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GATE Life Sciences Electrochemistry Syllabus

The Electrochemistry syllabus for GATE Life Sciences in full: 3 chapters and 3 topics, every one listed below, plus 50 Electrochemistry flashcards with answers.

3Chapters
3Topics
50Flashcards

Electrochemistry syllabus: all 3 chapters

Expand any chapter to see its topics and sub-topics.

  1. Conductance

     1 topic
    • Kohlrausch Law

  2. Cell Potentials

     2 topics
    • EMF
    • Nernst Equation

  3. Thermodynamic Aspects and Applications

     overview

    No separate topics listed for this chapter.

GATE Life Sciences Electrochemistry flashcards — 50 questions with 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.

Show the other 30 Electrochemistry flashcards

  1. 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.

  2. 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: $\Delta G = -nFE_{cell}$.

  3. 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, $E^{\circ}_{cell} = \dfrac{0.0592}{n}\log_{10} K\ \text{V}$.

  4. 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.

  5. 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 $\dfrac{RT}{F}\ln 10 \approx 0.0592\ \text{V}$.

  6. For the half-reaction $\ce{M^{n+} + n e- -> M}$, write the Nernst equation for the electrode potential.

    $E = E^{\circ} - \dfrac{0.0592}{n}\log_{10}\dfrac{1}{[\ce{M^{n+}}]} = E^{\circ} + \dfrac{0.0592}{n}\log_{10}[\ce{M^{n+}}]\ \text{V}$ (solid M has unit activity).

  7. Write the Nernst equation for the Daniell cell at 298 K.

    $E_{cell} = E^{\circ}_{cell} - \dfrac{0.0592}{2}\log_{10}\dfrac{[\ce{Zn^{2+}}]}{[\ce{Cu^{2+}}]}\ \text{V}$, with $E^{\circ}_{cell} = 1.10\ \text{V}$ and $n = 2$.

  8. How is the reaction quotient $Q$ written for a general cell reaction $aA + bB \to cC + dD$?

    $Q = \dfrac{a_C^{\,c}\,a_D^{\,d}}{a_A^{\,a}\,a_B^{\,b}}$, using activities (approximated by concentrations for solutes and partial pressures for gases); pure solids and liquids have activity 1.

  9. What does the Nernst equation reduce to at equilibrium, and what is $E_{cell}$ then?

    At equilibrium $Q = K$ and the net reaction stops, so $E_{cell} = 0$, giving $E^{\circ}_{cell} = \dfrac{RT}{nF}\ln K$. A discharged battery has $E_{cell} = 0$.

  10. What is a concentration cell, and what is its standard EMF?

    A concentration cell has identical electrodes/electrolytes differing only in concentration; the EMF arises solely from the concentration difference. Its $E^{\circ}_{cell} = 0$, so $E_{cell} = -\dfrac{0.0592}{n}\log_{10}\dfrac{C_{anode}}{C_{cathode}}$ (electrolyte version).

  11. Write the EMF expression for a concentration cell $\ce{M | M^{n+}(C_1) \|\| M^{n+}(C_2) | M}$ with $C_2 > C_1$.

    $E_{cell} = \dfrac{0.0592}{n}\log_{10}\dfrac{C_2}{C_1}\ \text{V}$; spontaneous when the dilute side is the anode ($C_2$ at cathode), driving ions toward equal concentration.

  12. Use the Nernst equation to express the potential of a hydrogen electrode in terms of pH.

    For $\ce{2H+ + 2e- -> H2}$ at $p_{\ce{H2}} = 1\ \text{bar}$: $E = -0.0592\,\text{pH}\ \text{V}$ at 298 K, since $E = -\dfrac{0.0592}{1}\log_{10}\dfrac{1}{[\ce{H+}]} = 0.0592\log_{10}[\ce{H+}]$.

  13. How does increasing temperature affect EMF, and what thermodynamic quantity gives the temperature coefficient?

    The temperature coefficient is $\left(\dfrac{\partial E}{\partial T}\right)_p = \dfrac{\Delta S}{nF}$. EMF rises with $T$ if $\Delta S > 0$ and falls if $\Delta S < 0$.

  14. Give the relations linking $\Delta S$ and $\Delta H$ of a cell reaction to EMF and its temperature coefficient.

    $\Delta S = nF\left(\dfrac{\partial E}{\partial T}\right)_p$ and $\Delta H = \Delta G + T\Delta S = -nFE + nFT\left(\dfrac{\partial E}{\partial T}\right)_p$.

  15. State Faraday's first law of electrolysis.

    The mass $m$ of substance deposited or liberated at an electrode is proportional to the charge passed: $m = Z\,Q = Z\,I\,t$, where $Z$ is the electrochemical equivalent.

  16. State Faraday's second law of electrolysis.

    When the same quantity of charge passes through different electrolytes, the masses deposited are proportional to their equivalent weights: $\dfrac{m_1}{m_2} = \dfrac{E_1}{E_2}$ (equivalent weights).

  17. How much charge is one mole of electrons, and how is moles deposited found?

    One mole of electrons carries one Faraday, $F = 96485\ \ce{C\,mol^{-1}}$. Moles of substance $= \dfrac{It}{nF}$, where $n$ is electrons per ion and $It$ the total charge in coulombs.

