Question

The standard potential at \(25^{\circ} \mathrm{C}\) for the following half reactions is given : $$ \begin{aligned} \mathrm{Zn}^{2+}+2 e^{-} & \mathrm{Zn} ; E^{\circ}=-0.762 \mathrm{~V} \\ \mathrm{Mg}^{2+}+2 e^{-} & \mathrm{Mg} ; E^{\circ}=-2.37 \mathrm{~V} \end{aligned} $$ When Zinc dust is added to the solution of \(\mathrm{MgCl}_{2}\). (a) \(\mathrm{ZnCl}_{2}\) is formed (b) \(\mathrm{Mg}\) is precipitated (c) Zn dissolved in the solution (d) No reaction takes place

Short answer

No reaction takes place when Zinc dust is added to the solution of MgCl2 because the tendency of magnesium to get oxidized (E° = -2.37V) is greater than the tendency of zinc to get reduced (E° = -0.762V).

Step-by-step solution

Identify the possible oxidation and reduction half-reactions

Firstly, understand the given half-reactions with their respective standard electrode potentials (E°). The potential for the zinc half-reaction is E°(Zn^{2+}/Zn) = -0.762V and for the magnesium half-reaction it is E°(Mg^{2+}/Mg) = -2.37V. Determine which metal has a higher tendency to get oxidized by comparing these values.

Compare standard electrode potentials

Looking at the standard potentials, note that magnesium has a more negative electrode potential, meaning it has a higher tendency to lose electrons (oxidize) compared to zinc. So, according to the electrochemical series, Mg would prefer to stay in its reduced form (Mg solid) rather than being oxidized to Mg^{2+}. Therefore, it will not be displaced out of solution by Zinc.

Determine the feasibility of reaction

Since the standard reduction potential for zinc is less negative than that of magnesium, it is less likely for zinc to be reduced when compared to magnesium. Therefore, when zinc dust is added to MgCl2, there will be no tendency for the magnesium ions to be reduced to magnesium metal, and consequently, no tendency for zinc to go into solution as Zn^{2+}.

Predict the reaction outcome

Based on the standard potentials, we can predict that when zinc dust is added to a solution of MgCl2, the more reactive Mg will not be replaced by Zn from the solution. There will be no tendency for the reaction to form ZnCl2 or for Mg to precipitate, and thus no reaction takes place.

Key concepts

Standard Electrode Potentials

Understanding standard electrode potentials is key to predicting the outcome of electrochemical reactions. It's a measure of the tendency of a chemical species to gain or lose electrons, known as reduction or oxidation, respectively. Each standard electrode potential is given with respect to the standard hydrogen electrode, which is set at 0 volts.

When comparing electrode potentials, if a metal has a more negative standard electrode potential, it means it is more likely to lose electrons and undergo oxidation. This knowledge helps us predict which metals can displace others from solutions, as seen in the standard reactions provided:

• Zinc: \(\text{Zn}^{2+} + 2e^- \rightarrow \text{Zn}\); \(E^\circ = -0.762 \text{ V}\)
• Magnesium: \(\text{Mg}^{2+} + 2e^- \rightarrow \text{Mg}\); \(E^\circ = -2.37 \text{ V}\)

Here, the potential for zinc is less negative than that for magnesium, hinting at different chemical behaviors which are crucial in determining the outcome of their reactions in solutions.

Oxidation and Reduction Half-Reactions

Delving into oxidation and reduction half-reactions helps us understand the components of a full electrochemical reaction. An oxidation half-reaction involves the loss of electrons, while a reduction half-reaction involves the gain of electrons. These half-reactions are crucial because they tell us which species will act as an oxidizing agent (gaining electrons) and which will act as a reducing agent (losing electrons).

For instance, in the given exercise, the magnesium and zinc half-reactions are both reduction reactions:

• Magnesium: \(\text{Mg}^{2+} + 2e^- \rightarrow \text{Mg}\)
• Zinc: \(\text{Zn}^{2+} + 2e^- \rightarrow \text{Zn}\)

The metal that more readily loses electrons (has a stronger oxidizing potential) typically remains in the solution as ions. Conversely, the metal with a stronger tendency to gain electrons (more negative electrode potential) is more likely to be reduced to its solid form, if conditions allow.

Reactivity of Metals

The reactivity of metals is influenced by their position in the electrochemical series, which is closely related to their standard electrode potentials. Metals that are more reactive have a greater tendency to lose electrons and form positive ions. In an electrochemical series, metals are arranged according to their standard electrode potentials, with the most reactive metals (those with the more negative electrode potentials) placed at the top.

Based on the exercise, magnesium (\(E^\circ = -2.37 \text{ V}\)) is more reactive than zinc (\(E^\circ = -0.762 \text{ V}\)), which means it has a stronger desire to give up its electrons and remain as \(\text{Mg}^{2+}\) ions in solution rather than being replaced by zinc atoms from the solid state. This influences whether a metal can displace another in a reaction, dictating the course of the electrochemical process.

Electrode Potential Comparison

Comparing electrode potentials of different metals allows us to predict which chemical reactions are possible. In a displacement reaction, a metal with a higher (less negative) electrode potential can potentially displace another metal with a lower (more negative) potential from a solution.

In our exercise, we compare the standard electrode potentials of magnesium and zinc. Since magnesium has the lower standard electrode potential, we understand that it is less likely to be displaced from the solution by zinc. Therefore, when zinc dust is added to \(\text{MgCl}_2\), no reaction occurs because zinc does not have the required tendency to displace magnesium. This comparison is a fundamental tool in chemistry, allowing us to predict the outcomes of reactions without performing them in a lab.