At \( 298 \, \text{K} \), a \( 1 \) litre solution containing \( 10 \, \text{mmol} \) of \( \mathrm{Cr_2O_7^{2-}} \) and \( 100 \, \text{mmol} \) of \( \mathrm{Cr^{3+}} \) shows a pH of \( 3.0 \).
Given : \( \mathrm{CrO_7^{2-} \rightarrow Cr^{3+}} \) ; \( E^\circ = 1.330 \, \text{V} \) and \( \frac{2.303 \, RT}{F} = 0.059 \, \text{V} \)
The potential for the half cell reaction is \( x \times 10^{-3} \, \text{V} \). The value of \( x \) is ________.
