Question

Calculate the potential of hydrogen electrode in contact with a solution whose pH is 10.

Answer 1

Hint: We need to calculate the potential of hydrogen electrode in contact with a solution whose pH is 10. This question is of chapter electrochemistry.

Formula used: $E_{cell}=E^0-{\displaystyle \frac{0.0591}{n}}\log {\displaystyle \frac{\left[P\right]}{\left[R\right]}}$
Here $n$ is the number of electrons
 $P$ stands for product
 $R$ stands for reactant.

Complete step by step answer
We already know that,
Given pH=10
We already that $pH=-\log \left[H^{+}\right]$
 $\left[H^{+}\right]={10}^{-10}M$
Also, for hydrogen electrode:
 $E=0$
 $E_{cell}=E^0-{\displaystyle \frac{0.0591}{1}}\log {\displaystyle \frac{\left[H_2\right]}{\left[H^{+}\right]}}$
Substituting the values:
 $E_{cell}=E^0-{\displaystyle \frac{0.0591}{1}}\log {\displaystyle \frac{1}{{10}^{-10}}}=-0.591\text{V}$
So, the potential of hydrogen electrode in contact with a solution whose pH is 10 is $-0.591\text{V}$ .

Note
In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full cell reaction) to the standard electrode potential, temperature, and activities (often approximated by concentrations) of the chemical species undergoing reduction and oxidation. Even under non-standard conditions, the cell potentials of electrochemical cells can be determined with the help of the Nernst equation. The Nernst equation is often used to calculate the cell potential of an electrochemical cell at any given temperature, pressure, and reactant concentration.
The Nernst equation is an important relation which is used to determine reaction equilibrium constants and concentration potentials as well as to calculate the minimum energy required in electrodialysis. It defines the relationship between cell potential to standard potential and to the activities of the electrically active species. It relates the effective concentrations of the components of a cell reaction to the standard cell potential.
To write the cell reaction corresponding to a cell diagram, the right-hand half reaction is written as a reduction, and the left-hand half-reaction, written as an oxidation.