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