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Q. $Cu ^{\oplus}+e^{-} \longrightarrow Cu , E^{\ominus}=x_1$ volt
$Cu ^{2+}+2 e^{-} \longrightarrow Cu , E^{\ominus}=x_2$ volt, then for
$Cu ^{2+}+e^{-} \longrightarrow Cu ^{\oplus}, E^{\ominus}$ (colt) will be

Electrochemistry

Solution:

$Cu ^{\oplus}+e^{-} \longrightarrow Cu , E^{\ominus}{ }_1=x_1 V......$(i)
$Cu ^{2+}+2 e^{-} \longrightarrow Cu , E^{\ominus}{ }_2=x_2 V.....$(ii)
Net equation $Cu ^{2+}+e^{-} \longrightarrow Cu ^{\oplus} E_3=$ ? ...(iii)
Is obtained by equations (ii) - (i)
$\therefore E_3=\frac{n_2 E_2-n_1 E_1}{n_3}$
$=\frac{2 \times x_1-1 \times x_1}{1}=2 x_2-x_1$