Question

Electrode potential of hydrogen electrode is 18 mV then \[[{{H}^{+}}]\] is:
A. 0.2
B. 1
C. 2
D. 5

Answer 1

Hint: By using Nernst equation we can calculate the concentration of the hydrogen ion.
The formula for Nernst equation is as follows.
\[E={{E}^{o}}+\dfrac{0.0591}{n}\log [{{H}^{+}}]\]
Where E = potential of the cell
\[{{E}^{o}}\] = potential of the electrode
n = number of electrons transferred in the cell reaction
\[[{{H}^{+}}]\] = concentration of the hydrogen ion

Complete step by step answer:
- In the question it is given that the potential of the cell is 18 mV.
- We have to calculate the concentration of the hydrogen ion.
\[E={{E}^{o}}+\dfrac{0.0591}{n}\log [{{H}^{+}}]\]
Where E = potential of the cell = 18 mV = \[18\times {{10}^{-3}}V\]
\[{{E}^{o}}\] = standard electrode potential of the hydrogen electrode = 0
n = number of electrons transferred in the cell reaction = 1
\[[{{H}^{+}}]\] = concentration of the hydrogen ion
- Substitute all the values in the formula to get the concentration of the hydrogen ion.
\[\begin{align}
  & 18\times {{10}^{-3}}V=0+\dfrac{0.0591}{1}\log [{{H}^{+}}] \\
 & \log [{{H}^{+}}]=0.3 \\
 & [{{H}^{+}}]=1.995M=2M \\
\end{align}\]
- Therefore Electrode potential of a hydrogen electrode is 18 mV then \[[{{H}^{+}}]\] is 2M.

- So, the correct option is C.

Additional information:
Major applications of Nernst equation are
- Used in determining ion concentration of unknown electrodes.
- Used to calculate the potential of an ion charge across the membrane.
- Used in the calculations of solubility products and potentiometric experiments.


Note: The absolute electrode potential of hydrogen electrode is 4.44 V at room temperature. But to form a source for assessment, standard electrode potential for hydrogen electrode is fixed as zero volts at all temperatures.