ELECTRODE POTENTIAL

PYQ-2024-Electrochemistry-Q9, PYQ-2023- Electrochemistry-Q5

For any electrode $\rightarrow$ oxidation potential $=-$ reduction potential

$\mathrm{E}_{\text {cell }}=$ R.P of cathode - R.P of anode

$E_{\text {cell }}=$ R.P. of cathode + O.P of anode

$\mathrm{E}_{\text {cell }}$ is always a +ve quantity & Anode will be electrode of low R.P

$\mathrm{E}_{\text {Cell }}^{\mathrm{o}}=\mathrm{SRP}$ of cathode $-\mathrm{SRP}$ of anode.

Greater the SRP value greater will be oxidizing power.

GIBBS FREE ENERGY CHANGE

$\Delta \mathrm{G}=-\mathrm{nFE}_{\text {cell }}$

$\Delta \mathrm{G}^{\circ}=-nF \mathrm{E}_{\text {cell }}^{\mathrm{o}}$

NERNST EQUATION:

PYQ-2024-Electrochemistry-Q3, PYQ-2023- Electrochemistry-Q4, PYQ-2023- Electrochemistry-Q3, PYQ-2023- Electrochemistry-Q1, PYQ-2023- Electrochemistry-Q7, PYQ-2023- Electrochemistry-Q9, PYQ-2023- Electrochemistry-Q12

(Effect of concentration and temp on emf of cell)

$\Delta G=\Delta G^{0}+R T$ lnQ (where $Q$ is reaction quotient)

PYQ-2023- Ionic equilibrium-Q9

$\Delta G^{0}=-R T$ ln $K_{\text {eq }}$

$ E_{cell}=E_{cell}^{\circ}-\frac{RT}{nF} \ln Q $

$E_{cell}=E_{cell}^{\circ}-\frac{2.303 RT}{nF} \log Q$

$E_{cell}=E_{cell}^{\circ}-\frac{0.0591 RT}{n} \log Q$ [At $298 K$ ]

At chemical equilibrium

$ \Delta \mathrm{G}=0 \quad ; \quad \mathrm{E}_{\text {cell }}=0 \text {. } $

$\log K_{eq}=\frac{n E_{cell}^{o}}{0.0591}$.

$E_{cell}^{o}=\frac{0.0591}{n} \log K_{eq}$

For an electrode $\mathrm{M}(\mathrm{s}) / \mathrm{M}^{\mathrm{n}+}$.

$ E_{M^{n+}/M} =\mathrm{E}_{\mathrm{M}^{n+} / \mathrm{M}}^{\mathrm{O}}-\frac{2.303 R T}{\mathrm{nF}} \log \frac{1}{\left[\mathrm{M}^{n+}\right]} $

CONCENTRATION CELL:

PYQ-2024-Electrochemistry-Q1

A cell in which both the electrodes are made up of same material.

For all concentration cell $\quad E_{\text {cell }}^{\circ}=0$.

(a) Electrolyte Concentration Cell:

e.g. $ Zn(s) / Zn^{2+} c_{1} || Zn^{2+}(c_2) / Zn(s)$

$E=\frac{0.0591}{2} \log \frac{C_{2}}{C_{1}}$

(b) Electrode Concentration Cell:

e.g. $Pt, H_{2} (P_{1} atm) / H^{+}(1M) \quad \quad / H_2(P_{2}atm ) / Pt$

$E=\frac{0.0591}{2} \log \left(\frac{P_{1}}{P_{2}}\right)$

DIFFERENT TYPES OF ELECTRODES :

PYQ-2024-Electrochemistry-Q6

1. Metal-Metal ion Electrode $M(s) / M^{n+} . \quad M^{n+}+n e^{-} \longrightarrow M(s)$

$$ E=E^{0}+\frac{0.0591}{n} \log \left[M^{n+}\right] $$

2. Gas-ion Electrode $ \mathrm{Pt} / \mathrm{H}_{2}(\mathrm{Patm}) / \mathrm{H}^{+}(\mathrm{XM})$

as a reduction electrode

$\quad \mathrm{H}^{+}(\mathrm{aq})+\mathrm{e}^{-} \longrightarrow \frac{1}{2} \mathrm{H}_{2}$ (Patm)

$\quad E=E^{\circ}-0.0591 \log \frac{P_{H_{2}}{ }^{\frac{1}{2}}}{\left[H^{+}\right]}$

