Question

At $298 \,K$, a 1 litre solution containing $10\, m\,mol$ of $Cr _2 O _7{ }^{2-}$ and $100\, m\,mol$ of $Cr ^{3+}$ shows a pH of 30.

Given: $Cr _2 O _7^{2-} \rightarrow Cr ^{3+} ; E ^{\circ}=1330 V$ and $\frac{2303 RT }{ F }=0059 V$.

The potential for the half cell reaction is $x \times 10^{-3} V$. The value of $x$ is ___ .

Answer 1

Cr2​O72−​+14H++6e−→2Cr3++7H2​O
E=1.33−60.059​log(10−2)(10−3)14(0.1)2​
E=1.33−60.059​×42=0.917
E=917×10−3
x=917

So, the correct answer is 917.