GATE Life Sciences Electrochemistry Flashcards

24 sample cards from the Electrochemistry deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. 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 $n = 2$.

2. 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.

3. 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 $E_{cell} = 0$.

4. 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).

5. 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.

6. 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 $E = -\dfrac{0.0592}{1}\log_{10}\dfrac{1}{[\ce{H+}]} = 0.0592\log_{10}[\ce{H+}]$.

7. 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 $\Delta S < 0$.

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

9. 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.

10. 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).

11. 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.

12. 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.

13. 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.

14. 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).

15. 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: $\ce{Pb + PbO2 + 2H2SO4 -> 2PbSO4 + 2H2O}$, $E_{cell}\approx 2.0\ \text{V}$.

16. 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.

17. 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.

18. 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).

19. 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.

20. 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.

21. 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.

22. 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).

23. 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 $\lambda^{\circ}(\ce{H+}) + \lambda^{\circ}(\ce{CH3COO-})$.

24. 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 $\dfrac{0.0592}{2} = 0.0296\ \text{V}$.

What this deck covers

Electrochemistry flashcards FAQ