GATE Life Sciences Electrochemistry Syllabus

Electrochemistry syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electrochemistry in GATE Life Sciences, not a summary of it.

1. 1

   Conductance

   1 topic

   • Kohlrausch Law
2. 2

   Cell Potentials

   2 topics

   • EMF
   • Nernst Equation
3. 3

   Thermodynamic Aspects and Applications

   overview

   Examined as a single unit within Electrochemistry — no further topic split in the official outline.

Electrochemistry flashcards for GATE Life Sciences

25 of 50 cards from the Electrochemistry deck — real questions with worked answers.

1. State Kohlrausch's law of independent migration of ions.

   At infinite dilution, each ion contributes a definite, characteristic value to the total molar conductivity independent of the counter-ion. Thus $\Lambda_m^{\circ} = \nu_{+}\lambda_{+}^{\circ} + \nu_{-}\lambda_{-}^{\circ}$, where $\lambda^{\circ}$ are the limiting molar ionic conductivities and $\nu$ the number of ions per formula unit.

2. Write the Kohlrausch expression for the limiting molar conductivity of $\ce{Al2(SO4)3}$.

   $\Lambda_m^{\circ}(\ce{Al2(SO4)3}) = 2\,\lambda^{\circ}(\ce{Al^{3+}}) + 3\,\lambda^{\circ}(\ce{SO4^{2-}})$

3. How does molar conductivity of a strong electrolyte vary with concentration (Kohlrausch's empirical equation)?

   $\Lambda_m = \Lambda_m^{\circ} - A\sqrt{c}$, where $\Lambda_m^{\circ}$ is the limiting molar conductivity, $c$ the concentration, and $A$ a constant depending on the electrolyte type and solvent.

4. Why can $\Lambda_m^{\circ}$ of a weak electrolyte not be found by extrapolating a $\Lambda_m$ vs $\sqrt{c}$ plot, and how is Kohlrausch's law used instead?

   A weak electrolyte's $\Lambda_m$ rises steeply near infinite dilution due to increasing dissociation, so extrapolation fails. Kohlrausch's law of independent migration lets you build $\Lambda_m^{\circ}$ from strong-electrolyte values, e.g. $\Lambda_m^{\circ}(\ce{CH3COOH}) = \Lambda_m^{\circ}(\ce{CH3COONa}) + \Lambda_m^{\circ}(\ce{HCl}) - \Lambda_m^{\circ}(\ce{NaCl})$.

5. Define degree of dissociation $\alpha$ in terms of molar conductivities (a key application of Kohlrausch's law).

   $\alpha = \dfrac{\Lambda_m}{\Lambda_m^{\circ}}$, the ratio of molar conductivity at concentration $c$ to the limiting molar conductivity.

6. Give the relation between the dissociation constant $K_a$ of a weak acid and $\Lambda_m$ (Ostwald dilution law in conductivity form).

   $K_a = \dfrac{c\alpha^{2}}{1-\alpha} = \dfrac{c\,\Lambda_m^{2}}{\Lambda_m^{\circ}(\Lambda_m^{\circ} - \Lambda_m)}$, where $\alpha = \Lambda_m/\Lambda_m^{\circ}$.

7. What is molar conductivity $\Lambda_m$ and how is it related to conductivity $\kappa$?

   $\Lambda_m = \dfrac{\kappa}{c}$, where $\kappa$ is the conductivity (specific conductance) and $c$ the molar concentration. In SI, $\Lambda_m = \dfrac{\kappa \times 1000}{c}$ when $\kappa$ is in $\ce{S\,cm^{-1}}$ and $c$ in $\ce{mol\,L^{-1}}$, giving $\ce{S\,cm^{2}\,mol^{-1}}$.

8. Define conductivity (specific conductance) $\kappa$ and give its SI unit.

   $\kappa$ is the reciprocal of resistivity, $\kappa = \dfrac{1}{\rho}$; equivalently $\kappa = G\dfrac{l}{A}$ where $G$ is conductance and $l/A$ the cell constant. SI unit: $\ce{S\,m^{-1}}$ (commonly $\ce{S\,cm^{-1}}$).

9. What is the cell constant of a conductivity cell and its unit?

   The cell constant $= \dfrac{l}{A}$, the ratio of electrode separation $l$ to electrode area $A$. Unit: $\ce{m^{-1}}$ (or $\ce{cm^{-1}}$). It is obtained by calibrating with a solution of known $\kappa$ (e.g. standard KCl).

10. Define ionic mobility and relate it to limiting ionic conductivity.

    Ionic mobility $u$ is the drift velocity per unit electric field. It relates to limiting ionic molar conductivity by $\lambda^{\circ} = z\,F\,u$, where $z$ is the ion charge magnitude and $F$ the Faraday constant.

