Question

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

Answer 1

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.

& 18\times {{10}^{-3}}V=0+\dfrac{0.0591}{1}\log [{{H}^{+}}] \\\ & \log [{{H}^{+}}]=0.3 \\\ & [{{H}^{+}}]=1.995M=2M \\\ \end{aligned}$$ \- Therefore Electrode potential of a hydrogen electrode is 18 mV then $$[{{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.