Tollen’s reagent is used to detect –CHO group in a compound when ammonical solution of ${AgNO}_{3}$ is added to Glucose, gluconic acid is formed according to the following reaction:
${2Ag}^{+} + C_{6} H_{12} O_{6} + H_{2} O \to 2Ag (s) + C_{6} H_{12} O_{7} + {2H}^{+}$
Find lnK for the above reaction, given that,
$C_{6} H_{12} O_{7} + 2 H^{+} + 2 e^{-} \to C_{6} H_{12} O_{6} + H_{2} O E^{0} = 0.05 V$
$A g^{+} + e \to A g E^{0} = 0.80 V$ and $\frac{F}{R T}$ = 38.92 at 298K.

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answer is 58.38.

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Detailed Solution

$2 A g^{+} 2 e^{-} \to 2 A g (s)$ $E^{0} = 0.80 V$
   $C_{6} H_{12} O_{6} + H_{2} O \to C_{6} H_{12} O_{7} + 2 H^{+} + 2 e^{-}$    $E^{0} = - 0.05 V$
The net reaction is
$2 A g^{+} + C_{6} H_{12} O_{6} + H_{2} O \to 2 A g (s) + C_{6} H_{12} O_{7} + 2 H^{+}$ $E^{0} = 0.75 V$
$E_{c e l l} = E^{0} - \frac{R T}{n F} \ln K = 0$
or $\ln K = \frac{n F E^{0}}{R T} = 2 \times 0.75 \times 38.92$ =58.38