At 298 K, a 1 litre solution containing 10 mmol of Cr_2 O_7^2- and 100 mmol of Cr^3+ shows a pH of 3.0. Given: Cr_2 O_7^2- → Cr^3+; E^°=1.330 V and…

At $\displaystyle 298$ K , a $\displaystyle 1$ litre solution containing $\displaystyle 10$ mmol of $\displaystyle \mathrm{Cr}_2 \mathrm{O}_7{ }^{2-}$ and $\displaystyle 100$ mmol of $\displaystyle \mathrm{Cr}^{3+}$ shows a pH of 3.0. Given: $\displaystyle \mathrm{Cr}_2 \mathrm{O}_7{ }^{2-} \rightarrow \mathrm{Cr}^{3+} ; \mathrm{E}^{\circ}=1.330 \mathrm{~V}$ and $\displaystyle \frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{~V}$ The potential for the half cell reaction is $\displaystyle x \times 10^{-3} \mathrm{~V}$. The value of $\displaystyle x$ is $\displaystyle \_\_\_\_$