is positive, so the reaction is spontaneous.

Processing Reaction (b)

For \( 2 \mathrm{Br}^-(aq) + \mathrm{Sn}^{2+}(aq) \rightarrow \mathrm{Br}_2(l) + \mathrm{Sn}(s) \), Br: \( E^0 \) for \( \mathrm{Br}_2 + 2e^- \rightarrow 2\mathrm{Br}^- \) is \(+1.07 \, \mathrm{V}\).Sn: \( E^0 \) for \( \mathrm{Sn}^{2+} + 2e^- \rightarrow \mathrm{Sn}(s) \) is \(-0.14 \, \mathrm{V}\).Calculate \( \Delta E^0 \): \(+1.07 - (-0.14) = 0.93 \, \mathrm{V}\). Positive \( \Delta E^0 \) indicates the reaction is spontaneous.

Processing Reaction (c)

For \( 2 \mathrm{Ag}(s) + \mathrm{Ni}^{2+} \rightarrow 2 \mathrm{Ag}^+(aq) + \mathrm{Ni}(s) \), Ag: \( E^0 \) for \( 2\mathrm{Ag}^+ + 2e^- \rightarrow 2\mathrm{Ag}(s) \) is \(+0.80 \, \mathrm{V}\).Ni: \( E^0 \) for \( \mathrm{Ni}^{2+} + 2e^- \rightarrow \mathrm{Ni}(s) \) is \(-0.23 \, \mathrm{V}\).Calculate \( \Delta E^0 \): \(-0.23 - (+0.80) = -1.03 \, \mathrm{V}\). This negative \( \Delta E^0 \) means the reaction is not spontaneous.

Processing Reaction (d)

For \( \mathrm{Cu}^+(aq) + \mathrm{Fe}^{3+}(aq) \rightarrow \mathrm{Cu}^{2+}(aq) + \mathrm{Fe}^{2+}(aq) \), Cu: \( E^0 \) for \( \mathrm{Cu}^{2+} + e^- \rightarrow \mathrm{Cu}^+ \) is \(+0.16 \, \mathrm{V}\).Fe: \( E^0 \) for \( \mathrm{Fe}^{3+} + e^- \rightarrow \mathrm{Fe}^{2+} \) is \(+0.77 \, \mathrm{V}\).Calculate \( \Delta E^0 \): \(+0.77 - (+0.16) = 0.61 \, \mathrm{V}\). Positive \( \Delta E^0 \) means the reaction is spontaneous.

Key concepts

Electromotive Force

The electromotive force (EMF) is an important concept in electrochemistry, as it represents the potential difference between two electrodes in a cell that causes electrons to flow. This "force" is not like a physical push, but rather the energy needed to move electrons through a conductor. In terms of chemical reactions, a positive EMF indicates that a reaction can occur spontaneously. Spontaneity implies that a reaction can occur without any external energy being supplied, which makes positive EMF a crucial indicator for predicting how and whether reactions will take place. The measurement of EMF is generally done in volts (V). Understanding how to calculate and interpret EMF helps predict reaction behavior in electrochemical cells and even in more general chemical reactions.

Standard Reduction Potentials

Standard reduction potentials (\( E^0 \) are values that measure the tendency of a chemical species to gain electrons and be reduced. These potentials are measured under standard conditions, which include solutions at a concentration of 1 M, a pressure of 1 atm, and a temperature of 25°C. The standard hydrogen electrode (SHE) is used as the reference point and is assigned a potential of 0.00 V. By using these standard reduction potentials, we can determine the strength of oxidizing and reducing agents. In calculating the EMF of a reaction, we take the difference between the reduction potentials of the reduction half-reaction and the oxidation half-reaction. If the EMF is positive, it tells us the reaction can occur spontaneously under standard conditions.

Spontaneity of Reactions

The spontaneity of a chemical reaction is a vital concept that denotes whether a reaction can proceed on its own. A reaction is said to be spontaneous if it occurs without the addition of external energy. For electrochemical reactions, the spontaneity can easily be identified by calculating the electromotive force (EMF). If the EMF is positive, the reaction will occur spontaneously. A negative EMF, however, implies that the reaction does not favor spontaneous occurrence. Knowing if a reaction is spontaneous is essential in fields ranging from battery design to industrial chemical processes, as it informs whether additional conditions or catalysts are necessary.

Aqueous Solution Reactions

Reactions in aqueous solutions are ubiquitous in both natural systems and industrial processes. In these reactions, water acts as a solvent, allowing ions to freely move and react with each other. The concentration of reactants, their respective standard reduction potentials, and the temperature all influence how these reactions proceed. Additionally, the solubility, presence of secondary interactions, and reaction conditions can greatly affect the outcome and efficiency of aqueous reactions. By analyzing reactions in aqueous solutions, chemists can determine factors like dissolution rates, formation of precipitates, and the ability of a reaction to reach equilibrium. Understanding these reactions and how they behave allows for optimized conditions in laboratories and various industries.