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If the half-cell reaction \[{\rm{A + }}{{\rm{e}}^{\rm{ - }}} \to {{\rm{A}}^{\rm{ - }}}\]
has a large negative reduction potential, it follows that:
A. A is readily reduced
B. A is readily oxidised
C. \[{{\rm{A}}^{\rm{ - }}}\] is readily reduced
D. \[{{\rm{A}}^{\rm{ - }}}\] is readily oxidised

Answer
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Hint: Electrode potential is the tendency of an electrode to lose or gain electrons when it is in contact with the solution of its ions. It is measured by relating it to the standard hydrogen electrode.

Complete Step by Step Solution:
A is placed in contact with its ions (\[{{\rm{A}}^ - }\]). We know that oxidation is defined as the process by which the loss of electrons happens. Reduction is the process by which the gain of electrons happens.

If A has a relatively higher tendency to get reduced, then it will gain electrons to form \[{{\rm{A}}^{\rm{ - }}}\].
As a result, A will develop a negative charge with respect to the solution.
\[{\rm{A + }}{{\rm{e}}^{\rm{ - }}} \to {{\rm{A}}^{\rm{ - }}}\]

If \[{{\rm{A}}^{\rm{ - }}}\] has a relatively higher tendency to get oxidised, then it will lose electrons.
These electrons will accumulate on A, as a result, it will develop a negative charge with respect to the solution.
\[{{\rm{A}}^ - } \to {\rm{A + }}{{\rm{e}}^{\rm{ - }}}\]
This tendency to either lose or gain electrons is called electrode potential.
It is measured by relating it to the standard hydrogen electrode.

If oxidation takes place at the electrode with respect to standard hydrogen potential, then it is called oxidation potential. If reduction takes place at the electrode with respect to standard hydrogen potential, then it is called reduction potential. As reduction half-reaction is the opposite of oxidation half-reaction.
So, reduction potential=(-oxidation potential)

It is mentioned that it has a large negative reduction potential.
Hence, this reaction has positive oxidation potential.
So,\[{{\rm{A}}^{\rm{ - }}}\] will be readily oxidised.
So, option D is correct.

Note: Electrolytic cells are used to transform electrical energy into chemical energy. It means electrical energy is supplied for the redox reaction to happen. Galvanic cells are used to transform chemical energy into electrical energy.