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JEE Advanced 2018Paper 2
Exam
JEE Advanced
Year
2018
Paper
Paper 2
Subject
Chemistry
Chapter
Electrochemistry

JEE Advanced 2018 · Paper 2 · Chemistry · Electrochemistry

Consider an electrochemical cell: A(s) | A ^ n+ (aq, 2 M)|| B ^ 2n+...

Consider an electrochemical cell: A(s)\text{A}\left(\text{s}\right) \left|{A\text{A}}^{n+\text{n+}} \left(\text{aq, 2 M}\right)\right|\left|B{\text{B}}^{\text{2n+}} \left(\text{aq, 1 M}\right)\right|B\text{B}\left(s\text{s}\right).. The value of{\text{\Delta H}$}^{$\text{o}}forthecellreactionistwicethatoffor the cell reaction is twice that of{\text{\Delta G}$}^{$\text{o}}atat\text{300 K}\text{.}$ If the $emf of the cell is zero, the magnitude of\Delta{\text{S}}^{o}\left(in\text{in}{J\text{J}}^{- 1} {K\text{K}}^{- 1} {mol\text{mol}}^{- 1}\right)ofofthe cell reaction per mole of B\text{B}formedatformed at300\text{300}\text{K} is ____<br />(Given: R=\text{=}8\text{8}.3\text{.3}{\text{JK}}^{-1\text{1}}{mol\text{mol}}^{- 1} .H,\text{H,}Sa\text{S} and G\text{G}aare enthalpy, entropy and Gibbs energy, respectively.)

Correct answer

0

Step-by-step solution

A(s)|A+n(aq.2M)||B+2n(aq.1M)|B(s)\text{A(s)}\text{|}{\text{A}}^{\text{+n}} \text{(aq}\text{.}\text{2}\text{M)}\text{||}{\text{B}}^{\text{+2n}} \text{(aq}\text{.}\text{1}\text{M)}\text{|}\text{B(s)}
\DeltaHo=2 \DeltaGoEcell=0{\text{\Delta H}}^{\text{o}}\text{=}{\text{2 \Delta G}}^{\text{o}}{\text{E}}_{\text{cell}}\text{=}\text{0}
CellReactionA→A+n+ne−×2\text{Cell}\text{Reaction}\text{A} \to {\text{A}}^{\text{+n}} + {\text{ne}}^{-} \times 2
B+2n+2ne−→B(s){\text{B}}^{\text{+2n}} + \text{2}{\text{ne}}^{-} \to \text{B(s)}
2A(s)+B+2n1M(aq)→2A+n2M(aq)+B(s)\text{2}\text{A(s)} + \mathop{{\text{B}}^{\text{+2n}}}_{1\text{M}} \text{(aq)} \to \mathop{\text{2}{\text{A}}^{\text{+n}}}_{\text{2}\text{M}} \text{(aq)} + \text{B(s)}
\text{\Delta G}\text{=}{\text{\Delta G}}^{o} \text{+}\text{RT}\text\ln\dfrac{{\left[{\text{A}}^{\text{+n}}\right]}^{\text{2}}}{\left[{\text{B}}^{\text{+2n}}\right]}
{\text{\Delta G}}^{\text{o}} \text{=} - \text{RT}\text\ln\dfrac{{\left[{\text{A}}^{\text{+n}}\right]}^{\text{2}}}{\left[{\text{B}}^{\text{+2n}}\right]} \text{=} - \text{RT}\text{\times}\text\ln\dfrac{{\text{2}}^{\text{2}}}{\text{1}} \text{=} - \text{RT}\text{\ln 4}
\DeltaGo=\DeltaHo−T \DeltaSo{\text{\Delta G}}^{\text{o}} \text{=}{\text{\Delta H}}^{\text{o}} - {\text{T \Delta S}}^{\text{o}}
\DeltaGo=2 \DeltaGo−T \DeltaSo{\text{\Delta G}}^{\text{o}} \text{=}{\text{2 \Delta G}}^{\text{o}} - {\text{T \Delta S}}^{\text{o}}
{\text{\Delta S}}^{\text{o}} \text{=}\dfrac{{\text{\Delta G}}^{\text{o}}}{\text{T}} \text{=} - \dfrac{\text{RT}\text{\ln 4}}{\text{T}}
=−8.3\times2\times0.7=−11.62J/Kmol−1\text{=} - \text{8}\text{.3}\text{\times}\text{2}\text{\times}\text{0}\text{.7}\text{=} - \text{11}\text{.62}\text{J/K}{\text{mol}}^{- 1}
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