Deck 5: Mechanistic Analysis

Question 1

Consider an elementary reaction $M _ { s o l } ^ { 3 + }+ 3 e ^ { - } \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } } M$



where M is a metal and
$$M _ { s o l } ^ { 3 + }$$
is metal ion in solution. F denotes faraday constant. The net faradaic current density due to metal deposition is given by

A) $$F k _ { 1 } \left[ M _ { s o l } ^ { 3 + } \right]$$
B) $$F \left\{ k _ { 1 } \left[ M _ { s a l } ^ { 3 + } \right] - k _ { - 1 } \right\}$$
C) $$3 F \left( k _ { 1 } \left[ M _ { s o l } ^ { 3 + } \right] + k _ { - 1 } \right)$$
D) $$3 F \left\{ k _ { 1 } \left[ M _ { s a l } ^ { 3 + } \right] - k _ { - 1 } \right\}$$

Answer 1

$$3 F \left\{ k _ { 1 } \left[ M _ { s a l } ^ { 3 + } \right] - k _ { - 1 } \right\}$$

Question 2

Consider a reaction given by $\begin{array} { l } M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } } M _ { a ds } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + }\underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } M _ { sol } ^ { + }\end{array}$ .

-In the standard notation, the fractional surface coverage ( $\theta$ ) of the adsorbed intermediate $$M _ { a t } ^ { + }$$
is described by

A) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { 2 } \theta$$
B) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { - 1 } \theta - k _ { 2 } \theta + k _ { - 2 } ( 1 - \theta ) C _ { M _ { 2a d } ^ { 2 + } }$$
C) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { - 1 } \theta$$
D) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { - 1 } \theta - k _ { 2 } \theta + k _ { - 2 } C _ { M _ { s a } ^ { 2+ } }$$

Answer 2

$$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { - 1 } \theta - k _ { 2 } \theta + k _ { - 2 } ( 1 - \theta ) C _ { M _ { 2a d } ^ { 2 + } }$$

Question 3

Consider a reaction given by $\begin{array} { l } M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } } M _ { a ds } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + }\underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } M _ { sol } ^ { + }\end{array}$ .

-In the same mechanism, the steady-state fractional surface coverage of the intermediate is given by

A) $$\theta _ { ss } = \frac { k _ { 1 { dc} } } { k _ { 1 \dot {dc } } + k _ { 2 } }$$
B) $$\theta _ { s s } = \frac { k _ { 1 d c } } { k _ { 1 \dot { dc } } + k _ { - 1 \dot { dc } } + k _ { 2 } + k _ { - 2 } }$$
C) $\theta_{ss}=\frac{k_{1 d c}+k_{-2} C_{M^{+2}_{sol}}}{k_{1 d c}+k_{-1 d c}+k_{2}+k_{-2} C_{M^{+2}_{sol}} }$
D) $$\theta _ { ss } = \frac { k _ { 1 \dot { dc } } - k _ { - 1 \dot { dc } } } { k _ { 1 \dot { dc } } + k _ { - 1 \dot { dc } } + k _ { 2 } + k _ { - 2 } C _ { M _ { 2a i } ^ { 2+ } } }$$

Answer 3

$\theta_{ss}=\frac{k_{1 d c}+k_{-2} C_{M^{+2}_{sol}}}{k_{1 d c}+k_{-1 d c}+k_{2}+k_{-2} C_{M^{+2}_{sol}} }$

Question 4

Consider a reaction given by $\begin{array} { l } M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } } M _ { a ds } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + }\underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } M _ { sol } ^ { + }\end{array}$ .

