For chromium, E deg(Cr^3+/Cr) = -0.74 V and E deg(Cr^3+/Cr^2+) = -0.42 V. The standard potential of Cr^2+/Cr and the stability of Cr^2+ towards disproportionation (3Cr^2+ -> 2Cr^3+ + Cr) are

-0.90 V; Cr^2+ does not disproportionate

-0.90 V; Cr^2+ disproportionates

-0.58 V; Cr^2+ does not disproportionate

-0.32 V; Cr^2+ disproportionates

JEE Advanced levelSingle correct optionDifficulty 3 of 3ec078

For chromium, $E^{\circ} (Cr X^{3 +} / Cr) = - 0.74 V$ and $E^{\circ} (Cr X^{3 +} / Cr X^{2 +}) = - 0.42 V$ . The standard potential of $Cr X^{2 +} / Cr$ and the stability of $Cr X^{2 +}$ towards disproportionation ( $3 Cr X^{2 +} 2 Cr X^{3 +} + Cr$ ) are

Gibbs energy additivity:

3 (- 0.74) = 1 (- 0.42) + 2 E^{\circ} (Cr X^{2 +} / Cr)

, so

E^{\circ} (Cr X^{2 +} / Cr) = \frac{- 2.22 + 0.42}{2} = - 0.90 V

. For disproportionation the cathode is

Cr X^{2 +} Cr

(

- 0.90 V

) and the anode is

Cr X^{2 +} Cr X^{3 +}

(

- 0.42 V

E^{\circ} = - 0.90 - (- 0.42) = - 0.48 V < 0

, so

Cr X^{2 +}

is stable to disproportionation (it is oxidised by air instead). Options C and D come from averaging or subtracting the potentials directly.