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 2 . 303 ? R T F = 0 . 059 ?V The potential for the half-cell reaction is x × 10 - 3

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Solution

Q.
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.

$Given: {Cr}_{2} O_{7}^{2 -} \to {Cr}^{3 +}, E ° = 1.330 V$

$and \frac{2.303 R T}{F} = 0.059 V$

The potential for the half-cell reaction is $x \times 10^{- 3}$ V. The value of $x$ is _______. [2023]

Ans.
(917)

${Cr}_{2} O_{7}^{2 -} + 14 H^{+} + 6 e^{-} \to 2 {Cr}^{3 +} + 7 H_{2} O$

$E = 1.33 - \frac{0.059}{6} \log \frac{{(0.1)}^{2}}{(10^{- 2}) {(10^{- 3})}^{14}}$

$= 1.33 - \frac{0.059}{6} \times 42 = 0.917$

$E = 917 \times 10^{- 3} V \Rightarrow x = 917$

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