-In the same mechanism, the faradaic current is given by

A) $$i _ { F } = F \left[ k _ { 1 } ( 1 - \theta ) \right]$$
B) $$i _ { F } = F \left[ k _ { 1 } ( 1 - \theta ) - k _ { - 1 } \theta \right]$$
C) $$i _ { F } = F \left[ k _ { 1 } ( 1 - \theta ) + k _ { - 1 } \theta \right]$$
D) $$i _ { F } = F \left[ k _ { 1 } ( 1 - \theta ) - k _ { - 1 } \theta - k _ { 2 } \theta \right]$$

Question 5

Consider a reaction given by $\begin{array} { l } M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } } M _ { a ds } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + }\underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } M _ { sol } ^ { + }\end{array}$ .

-In the same mechanism, the value of $$\frac { d \theta } { d E }$$
is given by

A) $\frac{\left(b_{1} k_{1 ak}\left(1-\theta_{s s}\right)-b_{-1} k_{-1ak} \theta_{ss}\right)}{\left(k_{1 dak}+k_{-1 ak}+k_{2}+k_{-2} C_{M_{2a}^{2}}+j \omega \Gamma\right)}$
B) $$\frac { \left( b _ { 1 } k _ { 1 \dot {dc } } - b _ { - 1 } k _ { - 1 \dot {dc } } \right) } { \left( k _ { 1 \dot { dc} } + k _ { - 1 \dot { dc } } + k _ { 2 } + k _ { - 2 } + j \omega \Gamma \right) }$$
C) $$\frac { \left( b _ { 1 } k _ { 1 \dot { d } } - b _ { - 1 } k _ { - 1 \dot { \alpha } } \right) } { \left( k _ { 1 \dot { \alpha } } + k _ { - 1 \dot { k } } + k _ { 2 } + j \Gamma \Gamma \right) }$$
D) $$\frac { \left( b _ { 1 } k _ { 1 \dot { dc } } \right) } { \left( k _ { 1 \dot { dc} } + k _ { - 1 \dot { dc } } + k _ { 2 } + j \omega \Gamma \right) }$$

Question 6

Consider a reaction given by $\begin{array} { l } M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } } M _ { a ds } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + }\underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } M _ { sol } ^ { + }\end{array}$ .

-In the same mechanism, the faradaic impedance (Z_F) is given by

A) $$\left( Z _ { F } \right) ^ { - 1 } = F \left( b _ { 1 } k _ { 1 \dot { dc } } \left( 1 - \theta _ { s s } \right) - b _ { - 1 } k _ { - 1 \dot { \alpha } } \theta _ { ss } + \left( k _ { 1 \dot { dc } } + k _ { - 1 \dot { dc } } + k _ { 2 } \right) \frac { d \theta } { d E } \right)$$
B) $$\left( Z _ { F } \right) ^ { - 1 } = F \left( b _ { 1 } k _ { 1 d \dot { c } } \left( 1 - \theta _ { s s } \right) - b _ { - 1 } k _ { - 1 \dot { } } \theta _ { s s } - \left( k _ { 1 \dot { dc } } + k _ { - 1 \dot {dc } } + k _ { 2 } \right) \frac { d \theta } { d E } \right)$$
C) $$\left( Z _ { F } \right) ^ { - 1 } = F \left( b _ { 1 } k _ { 1 \dot { dc } } \left( 1 - \theta _ { s s } \right) - b _ { - 1 } k _ { - 1 \dot {dc } } \theta _ { s s } - \left( k _ { 1 d \dot {c } } + k _ { - 1 \dot { dc } } \right) \frac { d \theta } { d E } \right)$$
D) $$\left( Z _ { F } \right) ^ { - 1 } = F \left( b _ { 1 } k _ { 1 d \dot { c} } \left( 1 - \theta _ { s s } \right) - b _ { - 1 } k _ { - 1 \dot { dc } } \theta _ { ss } + \left( k _ { 1 d \dot { c} } + k _ { - 1 d \dot {c } } \right) \frac { d \theta } { d E } \right)$$

Question 7

Consider a reaction given by .

