An acidic solution of dichromate is electrolyzed for 8 minutes using $2\mathrm{A}$  current. As per the following equation ${\mathrm{C}\mathrm{r}}_2{\mathrm{O}}_7^{2-}+14{\mathrm{H}}^{+}+6{\mathrm{e}}^{-}\to 2{\mathrm{C}\mathrm{r}}^{3+}+7{\mathrm{H}}_2\mathrm{O}$   . The amount of ${\mathrm{C}\mathrm{r}}^{3+}$ obtained was $0.104\mathrm{g}$   . The efficiency of the process (in %) is (Take: $\mathrm{F}=96000\mathrm{C}$   , At. Mass of chromium $=52$    )

<p>According to Faraday law</p><p>&nbsp;<span contenteditable="false"> <math> <mi mathvariant="normal">W</mi> <mo>=</mo> <mi mathvariant="normal">Z</mi> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">t</mi> <mo>×</mo> <mi>η</mi> <mrow> <mi mathvariant="normal"> </mi> </mrow> </math> </span>Where <span contenteditable="false"> <math> <mi>η</mi> <mo>=</mo> </math> </span>efficiency</p><p>or <span contenteditable="false"> <math> <mi>W</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <mn>96500</mn> </mrow> </mrow> </mfrac> <mo>×</mo> <mn>1</mn> <mo>×</mo> <mi>t</mi> <mo>×</mo> <mi>η</mi> </math> </span>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p>Putting values</p><p><span contenteditable="false"> <math> <mo>.</mo> <mn>104</mn> <mo>=</mo> <mfrac> <mrow> <mrow> <mo> (</mo> <mn>52</mn> <mo>/</mo> <mn>3</mn> <mo>)</mo> <mo>×</mo> <mn>2</mn> <mo>×</mo> <mn>8</mn> <mo>×</mo> <mn>60</mn> <mo>×</mo> <mi>η</mi> </mrow> </mrow> <mrow> <mrow> <mn>96500</mn> </mrow> </mrow> </mfrac> <mo>⇒</mo> <mi>η</mi> <mo>=</mo> <mn>0.6</mn> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p>So percentage efficiency <span contenteditable="false"> <math> <mo>=</mo> <mn>60</mn> <mi mathvariant="normal">%</mi> </math> </span>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p>

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