Consider the following half cell reaction Cr_2 O_7^2-( aq )+6 e^-+14 H^+( aq ) → 2 Cr^3+( aq )+7 H_2 O (1) The reaction was conducted with the ratio…

Consider the following half cell reaction $$\mathrm{Cr}_2 \mathrm{O}_7^{2-}(\mathrm{aq})+6 \mathrm{e}^{-}+14 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_2 \mathrm{O}(1) $$ The reaction was conducted with the ratio of $\displaystyle \frac{\left[\mathrm{Cr}^{3+}\right]^2}{\left[\mathrm{Cr}_2 \mathrm{O}_7^{2-}\right]}=10^{-6}$. The pH value at which the EMF of the half cell will become zero is $\displaystyle \_\_\_\_$ . (nearest integer value) [Given : standard half cell reduction potential $\displaystyle \mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-}, \mathrm{H}^{+} / \mathrm{Cr}^{3+}}^{\circ}=1.33 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{~V}$.]