-In the above reaction, the rate constants are given by
$$k _ { i } = k _ { i 0 } e ^ { b ^ { \prime } E }$$
where E is measured wrt equilibrium potential. Given that k₁₀ = 10^-7 mol cm^-2 s^-1, b₁ = 20 V^-1, b_-1 = -18 V^-1 , k₂ = 10^-5 mol cm^-2 s^-1, k_-2 = 10⁰ cm s^-1 and the concentration of
$$M _ { s o l } ^ { 2 + }$$
as 25 mM, determine (i) k_-10 = ___________ mol cm^-2 s^-1 . At E = 0.3 V vs. "Equilibrium. potential", (ii) value of k_1dc = ___________mol cm^-2 s^-1, (iii) k_-1dc = ___________mol cm^-2 s^-1, (iv) steady state fractional surface coverage of the intermediate is _______
Remember that 1 M = 1 mol/lit = 10^-3 mol/ cm³.

Question 8

When kinetics is rate-limiting, the faradaic impedance of a simple electron transfer reaction can be modeled as

A) a simple resistor
B) a simple capacitor
C) a capacitor in parallel with a resistor
D) none of the above

Question 9

Consider the reaction $$\begin{array} { l } P _ { s a } \stackrel { k _ { 1 } } { \longrightarrow } Q _ { s a } + e ^ { - } \\A _ { s i l } ^ { - } \underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } A _ { \alpha i j } + e ^ { - } \\\end{array}$$
The kinetic parameters are given by k₁₀ = 10^-5 cm s^-1, b₁ = 20 V^-1, k₂₀ = 10^-6 cm s^-1, b₂ = 20 V^-1, k_-20 =10^-6 mol cm^-2 s^-1 , b_-2 = -18 V^-1 and $\varGamma$ = 10^-8 mol cm^-2. Solution species concentrations are given by [P_sol] = [Q_sol] =[
$$A _ { s o l } ^ { - }$$ ] = 100 mM.

-The equation for fractional surface coverage of A_ads is given by

A) $$\frac { k _ { 2 \dot { dc } } } { k _ { 2 k \dot { dc } } + k _ { - 2 \dot { dc } } + k _ { 1 \dot { dc } } }$$
B) $$\frac { k _ { 2 dc } } { k _ { 2dc } + k _ { - 2 \dot {dc } } }$$
C) $\frac{k_{2 dc} C_{\mathcal{A}^-_{\mathrm{sol}}}}{k_{2 dc} C_{A^-_{sol}}+k_{-2 d c}+k_{1 d c} C_{P_{sol}}}$

D) $\frac{k_{2 dc} C_{A^-_{sol}}}{k_{2 dc} C_{A^-_{sol}}+k_{-2dc}}$

Question 10

Consider the reaction $$\begin{array} { l } P _ { s a } \stackrel { k _ { 1 } } { \longrightarrow } Q _ { s a } + e ^ { - } \\A _ { s i l } ^ { - } \underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } A _ { \alpha i j } + e ^ { - } \\\end{array}$$
The kinetic parameters are given by k₁₀ = 10^-5 cm s^-1, b₁ = 20 V^-1, k₂₀ = 10^-6 cm s^-1, b₂ = 20 V^-1, k_-20 =10^-6 mol cm^-2 s^-1 , b_-2 = -18 V^-1 and $\varGamma$ = 10^-8 mol cm^-2. Solution species concentrations are given by [P_sol] = [Q_sol] =[
$$A _ { s o l } ^ { - }$$ ] = 100 mM.

-At E_dc = 0.25 V vs. OCP, the value of fractional surface coverage of A_ads is given by,
$\theta$ _ss = _________

Question 11

Consider the reaction $$\begin{array} { l } P _ { s a } \stackrel { k _ { 1 } } { \longrightarrow } Q _ { s a } + e ^ { - } \\A _ { s i l } ^ { - } \underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } A _ { \alpha i j } + e ^ { - } \\\end{array}$$
The kinetic parameters are given by k₁₀ = 10^-5 cm s^-1, b₁ = 20 V^-1, k₂₀ = 10^-6 cm s^-1, b₂ = 20 V^-1, k_-20 =10^-6 mol cm^-2 s^-1 , b_-2 = -18 V^-1 and $\varGamma$ = 10^-8 mol cm^-2. Solution species concentrations are given by [P_sol] = [Q_sol] =[
$$A _ { s o l } ^ { - }$$ ] = 100 mM.