3. Oxidation-reduction Electrode $\mathrm{Pt} / \mathrm{Fe}^{2+}, \mathrm{Fe}^{3+}$

$\quad$ as a reduction electrode $\mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+}$

$\quad E=E^{0}-0.0591 \log \frac{\left[\mathrm{Fe}^{2+}\right]}{\left[\mathrm{Fe}^{3+}\right]}$

PYQ-2023- Electrochemistry-Q8

4. Metal-Metal insoluble salt Electrode e.g. $\mathrm{Ag} / \mathrm{AgCl}, \mathrm{Cl}^{-}$

$\quad$ as a reduction electrode $\mathrm{AgCl}(\mathrm{s})+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(\mathrm{s})+\mathrm{Cl}^{-}$

$\quad E_{Cl^{-} / AgCl /Ag} =E_{Cl^{-} / AgCl / Ag}^{0} - 0.0591 \log [Cl^{-}]$.

ELECTROLYSIS:

PYQ-2023- Electrochemistry-Q10

$\quad$ (a)$ \xrightarrow[\text { Increasing order of deposition }] {K^{+}, \mathrm{Ca}^{+2}, \mathrm{Na}^{+}, \mathrm{Mg}^{+2}, \mathrm{Al}^{+3}, \mathrm{Zn}^{+2}, \mathrm{Fe}^{+2}, \mathrm{H}^{+},\mathrm{Cu}^{+2}, \mathrm{Ag}^{+}, \mathrm{Au}^{+3}}$

$\quad$ (b) Similarly the anion which is stronger reducing agent(low value of SRP) is liberated first at the anode.

$$ \xrightarrow[\text { Increasing order of deposition }]{SO_{4}^{2-}, NO_{3}^{-}, OH^{-}, Cl^{-}, Br^{-}, I^{-}} $$

FARADAY’S LAW OF ELECTROLYSIS

PYQ-2024-Electrochemistry-Q12, PYQ-2024-Electrochemistry-Q7, PYQ-2024-Electrochemistry-Q8, PYQ-2024-Electrochemistry-Q2, PYQ-2024-Electrochemistry-Q4

First Law :

$\mathrm{w}=\mathrm{zq} \quad \quad \mathrm{w}=\mathrm{Z}it$ $\quad \quad\mathrm{Z}=$ Electrochemical equivalent of substance

Second Law

$W \alpha E $

$\frac{\mathrm{W}}{\mathrm{E}}=\mathrm{constant} \quad \frac{W_{1}}{E_{1}}=\frac{W_{2}}{E_{2}}=\ldots \ldots \ldots $

$\frac{\mathrm{W}}{\mathrm{E}}=\frac{\mathrm{i} \times \mathrm{t} \times \text { current efficiency factor }}{96500} .$

$\text { Current efficiency } =\frac{\text { actual mass deposited/produced }}{\text { Theoritical mass deposited/produced }} \times 100$

CONDITION FOR SIMULTANEOUS DEPOSITION OF Cu & Fe AT CATHODE

$ \mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{\circ}-\frac{0.0591}{2} \log \frac{1}{\mathrm{Cu}^{2+}}$

$=\mathrm{E}_{\mathrm{Fe}^{2+} / \mathrm{Fe}}^{\circ}-\frac{0.0591}{2} \log \frac{1}{\mathrm{Fe}^{2+}} $

Condition for the simultaneous deposition of Cu & Fe on cathode.

CONDUCTANCE :

Conductance $=\frac{1}{\text { Resistance }}$

Specific conductance or conductivity:

PYQ-2024-Electrochemistry-Q13

(Reciprocal of specific resistance)$ \quad K=\frac{1}{\rho} $

$\mathrm{K}$ = specific conductance

Equivalent conductance :

$\lambda_{\mathrm{E}}=\frac{\mathrm{K} \times 1000}{\text { Normality }}$ $\quad \quad $ unit : $\mathrm{ohm}^{-1} \mathrm{~cm}^{2} \mathrm{eq}^{-1}$

Molar conductance :

PYQ-2023- Electrochemistry-Q11

PYQ-2023- Electrochemistry-Q13

PYQ-2023- Electrochemistry-Q6

$ \lambda_{\mathrm{m}}=\frac{\mathrm{K} \times 1000}{\text { Molarity }}$ $\quad \quad $ unit : $\mathrm{ohm}^{-1} \mathrm{~cm}^{2} \mathrm{mole}^{-1}$

specific conductance $=$ conductance $\times \frac{\ell}{\mathrm{a}}$

Factors affecting Electrolytic Conductance

PYQ-2024-Electrochemistry-Q11

The following are the factors affecting electrolytic conductance:

1. The nature of the electrolyte: The nature of the electrolyte affects the electrolytic conductance. For example, a strong electrolyte will have a higher electrolytic conductance than a weak electrolyte.

