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  4. 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 3.0. Given: Cr 2 O 72- arrow Cr 3+ ; E °=1.330 V and (2.303 RT / F )=0.059 V The potential for the half cell reaction is x × 10-3 V. The value of x is

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Q. 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 3.0.
Given: $Cr _2 O _7^{2-} \rightarrow Cr ^{3+} ; E ^{\circ}=1.330 V$
and $\frac{2.303 RT }{ F }=0.059 V$
The potential for the half cell reaction is $x \times 10^{-3} V$. The value of $x$ is ___

JEE MainJEE Main 2023Electrochemistry

Solution:

$ Cr _2 O _7^{2-}+14 H ^{+}+6 e ^{-} \rightarrow 2 Cr ^{3+}+7 H _2 O$
$E =1.33-\frac{0.059}{6} \log \frac{(0.1)^2}{\left(10^{-2}\right)\left(10^{-3}\right)^{14}} $
$ E =1.33-\frac{0.059}{6} \times 42=0.917 $
$E =917 \times 10^{-3} $
$ x =917$