-At the same potential (E_dc = 0.25 V vs. OCP), the total Faradaic current is given by,
i_F-dc = ______________ mA cm^-2

Question 12

The polarization plot of an electrochemical system is given below.

-If an impedance spectrum is acquired at E_dc = 0.7 V vs. OCP, then the polarization resistance is expected to be.

A) negative
B) positive
C) can be either negative or positive
D) zero.

Question 13

The polarization plot of an electrochemical system is given below.

-In the same system, if an impedance spectrum is acquired at E_dc = 1.2 V vs. OCP, then the polarization resistance is expected to be.

A) negative
B) positive
C) can be either negative or positive
D) zero.

Question 14

Consider the reaction
$$\begin{array} { l } M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } } M _ { a ds } ^ { + } + e ^ { - } \\M _ { a ds } ^ { + } + M \stackrel { k _ {2 } } { \longrightarrow } M _ { ads} ^ { + } +M _ { sol } ^ { + } + e ^ { - }\end{array}$$

The kinetic parameters are given by k₁₀ = 10^-9 mol cm^-2 s^-1, b₁ = 10 V^-1, k_-10 = 10^-8 mol cm^-2 s^-1, b_-1 = -10 V^-1, k₂₀ = 10^-8 mol cm^-2 s^-1, b₂ = 10 V^-1 and $\varGamma$ = 10^-8 mol cm^-2.

-At E_dc = 0.1 V vs. OCP, the fractional surface coverage of M_ads is given by,
$\theta$ _ss = _________

Question 15

Consider the reaction
$$\begin{array} { l } M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } } M _ { a ds } ^ { + } + e ^ { - } \\M _ { a ds } ^ { + } + M \stackrel { k _ {2 } } { \longrightarrow } M _ { ads} ^ { + } +M _ { sol } ^ { + } + e ^ { - }\end{array}$$

The kinetic parameters are given by k₁₀ = 10^-9 mol cm^-2 s^-1, b₁ = 10 V^-1, k_-10 = 10^-8 mol cm^-2 s^-1, b_-1 = -10 V^-1, k₂₀ = 10^-8 mol cm^-2 s^-1, b₂ = 10 V^-1 and $\varGamma$ = 10^-8 mol cm^-2.

-To model a system with the above mechanism, the minimum number of dc potentials at which EIS data should be taken to avoid an infinite number of solutions is __________

Question 16

In a kinetic limited electrochemical reaction, the number of loops appearing in the complex plane plot of EIS can be related to the

A) number of steps in the mechanism
B) the number of reacting species
C) the number of product species
D) the number of adsorbed intermediates

Question 17

Consider the reaction
$$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds} ^ { + } + e ^ { - } \\M _ { a ds } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { s o l } ^ { + }\end{array}$$ . Frumkin isotherm is used to describe the adsorption. The kinetic parameter values are k₁₀ = 10^-9 mol cm^-2 s^-1, b₁ = 10 V^-1, g = 15, $\beta$ ₁ = -0.5 , k₂₀ = 10^-8 mol cm^-2 s^-1, $\beta$ ₂ = +0.5 and $\varGamma$ = 10^-8 mol cm^-2.

