Q.(a) Derive an expression for Nernst equation. OR

(a) Combining the general thermodynamic relation $\Delta G=\Delta G°+RT\ln Q$ with $\Delta G=-nFE$ yields the Nernst equation, which relates a cell/electrode's actual potential to its standard potential and reactant/product concentrations. OR (b) three classic dehydration reactions convert simple alcohols/polyols into an alkene, a cyclic ether, and an unsaturated aldehyde respectively.

(a) Derivation of the Nernst equation: consider a general electrode reaction $M^{n+}(aq) + ne^- \rightarrow M(s)$ The Gibbs free energy change for this process is related to the reaction quotient $Q$ by $\Delta G = \Delta G° + RT\ln Q$ Since the activity of the pure solid metal is taken as 1, $Q = 1/[M^{n+}]$. Also, the free energy change is related to the electrode potential by $\Delta G = -nFE$ (and $\Delta G° = -nFE°$), where $n$ is the number of electrons transferred and $F$ is the Faraday constant. Substituting: $-nFE = -nFE° + RT\ln\dfrac{1}{[M^{n+}]}$ Dividing throughout by $-nF$: $E = E° - \dfrac{RT}{nF}\ln\dfrac{1}{[M^{n+}]} = E° + \dfrac{RT}{nF}\ln[M^{n+}]$ For a full cell reaction (with reaction quotient $Q$ for the overall cell reaction), this generalises to: $E_{cell} = E°_{cell} - \dfrac{RT}{nF}\ln Q$ Converting from natural log to $\log_{10}$ ($\ln x = 2.303\log x$) and substituting the values of $R$, $F$ at $T=298\ K$: $E_{cell} = E°_{cell} - \dfrac{0.0591}{n}\log Q$ This is the Nernst equation.

OR (b)(i) Ethyl alcohol $\rightarrow$ ethene: dehydration of ethanol with concentrated sulphuric acid at $443\ K$ (or by passing vapour over hot $Al_2O_3$ at $623\ K$): $C_2H_5OH \xrightarrow[443K]{conc.\ H_2SO_4} CH_2=CH_2 + H_2O$

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