Consider the following half cell reaction \( \mathrm{Cr_2O_7^{2-}(aq)} + 6e^- + 14\mathrm{H^+(aq)} \rightarrow 2\mathrm{Cr^{3+}(aq)} + 7\mathrm{H_2O(\ell)} \). The reaction was conducted with the ratio of \( \dfrac{[\mathrm{Cr^{3+}}]^2}{[\mathrm{Cr_2O_7^{2-}}]} = 10^{-6} \). The pH value at which the EMF of the half cell will become zero is ______. (Nearest integer value)
[Given: standard half cell reduction potential \( E^\circ_{\mathrm{Cr_2O_7^{2-},\,H^+/Cr^{3+}}} = 1.33 \, \text{V} \), \( \dfrac{2.303\,RT}{F} = 0.059 \, \text{V} \)]