-The maximum number of 'loops' that can appear in complex plane plots is _____________

Question 18

Consider the reaction
$$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds} ^ { + } + e ^ { - } \\M _ { a ds } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { s o l } ^ { + }\end{array}$$ . Frumkin isotherm is used to describe the adsorption. The kinetic parameter values are k₁₀ = 10^-9 mol cm^-2 s^-1, b₁ = 10 V^-1, g = 15, $\beta$ ₁ = -0.5 , k₂₀ = 10^-8 mol cm^-2 s^-1, $\beta$ ₂ = +0.5 and $\varGamma$ = 10^-8 mol cm^-2.

-In the above question, the total number of electrical elements required to model the reaction (i.e., only the Faradaic part, without considering the double-layer capacitor or solution resistance) is ____

Question 19

An impedance spectrum of an electrochemical reaction could be modeled well by the equivalent circuit given below. The solution resistance was negligible, mass transfer was rapid, and there was not film formation on the surface.
If a mechanism is proposed to explain the results, what is the minimum number of adsorbed intermediate species necessary to model the data? __________

Question 20

Choose the mechanism(s), which, for appropriate values of kinetic parameters and dc potentials, can yield negative differential impedance.

A) $$\begin{array} { l } M \rightarrow M _ { a ds } ^ { + } + e ^ { - } \\\\M _ { a ds } ^ { + } \rightarrow M _ { a d s } ^ { 2 + } + e ^ { - } \\\\M _ { a d s } ^ { + } \rightarrow M _ { s o l } ^ { 2 + }\end{array}$$
B) $$M \rightarrow M _ { s o l } ^ { + } + e ^ { - }$$
C) $$\begin{array} { l } M \rightarrow M _ { a d s } ^ { + } + e ^ { - } \\\\M _ { a ds } ^ { + } \rightarrow M _ { \text {sol } } ^ { 2 + } + e ^ { - }\end{array}$$
D) $$\begin{array} { l } M \rightarrow M _ { a ds } ^ { + } + e ^ { - } \\\\M _ { a d s } ^ { + } + M ^ { } \rightarrow M _ { a d s } ^ { + } + M _ { s o l } ^ { + }\end{array}$$

Question 21

Consider the following mechanism.
$$\begin{array} { l } M \rightarrow M _ { a ds } ^ { + } + e ^ { - } \\\\M _ { a d s } ^ { + } \rightarrow M _ { a d i } ^ { 2 + } + e ^ { - } \\\\M _ { a d s} ^ { + } \rightarrow M _ { s o l } ^ { 2 + }\end{array}$$
The faradaic impedance of this system is to be modeled using the Maxwell type circuit with resistances and capacitances. Apart from polarization resistance, how many Maxwell pairs are necessary to adequately model an impedance spectrum from this system? ________
At how many potentials should EIS be acquired to eliminate the possibility of an infinite number of solutions _________

Question 22

A Frumkin isotherm model will reduce to Langmuir isotherm when parameter "g" is _____

Question 23

Temkin model describes the relationship between _______ and fractional surface coverage

A) rate constant
B) equilibrium constant
C) potential
D) current

Question 24

Consider the reaction $$\left[ \mathrm { Fe } ( \mathrm { CN } ) _ { 6 } \right] ^ { 4 - } \underset { k _ { - 1 } } { \longleftarrow } \left[ \mathrm { Fe } ( \mathrm { CN } ) _ { 6 } \right] ^ { 3 - } + e ^ { - }$$
The net reaction rate is given by

A) $$k _ { 1 } \left[ F e ^ { 2 + } \right]$$
B) $$k _ { 1 } \left[ F e ^ { 2 + } \right] - k _ { - 1 } \left[ F e ^ { 3 + } \right]$$
C) $$k _ { 1 } \left[ F e ^ { 2 + } \right] + k _ { - 1 } \left[ F e ^ { 3 + } \right]$$
D) none of the above

Question 25

The following impedance spectrum was obtained for an electrochemical system.
Which of the following mechanisms can be considered to describe the electrochemical system?

