Question

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

${\mathrm{Cr}}_2{{\mathrm{O}}_7}^{2-}+14{\mathrm{H}}^{+}+6{\mathrm{e}}^{–}\to 2{\mathrm{Cr}}^{3+}++7{\mathrm{H}}_2\mathrm{O}$

The amount of ${\mathrm{Cr}}^{3+}$ obtained was $0.104\mathrm{g}$. The efficiency of the process (in $\%$) is _______(Take: $\mathrm{F}$ = $96000C$, At. mass of chromium = $52$).

Answer 1

Step 1: It is given that time taken in electrolysis,

$$\begin{gathered} t=8minutes \\ =8\times 60s \\ =480s \end{gathered}$$

Current, $I=2A$, mass of ${\mathrm{Cr}}^{3+}$ is $m=0.104g$.

Step 2: Determination of flow of charge: We know that $q=I\times t$ where, $q$ is flow of charge, $I$ is current and $t$ is time taken.

Step 3: Putting the given values in the equation above: $$\begin{gathered} q=2\times 480 \\ =960C \end{gathered}$$

Converting flow of charge into faraday: $$\begin{gathered} q=\frac{960}{96500}F \\ =9.948\times {10}^{-3}F \end{gathered}$$

The flow of charge in terms of moles of ​${\mathrm{Cr}}^{3+}$ is: $$\begin{gathered} q=\frac{1}{3}\times 9.948\times {10}^{-3} \\ =3.316\times {10}^{-3}F \end{gathered}$$ as, $\mathrm{Cr}$ is converted from $+6$ to $+3$.

Theoretical mass of ${\mathrm{Cr}}^{3+}$: $$\begin{gathered} m=3.316\times {10}^{-3}\times 52 \\ =172.43\times {10}^{-3}g \end{gathered}$$ where $52$ is the atomic mass of ${\mathrm{Cr}}^{3+}$

The efficiency of the process: $$\begin{gathered} efficiency\left(\%\right)=\frac{W_{actual}}{W_{theoritical}}\times 100 \\ =\frac{0.104}{172.43\times {10}^{-3}}\times 100 \\ =60.31\% \end{gathered}$$

Therefore, the efficiency of the process is $\mathbf{60}\mathbf{.}\mathbf{31}\mathbf{\%}$.