Animated Solution for Chemistry - Electrochemistry: The standard reduction potentials for ${\text{Zn}}^{2+}/\text{Zn}$, ${\text{Ni}}^{2+}/\text{Ni}$ and ${\text{Fe}}^{2+}/\text{Fe}$ are $-0.76$, $-0.23$ and $-0.44\text{ V}$, respectively. The reaction $X+Y^{2+}⟶X^{2+}+Y$ will be spontaneous when

The problem asks us to determine which combination of metals $X$ and $Y$ will make the given redox reaction spontaneous. This is a classic application of electrochemical principles, specifically the relationship between standard cell potential and Gibbs free energy.

For any chemical reaction to occur spontaneously under standard conditions, its standard Gibbs free energy change, $\Delta G^{\circ }$, must be negative. In the realm of electrochemistry, this is directly tied to the standard cell potential, $E_{\text{cell}}^{\circ }$, through the equation:

Here, $n$ is the number of moles of electrons transferred, and $F$ is Faraday's constant. Since both $n$ and $F$ are positive values, the only way for $\Delta G^{\circ }$ to be negative is if $E_{\text{cell}}^{\circ }$ is positive.

Let's look at the general reaction provided:

In this process, metal $X$ is losing two electrons to form $X^{2+}$. Loss of electrons is oxidation, which means $X$ is acting as the anode. Conversely, the $Y^{2+}$ ion is gaining two electrons to form solid metal $Y$. Gain of electrons is reduction, meaning $Y$ is acting as the cathode.

The standard cell potential is calculated as the reduction potential of the cathode minus the reduction potential of the anode:

For the reaction to be spontaneous, we need $E_{\text{cell}}^{\circ }>0$, which implies:

In simpler terms, the metal getting reduced ($Y$) must have a higher (less negative) standard reduction potential than the metal getting oxidized ($X$).

We are given the following standard reduction potentials: $E_{{\text{Zn}}^{2+}/\text{Zn}}^{\circ }=-0.76\text{ V}$ $E_{{\text{Fe}}^{2+}/\text{Fe}}^{\circ }=-0.44\text{ V}$ * $E_{{\text{Ni}}^{2+}/\text{Ni}}^{\circ }=-0.23\text{ V}$

We need to find a pair where the reduction potential of $Y$ is greater than that of $X$. Let's test the options:

Option (a): $X=\text{Ni},Y=\text{Fe}$ (Negative, non-spontaneous)

Option (b): $X=\text{Ni},Y=\text{Zn}$ (Negative, non-spontaneous)

Option (c): $X=\text{Fe},Y=\text{Zn}$ (Negative, non-spontaneous)

Option (d): $X=\text{Zn},Y=\text{Ni}$ (Positive, spontaneous!)

Therefore, Zinc can spontaneously reduce Nickel ions, making option (d) the correct answer. A great rule of thumb to remember is that a metal lower on the reduction potential series (more negative) can always displace a metal higher up (less negative) from its aqueous salt solution.