A) $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds } ^ { + } + e ^ { - } \\\\M _ { a ds } ^ { + } + M \stackrel { k _ { 2 } } { \longrightarrow } M _ { a ds } ^ { + } + M _ { s o l } ^ { 2 + } + 2 e ^ { - }\end{array}$$
B) $$\begin{array} { l } M \stackrel { x _ { 1 } } { \longrightarrow } M _ { ads } ^ { + } + e ^ { - } \\\\M + M _ { a d s } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { s d } ^ { 2 + } + M + e ^ { - }\end{array}$$
C) $$\begin{array} { l } M \stackrel { k } { \longrightarrow } M _ { a ds} ^ { + } + e ^ { - } \\\\M _ { ads } ^ { + } \stackrel { k _ { 3 } } { \longrightarrow } M _ { ad s } ^ { 2 + } + e ^ { - } \\\\M _ { ads } ^ { 2 + } \stackrel { k _ { 3 } } { \longrightarrow } M _ { s o l } ^ { 2 + }\end{array}$$
D) $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds} ^ { + } + e ^ { - } \\\\M _ { a ds } ^ { + } \stackrel { k _ { 3 } } { \longrightarrow } M _ { s o l } ^ { 2 + } + e ^ { - } \\\\M \stackrel { k _ { 3 } } { \longrightarrow } M _ { so l } ^ { 2 + } + 2 e ^ { - }\end{array}$$

Question 26

A unique method of representing impedance spectrum is

A) Voigt representation
B) Maxwell representation
C) Ladder representation
D) Zero-pole representation

Question 27

Consider the following elementary reaction $$M \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } }M _ { s ol } ^ { 2 + } + 2 e ^ { - }$$

where M is metal and
$$M _ { \text {sol } } ^ { 2 + }$$
is metal ion in solution, F denotes Faraday constant. The net faradaic current density due to metal dissolution is

A) $$2 F \left( k _ { 1 } \left[ M _ { s d } ^ { + } \right] - k _ { - 1 } \right)$$
B) $$2 F \left\{ k _ { 1 } - k _ { - 1 } \left[ M _ { s o l } ^ { 2 + } \right] \right\}$$
C) $$F \left\{ k _ { 1 } - k _ { - 1 } \left[ M _ { s o l } ^ { 2 + } \right] \right\}$$
D) $$2 F \left\{ k _ { 1 } + k _ { - 1 } \left[ M _ { s o l } ^ { 2 + } \right] \right\}$$

Question 28

Consider the reaction given by $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { ads } ^ { + } + e ^ { - } \\\\M _ { a d s} ^ { + } \frac { k _ { 2 } } { \longleftarrow k _ { - 2 } } M _ { s o l } ^ { 2 + } + e ^ { - }\end{array}$$ .

-In standard notation, the fractional surface coverage ( $\theta$ ) of the adsorbed intermediate $$M _ { a ds } ^ { + }$$
is given by

A) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { 2 } \theta - k _ { - 2 } C _ { M _ { a d } ^ { 2 + } }$$
B) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { 2 } \theta + k _ { - 2 } C _ { M _ { sol } ^ { +2} } ( 1 - \theta )$$
C) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { 2 } \theta$$
D) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { - 2 } C _ {M_ {sol } ^ { + 2 } }$$

Question 29

Consider the reaction given by $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { ads } ^ { + } + e ^ { - } \\\\M _ { a d s} ^ { + } \frac { k _ { 2 } } { \longleftarrow k _ { - 2 } } M _ { s o l } ^ { 2 + } + e ^ { - }\end{array}$$ .

