An acidic solution of dichromate is electrolyzed for 8 minutes using 2 A current. As per the following equation $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+14 \mathrm{H}^{+}+6 \mathrm{e}^{-} \rightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O}$. The amount of $\mathrm{Cr}^{3+}$ obtained was 0.104 g . The efficiency of the process (in \%) is (Take: F $=96000 \mathrm{C}$, At. Mass of chromium = 52) ____.

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Redox Reactions and Electrochemistry

An acidic solution of dichromate is electrolyzed for 8 minutes using 2 A current. As per the following equation

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

. The amount of

Cr^{3 +}

obtained was 0.104 g . The efficiency of the process (in %) is (Take: F

= 96000 C

, At. Mass of chromium = 52) ____.

Answer: 60

By Faraday's law the mass of chromium formed is

W = \frac{E I t η}{F}

, where the equivalent weight is

E = \frac{52}{3}

since six electrons reduce two chromium atoms,

I = 2 A

t = 8 \times 60 = 480 s

and

F = 96000 C

. Putting

W = 0.104 g

0.104 = \frac{( 52/3 ) \times 2 \times 480 \times η}{96000} = \frac{16640 η}{96000}

, so

η = \frac{0.104 \times 96000}{16640} = 0.6

. The efficiency is

60%

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Integer answer