  18. Define a salt bridge and state its two main functions.

    A salt bridge (e.g. KCl/$\ce{KNO3}$ in agar) connects the two half-cells. It (1) completes the internal circuit by allowing ion flow and (2) maintains electrical neutrality in each half-cell, minimizing the liquid-junction potential.

  19. What is electrode polarization and overpotential?

    Polarization is the deviation of an electrode's working potential from its equilibrium value when current flows. Overpotential $\eta = E_{applied} - E_{equilibrium}$ is the extra voltage (beyond reversible potential) needed to drive a reaction at a useful rate.

  20. Distinguish a primary cell from a secondary cell.

    A primary cell uses an irreversible reaction and cannot be recharged (e.g. dry Leclanché cell). A secondary (storage) cell uses a reversible reaction and can be recharged by reversing current (e.g. lead-acid, $\ce{Li}$-ion).

  21. Write the discharge electrode reactions of a lead-acid battery.

    Anode: $\ce{Pb + SO4^{2-} -> PbSO4 + 2e-}$. Cathode: $\ce{PbO2 + 4H+ + SO4^{2-} + 2e- -> PbSO4 + 2H2O}$. Overall: $\ce{Pb + PbO2 + 2H2SO4 -> 2PbSO4 + 2H2O}$, $E_{cell}\approx 2.0\ \text{V}$.

  22. Define a reversible (reference) electrode of the second kind and give an example.

    An electrode of the second kind is a metal coated with its insoluble salt in a solution of a common anion, e.g. the calomel electrode $\ce{Hg | Hg2Cl2 | KCl}$ or $\ce{Ag | AgCl | Cl-}$; its potential depends on the anion activity and is stable, so it serves as a reference.

  23. What is the standard reduction potential and half-reaction of the saturated calomel electrode (SCE)?

    $\ce{Hg2Cl2 + 2e- -> 2Hg + 2Cl-}$ with $E \approx +0.242\ \text{V}$ vs SHE (saturated KCl). Its potential depends only on chloride activity, making it a convenient secondary reference electrode.

  24. Compare electrolytic conduction with metallic conduction.

    Metallic conduction is by free electrons, no matter transfer, and conductivity decreases with rising temperature. Electrolytic conduction is by ion migration, involves chemical change at electrodes, and conductivity increases with temperature (lower viscosity, more dissociation).

  25. State the electrochemical series and one of its uses.

    The electrochemical series ranks elements by standard reduction potential. Uses: predict spontaneity of redox reactions (a more negative $E^{\circ}$ metal displaces a more positive one), relative reactivity/reducing power, and which species is preferentially discharged in electrolysis.

  26. How does standard reduction potential relate to oxidizing and reducing strength?

    A more positive $E^{\circ}$ means a stronger oxidizing agent (species is easily reduced); a more negative $E^{\circ}$ means a stronger reducing agent. E.g. $\ce{F2}$ ($+2.87\ \text{V}$) is the strongest common oxidant; $\ce{Li}$ ($-3.04\ \text{V}$) the strongest common reductant.

  27. Using $E^{\circ}_{cell}$, how do you determine whether a redox reaction is spontaneous?

    Compute $E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode}$. If $E^{\circ}_{cell} > 0$ then $\Delta G^{\circ} = -nFE^{\circ}_{cell} < 0$ and the reaction is spontaneous; if $E^{\circ}_{cell} < 0$ it is non-spontaneous.

  28. What is the effect of dilution on $\kappa$ (conductivity) and on $\Lambda_m$ (molar conductivity)?

    On dilution, $\kappa$ decreases (fewer ions per unit volume), but $\Lambda_m$ increases (because it accounts for all ions from a mole of electrolyte, and inter-ionic interactions weaken / dissociation increases).

  29. Derive the limiting molar conductivity of acetic acid from Kohlrausch's law (formula).

    $\Lambda_m^{\circ}(\ce{CH3COOH}) = \Lambda_m^{\circ}(\ce{CH3COONa}) + \Lambda_m^{\circ}(\ce{HCl}) - \Lambda_m^{\circ}(\ce{NaCl})$, which equals $\lambda^{\circ}(\ce{H+}) + \lambda^{\circ}(\ce{CH3COO-})$.

  30. For the cell reaction $\ce{Cu^{2+} + 2e- -> Cu}$, how does $E$ change if $[\ce{Cu^{2+}}]$ decreases tenfold (298 K)?

    $E = E^{\circ} + \dfrac{0.0592}{2}\log_{10}[\ce{Cu^{2+}}]$, so a tenfold decrease in $[\ce{Cu^{2+}}]$ lowers $E$ by $\dfrac{0.0592}{2} = 0.0296\ \text{V}$.

GATE Life Sciences Electrochemistry FAQ

What is in the GATE Life Sciences Electrochemistry syllabus?

GATE Life Sciences Electrochemistry is split into 3 chapters: Conductance, Cell Potentials and Thermodynamic Aspects and Applications. Together they contain 3 topics.

How many chapters are in GATE Life Sciences Electrochemistry?

3 chapters, containing 3 topics. The largest chapter is Cell Potentials, with 2 topics.

Are there flashcards for GATE Life Sciences Electrochemistry?

Yes — a 50-card Electrochemistry deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.