Exercise 2.1
Arrange the following metals in the order in which they displace each other from the solution of their salts. Al, Cu, Fe, Mg and Zn.
Not cross-checked
This solution has not been cross-checked against the answer printed in NCERT.
A metal displaces another from its salt solution only if it is a stronger reducing agent than that metal — and the strength of a metal as a reducing agent is read directly off its standard reduction potential.The relevant half-reaction for any metal \(\displaystyle \mathrm{M} \) is
\[\mathrm{M}^{n+}(aq) + n\mathrm{e}^- \rightarrow \mathrm{M}(s), \quad E^\circ
\]
where \(\displaystyle E^\circ \) is the standard reduction potential — how much the metal "wants" to gain electrons and plate out as solid metal. A more negative \(\displaystyle E^\circ \) means the reverse process, \(\displaystyle \mathrm{M}(s) \rightarrow \mathrm{M}^{n+}(aq) + n\mathrm{e}^- \) (oxidation, losing electrons), is favoured instead — so that metal gives up electrons readily and is the stronger reducing agent.This is the step people get wrong: displacement is governed by which metal is more easily oxidised, so you rank by increasing \(\displaystyle E^\circ_{\text{red}} \) (most negative first), not by the numerical value ignoring sign.The standard reduction potentials (vs. SHE, in volts) for the five metals are:\[\begin{aligned}
\mathrm{Mg}^{2+} + 2e^- &\rightarrow \mathrm{Mg}, & E^\circ &= -2.36\ \text{V} \\
\mathrm{Al}^{3+} + 3e^- &\rightarrow \mathrm{Al}, & E^\circ &= -1.66\ \text{V} \\
\mathrm{Zn}^{2+} + 2e^- &\rightarrow \mathrm{Zn}, & E^\circ &= -0.76\ \text{V} \\
\mathrm{Fe}^{2+} + 2e^- &\rightarrow \mathrm{Fe}, & E^\circ &= -0.44\ \text{V} \\
\mathrm{Cu}^{2+} + 2e^- &\rightarrow \mathrm{Cu}, & E^\circ &= +0.34\ \text{V}
\end{aligned}
\]A metal with a more negative \(\displaystyle E^\circ \) will reduce the ion of a metal with a less negative (or positive) \(\displaystyle E^\circ \), oxidising itself in the process — that is, it displaces that metal from solution. For example, since \(\displaystyle E^\circ_{\mathrm{Mg}^{2+}/\mathrm{Mg}} = -2.36\ \text{V} \) is more negative than \(\displaystyle E^\circ_{\mathrm{Cu}^{2+}/\mathrm{Cu}} = +0.34\ \text{V} \), the spontaneous reaction is
\[\mathrm{Mg}(s) + \mathrm{Cu}^{2+}(aq) \rightarrow \mathrm{Mg}^{2+}(aq) + \mathrm{Cu}(s)
\]
so magnesium metal displaces copper from copper sulphate solution.Arranging the five values from most negative to least negative:
\[-2.36\ (\mathrm{Mg}) \;<\; -1.66\ (\mathrm{Al}) \;<\; -0.76\ (\mathrm{Zn}) \;<\; -0.44\ (\mathrm{Fe}) \;<\; +0.34\ (\mathrm{Cu})
\]This gives the order of decreasing reactivity — decreasing power to displace the others from their salt solutions:\[\mathrm{Mg} > \mathrm{Al} > \mathrm{Zn} > \mathrm{Fe} > \mathrm{Cu}
\]So magnesium can displace aluminium, zinc, iron, and copper from their salt solutions; aluminium can displace zinc, iron, and copper (but not magnesium); zinc can displace iron and copper; and iron can displace only copper. Copper, with the least negative (positive) \(\displaystyle E^\circ \), displaces none of the others.Answer: \(\displaystyle \mathrm{Mg} > \mathrm{Al} > \mathrm{Zn} > \mathrm{Fe} > \mathrm{Cu} \) — this is the order of decreasing reactivity, i.e., each metal displaces every metal listed after it from the solution of its salt.