Question

Calculate reduction potential of the following half-cell reaction at ${25^ \circ} C$ \[0.4137volt\]
\[2{H_2}O + 2e \to {H_2} + 2O {H^ -}\]
(\[1\]\[atm\]) (\[{10^ {- 7}}\])

Answer 1

Hint:
A half-cell reaction can either be oxidation or reduction depending upon whether electrons are lost or electrons are gained, respectively. The non-metals are oxidising agents because they take away electrons from the other elements or compounds.

Complete answer:
The half-cell reaction we have is
\[2{H_2}O + 2e \to {H_2} + 2O {H^ -}\]
Using the reduction potential formula
\[E = {E^0} - \dfrac{{0.0591}}{2}\log {[O {H^ -}] ^2} [p {H_2}]\]
Now we have to just replace the information that is given in the question and get the answer
\[
   = 0 - \dfrac{{0.0591}}{2}\log ({10^ {- 7}}) (1) \\
   = 0.4137volt \\
 \]
So, the reduction potential for the half-cell reaction is \[0.4137volt\].

Additional information:
Half-cell reactions mostly occur in galvanic and volcanic cells where the electrons move from anode to cathode with the help of an electrolyte to generate EMF. Half-cell reactions either increase or decrease the electrons. Corrosion is a process in which both oxidation and reduction takes place in a cell, which is known as the redox reaction. The voltage or cell potential, for an electrochemical cell can be known from the half-cell reaction or chemical nature of materials such as (temperature, gas partial pressure and concentration). To determine the ${E_ {cell}} ^0$we use the nernst equation
\[
  aA + bB \to cC + dD \\
  Q = \dfrac{{{{[C]}^c}{{[D]}^d}}}{{{{[A]}^a}{{[B]}^b}}} \\
 \]
${E_ {cell}} = {E_ {cell}} ^0 - (\dfrac{{RT}}{{nF}})\ln Q$, where
${E^0} $= cell potential at non-Standard state condition.
${E_ {cell}} ^0$= standard state cell potential.
$R$= constant \[8.31\dfrac{j}{{mole}} - k\]
T = absolute temperature (Kelvin scale)
F = faraday’s constant \[(96,485\dfrac{C} {{mole {e^ -}}})\]
n = number of moles of electrons transferred in the balanced equation for the reaction occurring in the cell.
Q = reaction quotient for the reaction

Note: In an electrochemical reaction, the cell potential can either be spontaneous when the reaction is moving in the forward direction. It can also be non-spontaneous when the reaction is moving in the backward direction. The cell potential is also dependent upon the ph. Of the solution. The cell potential also decides which element in a reaction is a better oxidising agent or reducing agent.