2. The concentration of the electrolyte: The concentration of the electrolyte also affects the electrolytic conductance. A higher concentration of electrolyte will result in a higher electrolytic conductance.

3. The temperature of the electrolyte: The temperature of the electrolyte also affects the electrolytic conductance. A higher temperature will result in a higher electrolytic conductance.

4. The size of the electrolyte: The size of the electrolyte also affects the electrolytic conductance. A smaller size will result in a higher electrolytic conductance.

KOHLRAUSCH’S LAW :

Variation of $\lambda_{\text {eq }} I \lambda_{\mathrm{M}}$ of a solution with concentration :

(i) Strong electrolyte

$\quad \lambda_{M}{ }^{c}=\lambda_{M}^{\infty}-b \sqrt{c}$

(ii) Weak electrolytes: $\quad \lambda_\infty = n_{+} \lambda^\infty_{+} + n_{-} \lambda^\infty_{-} $

$\quad $ where $\lambda$ is the molar conductivity

$ \quad \mathrm{n}_{+}$=No. of cations obtained after dissociation per formula unit

$ \quad \mathrm{n}_{-}$=No. of anions obtained after dissociation per formula unit

APPLICATION OF KOHLRAUSCH LAW

1. Calculation of $\lambda^{0}{ }_{\mathrm{M}}$ of weak electrolytes :

$\quad \quad \lambda^{0}_M(CH_3COOH)=\lambda^{0}_M(CH_3COONa)+\lambda^{0}_M(HCl)-\lambda^{0}_M(NaCl)$

2. To calculate degree of dissociation of a week electrolyte

$$ \alpha=\frac{\lambda_{\mathrm{m}}^{\mathrm{c}}}{\lambda_{\mathrm{m}}^{0}} \quad ; \quad \mathrm{K}_{\mathrm{eq}}=\frac{\mathrm{c} \alpha^{2}}{(1-\alpha)} $$

3. Solubility (S) of sparingly soluble salt & their $\mathrm{K}_{\mathrm{sp}}$

$$ \begin{aligned} & \lambda_{\mathrm{M}}{ }^{c}=\lambda_{\mathrm{M}}^{\infty}=\kappa \times \frac{1000}{\text { solubility }} \ & \mathrm{K}_{\mathrm{sp}}=\mathrm{S}^{2} \end{aligned} $$

Transport Number :

$t_{c}=[\frac{\mu_{c}}{\mu_{c}+\mu_{a}}], \quad \quad t_{a}=[\frac{\mu_{a}}{\mu_{a}+\mu_{c}}]$.

Where $t_{c}$= Transport Number of cation & $t_{a}$= Transport Number of anion

Rusting of Iron

PYQ-2024-Electrochemistry-Q5

When iron is exposed to wooden or air over a pained of time, the iron reach with oxygen in the presence of moisture to form a reddish-brown chemical compound, iron acid . This is refereed to

$4Fe(OH)_2 + O_2 + xH_2 O \rightarrow 2Fe_2 O_3 + (x+4)H_2 O$

Cell and Battery

PYQ-2024-Electrochemistry-Q10

Battery or cells are referred to as the parallel combination of electrochemical cells. The major difference between a primary cell and the secondary cell is that primary cells are the ones that cannot be charged but secondary cells are the ones that are rechargeable.

Primary cell Primary cells have high density and get discharged slowly. Since there is no fluid inside these cells they are also known as dry cells. The internal resistance is high and the chemical reaction is irreversible. Its initial cost is cheap and also primary cells are easy to use. examples Daniel cell, and. Leclanche cell.

Secondary cell Secondary cells have low energy density and are made of molten salts and wet cells. The internal resistance is low and the chemical reaction is reversible. Its initial cost is high and is a little complicated to use when compared to the primary cell. examples lead-acid accumulator, nickel cadmium (NiCd), nickel metal hydride (NiMH), lithium ion (Li-ion) etc.