Question

For the EMF of a hydrogen electrode to be zero, the pressure of hydrogen required in neutral $pH$ is:

• A. $1\times {10}^{-7}atm$
• B. $1\times {10}^{-14}atm$
• C. $1.0atm$
• D. $0.0atm$

Answer 1

The correct option is B $1\times {10}^{-14}atm$

$2H^{+}+2e^{-}⟶{H_2}_{\left(g\right)}$

According to Nernst equation-

$E=E^0-\frac{0.0591}{2}\log \frac{p_{H_2}}{{\left[H^{+}\right]}^2}$

For $E=0;E^0=0$

$\therefore 0=0-\frac{0.0591}{2}\log \frac{p_{H_2}}{{\left({10}^{-7}\right)}^2}(\because \left[H^{+}\right]={10}^{-7})$

$\Rightarrow \log \frac{p_{H_2}}{{10}^{-14}}=0$

$\Rightarrow \log \frac{p_{H_2}}{{10}^{-14}}=\log 1(\because \log 1=0)$

$\Rightarrow \frac{p_{H_2}}{{10}^{-14}}=1$

$\Rightarrow p_{H_2}={10}^{-14}\text{atm}$

Hence for the EMF of a hydrogen electrode to be zero, the pressure of hydrogen required in neutral pH is $1\times {10}^{-14}\text{atm}$.