The order of negative standard potential values of $\text{Li}, \text{Na}, \text{K}$ is
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For alkali metals, the standard reduction potential does not follow the simple trend of ionization energy. The unusually high (most negative) potential of Li is due to the small size and high charge density of the $\text{Li}^+$ ion, which leads to a massive, highly stabilizing (negative) hydration enthalpy.
Step 1: Understand the meaning of negative standard potential.
The standard potential value here refers to the standard reduction potential, $E^\circ$ (for the half-reaction $\text{M}^+(\text{aq}) + e^- \to \text{M}(\text{s})$).
A highly negative $E^\circ$ indicates a strong tendency for the metal to undergo oxidation ($\text{M} \to \text{M}^+ + e^-$), meaning the metal is a strong reducing agent.
The question asks for the order of negative $E^\circ$ values, so we are looking for the order of strength of the reducing agent.
Step 2: Analyze the factors determining the standard reduction potential for Alkali Metals.
The process of hydration of a metal ion $\text{M}^+(\text{g}) \to \text{M}^+(\text{aq})$ is highly exothermic for small ions (high charge density). The overall process for reduction is:
\[
\text{M}(\text{s}) \xrightarrow{\Delta H_{\text{sub}}} \text{M}(\text{g}) \xrightarrow{IE} \text{M}^+(\text{g}) + e^- \xrightarrow{\Delta H_{\text{hyd}}} \text{M}^+(\text{aq}).
\]
The standard potential is determined by the sum of these energy changes. For alkali metals, the trend is governed by the exceptionally high magnitude of the hydration enthalpy ($\Delta H_{\text{hyd}}$) for the smallest ion, $\text{Li}^+$.
Step 3: Compare the reduction potentials of $\text{Li, \text{Na}, \text{K}$.}
The standard reduction potentials are (in Volts):
$\text{Li}^+/\text{Li}: -3.05 \text{ V}$.
$\text{Na}^+/\text{Na}: -2.71 \text{ V}$.
$\text{K}^+/\text{K}: -2.93 \text{ V}$.
The order of the actual potential values is $\text{Li}<\text{K}<\text{Na}$.
Step 4: Determine the order of negative standard potential values.
The negative standard potential values are the magnitudes of these numbers: $|\text{Li}^+/\text{Li}| = 3.05$, $|\text{K}^+/\text{K}| = 2.93$, $|\text{Na}^+/\text{Na}| = 2.71$.
The order of negative standard potential values is $\text{Li}>\text{K}>\text{Na}$.
This is because $\text{Li}$ is the strongest reducing agent among the three due to the extremely high hydration energy of the small $\text{Li}^+$ ion, which makes its reduction potential the most negative.
