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Q. Tollen's reagent is used for the detection of aldehyde when a solution of $AgNO _{3}$ is added to glucose with $NH _{4} OH$ then gluconic acid is formed
$ Ag ^{+}+e^{-} \rightarrow Ag ; E_{ red }^{+}=0.8 \,V$
$ C _{6} H _{12} O _{6}+ H _{2} O \rightarrow $ Gluconic acid $\left( C _{6} H _{12} O _{7}\right)+2 H ^{+}+2 e^{-} $
$E_{ red }{ }^{\circ}=-0.05 \,V $
$ Ag \left( NH _{3}\right)_{2}{ }^{+}+e^{-} \rightarrow Ag ( s )+2 NH _{3} ; E_{ red }{ }^{\circ}=0.337 \,V$
[Use $2.303 \times \frac{R T}{F}=0.0592$ and $ \frac{F}{R T}=38.92$ at $398\, K ]$
When ammonia is added to the solution, $pH$ is raised to $11$ . Which half- cell reaction is affected by $pH$ and by how much?

JEE AdvancedJEE Advanced 2006

Solution:

The expression for oxidation reaction is
$E_{\text {oxd }}=E_{\text {oxd }}{ }^{\circ}-\frac{2.303 R T}{n F} \log \frac{\left[ C _{6} H _{12} O _{6}\right]}{\left[ C _{6} H _{12} O _{7}\right]\left[ H ^{+}\right]^{2}}$
The expression for reduction is
$E_{ red }=E_{ red }{ }^{\circ}-\frac{2.303 R T}{n F} \log \frac{1}{\left[ Ag ^{+}\right]}$
The addition of $NH _{3}$ results in formation of more $\left[ Ag \left( NH _{3}\right)_{2}\right]^{+}$ complex, thus reducing the concentration of $Ag ^{+}$ions available for reduction. Thus addition of $NH _{3}$ causes concentration of $\left[H^{+}\right]$to decrease and $pH$ to increase. So $E_{ red }$ increases approximately by a factor of $0.65 \,V$.
$E_{ red }=E_{ red }{ }^{\circ}-\frac{2.303 R T}{n F} \log \left[H^{+}\right]^{2}$
$=0-\frac{0.0592}{2} \times 2 \times 11=0.6512$