Chemistry - Electrochemistry Question with Solution | TestHub

Consider the following half cell reaction
${\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}(\mathrm{aq})+6{\mathrm{e}}^{-}+14{\mathrm{H}}^{+}(\mathrm{aq})$ $\to 2{\mathrm{Cr}}^{3+}(\mathrm{aq})+7{\mathrm{H}}_2\mathrm{O}(\mathrm{l})$
The reaction was conducted with the ratio of $\frac{{\left[{\mathrm{Cr}}^{3+}\right]}^2}{\left[{\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}\right]}=10^{-6}$. The pH value at which the EMF of the half cell will become zero is ________. (nearest integer value)
[Given : standard half cell reduction potential
${\mathrm{E}}_{{\mathrm{Cr}}_2{\mathrm{O}}_7^{2-},{\mathrm{H}}^{+}/{\mathrm{Cr}}^{3+}}^{\mathrm{o}}=1.33\mathrm{V},\frac{2.303\mathrm{RT}}{\mathrm{F}}=0.059\mathrm{V}]$