11. What is the transport (transference) number of an ion?

    The fraction of total current carried by that ion: $t_{+} = \dfrac{\lambda_{+}^{\circ}}{\lambda_{+}^{\circ} + \lambda_{-}^{\circ}}$ and $t_{-} = \dfrac{\lambda_{-}^{\circ}}{\lambda_{+}^{\circ} + \lambda_{-}^{\circ}}$, with $t_{+} + t_{-} = 1$.

12. Why does $\ce{H+}$ (and $\ce{OH-}$) have anomalously high ionic conductivity?

    Because of the Grotthuss (proton-hopping) mechanism: protons relay through hydrogen bonds of the water network rather than physically migrating as hydrated ions, giving $\ce{H+}$ and $\ce{OH-}$ much larger $\lambda^{\circ}$ than other ions.

13. Define an electrochemical cell and distinguish galvanic from electrolytic cells.

    An electrochemical cell interconverts chemical and electrical energy via redox reactions. A galvanic (voltaic) cell uses a spontaneous reaction ($\Delta G < 0$) to produce electricity; an electrolytic cell uses external electricity to drive a non-spontaneous reaction ($\Delta G > 0$).

14. In a galvanic cell, which electrode is the anode and which is the cathode, and what is their sign?

    Oxidation occurs at the anode (negative terminal in a galvanic cell); reduction occurs at the cathode (positive terminal). Mnemonic: an ox / red cat.

15. Define the electromotive force (EMF) of a cell.

    EMF is the maximum potential difference between the two electrodes of a cell measured under zero current (no flow / open circuit) conditions, i.e. when no current is drawn so there is no internal IR drop: $E_{cell} = E_{cathode} - E_{anode}$ (reduction potentials).

16. Why must EMF be measured at zero current (e.g. by a potentiometer)?

    Drawing current causes an internal $IR$ drop and electrode polarization, so the terminal voltage falls below the true EMF. At zero current $E_{cell} = E_{EMF}$; under load, $V = E_{cell} - I r_{internal}$.

17. Write the standard IUPAC cell notation rules and an example for the Daniell cell.

    Anode on the left, cathode on the right; single bar $|$ = phase boundary, double bar $\|$ = salt bridge. Example: $\ce{Zn(s) | Zn^{2+}(aq) \|\| Cu^{2+}(aq) | Cu(s)}$.

18. Give the overall cell reaction and standard EMF of the Daniell cell.

    $\ce{Zn(s) + Cu^{2+}(aq) -> Zn^{2+}(aq) + Cu(s)}$, with $E^{\circ}_{cell} = E^{\circ}_{\ce{Cu^{2+}/Cu}} - E^{\circ}_{\ce{Zn^{2+}/Zn}} = 0.34 - (-0.76) = 1.10\ \text{V}$.

19. What is the standard hydrogen electrode (SHE) and its assigned potential?

    The SHE is the reference electrode $\ce{Pt | H2(g, 1\ bar) | H+(aq, 1\ M)}$ with the half-reaction $\ce{2H+ + 2e- <=> H2}$ assigned $E^{\circ} = 0.00\ \text{V}$ at all temperatures.

20. Define standard electrode potential $E^{\circ}$.

    The electrode potential of a half-cell relative to the SHE when all species are at unit activity (1 M ions, 1 bar gases) and at the stated temperature (usually 298 K). By convention these are tabulated as reduction potentials.

21. Write the formula relating cell EMF to electrode reduction potentials.

    $E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode}$, both taken as standard reduction potentials. A positive $E^{\circ}_{cell}$ indicates a spontaneous (galvanic) reaction.

22. What is the relation between standard cell EMF and standard Gibbs free energy change?

    $\Delta G^{\circ} = -nFE^{\circ}_{cell}$, where $n$ is the number of electrons transferred and $F = 96485\ \ce{C\,mol^{-1}}$ is the Faraday constant. For any state: $\Delta G = -nFE_{cell}$.

23. Relate the standard cell EMF to the equilibrium constant of the cell reaction.

    $\Delta G^{\circ} = -nFE^{\circ}_{cell} = -RT\ln K$, so $E^{\circ}_{cell} = \dfrac{RT}{nF}\ln K$, and at 298 K, $E^{\circ}_{cell} = \dfrac{0.0592}{n}\log_{10} K\ \text{V}$.

24. State the Nernst equation in its general logarithmic form.

    $E = E^{\circ} - \dfrac{RT}{nF}\ln Q$, where $Q$ is the reaction quotient, $n$ the number of electrons, $R$ the gas constant, $T$ the temperature, and $F$ the Faraday constant.

25. Write the Nernst equation at 298 K using base-10 logarithm.

    $E = E^{\circ} - \dfrac{0.0592}{n}\log_{10} Q\ \text{V}$ at $T = 298\ \text{K}$, obtained from $\dfrac{RT}{F}\ln 10 \approx 0.0592\ \text{V}$.

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