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Question
CBSEENCH12010376
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Calculate e.m.f of the following cell at 298 K:

2 Cr space left parenthesis straight s right parenthesis space plus 3 Fe to the power of 2 plus end exponent space left parenthesis 0.1 space straight M right parenthesis space rightwards arrow space 2 Cr to the power of 3 plus end exponent space left parenthesis 0.01 space straight M right parenthesis space plus 3 Fe left parenthesis straight s right parenthesis space Given colon space straight E to the power of 0 space left parenthesis Cr to the power of 3 plus end exponent vertical line Cr right parenthesis space equals space minus 0.70 space straight V space space space space space space space space space space space straight E to the power of 0 space left parenthesis Fe to the power of 2 plus end exponent vertical line Fe right parenthesis space equals negative 0.44 space straight V

Solution
2 Cr space left parenthesis straight s right parenthesis space space plus 3 Fe to the power of 2 plus end exponent space left parenthesis 0.1 straight M right parenthesis space rightwards arrow space 2 Cr cubed left parenthesis 0.01 straight M right parenthesis space plus 3 Fe left parenthesis straight s right parenthesis Given colon space straight E subscript Cr to the power of 3 plus end exponent divided by Cr end subscript superscript 0 space equals negative 0.74 straight V straight E subscript Fe to the power of 2 plus end exponent divided by Fe end subscript superscript 0 space equals space minus 0.44 straight V The space cell space can space be space represented space as space follows colon Cr vertical line space Cr to the power of 3 plus end exponent space left parenthesis 0.01 straight M right parenthesis space vertical line vertical line space Fe to the power of 2 plus end exponent left parenthesis 0.1 straight M right parenthesis vertical line space Fe left parenthesis straight s right parenthesis straight E subscript cel superscript 0 space equals space straight E subscript Fe to the power of 2 plus end exponent divided by Fe end subscript superscript 0 space minus straight E subscript Cr to the power of 3 plus end exponent divided by Cr end subscript superscript 0 straight E subscript cell superscript 0 space equals negative 0.44 minus left parenthesis negative 0.74 right parenthesis space equals space 0.30 space straight V straight E subscript cell space equals space straight E subscript cell superscript 0 space minus fraction numerator 2.303 space RT over denominator nF end fraction space log space fraction numerator left square bracket Cr to the power of 3 plus end exponent right square bracket squared over denominator left square bracket Fe to the power of 2 plus end exponent right square bracket cubed end fraction straight E subscript cell space equals space 0.30 space minus fraction numerator 0.0591 over denominator 6 space end fraction log space fraction numerator left parenthesis 0.01 right parenthesis squared over denominator left parenthesis 0.1 right parenthesis cubed end fraction straight E subscript cell space equals space 0.30 space plus 0.01 straight E subscript cell space equals space 0.31 space straight V

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