Finding the Transition Metal with Positive Standard Electrode Potential

The question asks us to identify the metal from the first transition series (Sc to Zn) that has a positive standard electrode potential (\(E^0_{M^{2+}/M}\)) value.

The standard electrode potential (\(E^0_{M^{2+}/M}\)) represents the tendency of a metal ion (\(M^{2+}\)) to be reduced to its metallic state (\(M\)). A positive value indicates that the reduction of the metal ion is thermodynamically favorable compared to the reduction of \({\rm H^+}\) ions to \({\rm H_2}\) (which is the reference with \(E^0 = 0\)). A negative value indicates that the metal itself has a stronger tendency to be oxidised to \(M^{2+}\) ions than \({\rm H_2}\) is oxidised to \({\rm H^+}\).

Standard Electrode Potentials in the First Transition Series

For the first transition series, the \(E^0_{M^{2+}/M}\) values are generally negative. This means that these metals tend to lose electrons and form \({\rm M^{2+}}\) ions rather than their ions gaining electrons to form the metal. However, there is one notable exception in the series.

Let's look at the approximate \(E^0_{M^{2+}/M}\) values for the first transition series elements:

Analysing the Options

Now let's examine the \(E^0_{M^{2+}/M}\) values for the metals given in the options:

• Cr (Chromium): The value is approximately -0.91 V. This is negative.
• V (Vanadium): The value is approximately -1.18 V. This is negative.
• Cu (Copper): The value is approximately +0.34 V. This is positive.
• Ni (Nickel): The value is approximately -0.25 V. This is negative.

Identifying the Metal with Positive \(E^0\)

From the table and the analysis of the options, we can see that only Copper (Cu) has a positive \(E^0_{M^{2+}/M}\) value (+0.34 V). All other metals in the options (Cr, V, Ni) have negative values.

Reason for Positive \(E^0_{Cu^{2+}/Cu}\)

The \(E^0_{M^{2+}/M}\) value depends on several factors, including the enthalpy of atomisation (energy required to convert the solid metal into gaseous atoms), the first and second ionisation enthalpies (energy required to remove two electrons from the gaseous atom to form a \({\rm M^{2+}}\) ion), and the enthalpy of hydration of the \({\rm M^{2+}}\) ion (energy released when the gaseous \({\rm M^{2+}}\) ion is hydrated). The sum of these enthalpy changes determines the overall energy change for the process \({\rm M(s)} \rightarrow {\rm M^{2+}(aq)}\). The standard electrode potential is related to this energy change.

For most transition metals, the energy released during hydration of the \({\rm M^{2+}}\) ion is sufficient to compensate for the energy required for atomisation and ionisation, resulting in a negative \(E^0\) value. However, Copper has a relatively high enthalpy of atomisation and a relatively low enthalpy of hydration for the \({\rm Cu^{2+}}\) ion. This combination makes the overall energy change for \({\rm Cu(s)} \rightarrow {\rm Cu^{2+}(aq)}\) less favourable (more positive Gibbs free energy change), leading to a positive standard electrode potential (\(E^0_{Cu^{2+}/Cu}\)).

Conclusion

Based on the standard electrode potential values for the first transition series, Copper (Cu) is the metal that exhibits a positive \(E^0_{M^{2+}/M}\) value.

Revision Table: First Transition Series \(E^0_{M^{2+}/M}\) Values

Additional Information: Factors Affecting Standard Electrode Potential

The standard electrode potential \(E^0_{M^{2+}/M}\) is a measure of the tendency of the electrode reaction \({\rm M^{2+}(aq) + 2e^- \rightarrow M(s)}\) to occur. The overall energy change associated with the formation of \({\rm M^{2+}}\) ions in aqueous solution from the solid metal involves the following steps:

1. Atomisation of the metal: \({\rm M(s) \rightarrow M(g)}\) (\(\Delta H_{\text{atomisation}}\))
2. Ionisation of the gaseous atom: \({\rm M(g) \rightarrow M^{2+}(g) + 2e^-}\) (\(\Delta H_{\text{ionisation}} = I.E._1 + I.E._2\))
3. Hydration of the gaseous ion: \({\rm M^{2+}(g) + aq \rightarrow M^{2+}(aq)}\) (\(\Delta H_{\text{hydration}}\))

The overall enthalpy change for \({\rm M(s) \rightarrow M^{2+}(aq)}\) is \(\Delta H = \Delta H_{\text{atomisation}} + (I.E._1 + I.E._2) + \Delta H_{\text{hydration}}\). The standard electrode potential \(E^0_{M^{2+}/M}\) is related to the standard Gibbs free energy change (\(\Delta G^0\)) for the reduction process \({\rm M^{2+}(aq) + 2e^- \rightarrow M(s)}\) by the equation \(\Delta G^0 = -nFE^0\), where \(n\) is the number of electrons (2 in this case) and \(F\) is Faraday's constant. A more positive \(E^0\) corresponds to a more negative \(\Delta G^0\) for reduction, meaning the reduction is more spontaneous.

Conversely, for the oxidation process \({\rm M(s) \rightarrow M^{2+}(aq) + 2e^-}\), \(\Delta G^0 = -\Delta H + T\Delta S\). A positive \(E^0_{M^{2+}/M}\) means the reduction \({\rm M^{2+}} \rightarrow {\rm M}\) is favourable, and the oxidation \({\rm M \rightarrow M^{2+}}\) is less favourable (more positive \(\Delta G^0_{oxidation}\) or less negative \(\Delta G^0_{oxidation}\)). Copper's positive \(E^0_{Cu^{2+}/Cu}\) is primarily due to the large energy required for atomisation and ionization combined with a relatively less negative hydration enthalpy compared to other transition metals, making the formation of aqueous \({\rm Cu^{2+}}\) ions from solid Cu less energetically favourable.