-In the same mechanism, the steady-state fractional surface coverage of the intermediate is given by

A) $$\theta _ { s s } = \frac { k _ { 1 \dot { dc } } } { k _ { 1 \dot {dc } } + k _ { 2 dc } }$$
B) $$\theta _ { s s } = \frac { k _ { 1 \dot {dc } } } { k _ { \mathrm { dc } } + k _ { 2 \dot { dc } } + k _ { - 2 \dot {dc } } }$$
C) $$\theta _ { s s } = \frac { k _ { 1dc } + k _ { - 2dc } C _ { M _ { sol} ^ {+2} } } { k _ { 1dc } + k _ { 2 dc } + k _ {- 2 dc} C _ { M _ {sol} ^ { +2 }} }$$
D) $$\theta _ { s s } = \frac { k _ { 1dc } - k _ { - 2dc} C _ { M _ { s ol } ^ { +2 } } } { k _ { 1 dc} + k _ { 2dc} + k _ { - 2dc } C _ { M _ {sol} ^ { +2 } } }$$

Question 30

Consider the reaction given by $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { ads } ^ { + } + e ^ { - } \\\\M _ { a d s} ^ { + } \frac { k _ { 2 } } { \longleftarrow k _ { - 2 } } M _ { s o l } ^ { 2 + } + e ^ { - }\end{array}$$ .

-In the same mechanism, the faradaic current is given by

A) $$i _ { F } = F \left[ k _ { 1 } ( 1 - \theta ) \right]$$
B) $$i _ { F } = F \left[ k _ { 1 } ( 1 - \theta ) + k _ { 2 } \theta - k _ { - 2 } ( 1 - \theta ) C _ { M _ { \mathbf { sol} } ^ { +2 } } \right]$$
C) $$i _ { F } = F \left[ k _ { 1 } ( 1 - \theta ) - k _ { 2 } \theta + k _ { - 2 } ( 1 - \theta ) C _ { M _ { \mathbf { sol } } ^ { +2 } } \right]$$
D) $$i _ { F } = F \left[ k _ { 1 } ( 1 - \theta ) + k _ { 2 } \theta + k _ { - 2 } ( 1 - \theta ) C _ { M _ { sol} ^ {{ +2 } } } \right]$$

Question 31

Consider the reaction given by $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { ads } ^ { + } + e ^ { - } \\\\M _ { a d s} ^ { + } \frac { k _ { 2 } } { \longleftarrow k _ { - 2 } } M _ { s o l } ^ { 2 + } + e ^ { - }\end{array}$$ .

-In the same mechanism, the value of $$\frac { d \theta } { d E }$$
is given by

A) $\frac {(b_{1}k_{1dc}(1-\theta _ { s s })-{b_{2}k_{2dc}}\theta _ { s s } +b_{-2}{k_{-2dc}C_{M^{+2}_{sol}}(1-\theta _ { s s })}}{k_{1dc}+k_{2dc}+{k_{-2d}C_{M^{+2}_{sol}}+{j??}}}$
B) $$\frac { \left( b _ { 1 } k _ { 1 dc} \left( 1 - \theta _ { s s } \right) - b _ { 2 } k _ { 2{ dc } } \theta _ { ss } \right) } { \left( k _ { 1 { dc } } + k _ { 2 dc } + k _ { - 2 dc } C _ {M _ { s ol { } } ^ { +2 } } + j \omega \Gamma \right) }$$
C) $\frac{\left(b_{1} k_{1dc}\left(1-\theta_{s s}\right)-b_{2} k_{2{dc}} \theta_{ss}+b_{-2} k_{-2 {dc}} C_{M_{sol}^{+2}}\right)}{\left(k_{1 {dc}}+k_{2{dc}}+k_{-2 {dc}} C_{M_{{ sol}}^{+2}}+j \omega \Gamma\right)}$

D) $\frac {(b_{1}k_{1dc}(1-\theta _ { s s })+{b_{2}k_{2dc}}\theta _ { s s } -b_{-2}{k_{-2dc}C_{M^{+2}_{sol}}(1-\theta _ { s s })}}{k_{1dc}+k_{2dc}+{k_{-2d}C_{M^{+2}_{sol}}+{j??}}}$

Question 32

Consider the reaction given by $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { ads } ^ { + } + e ^ { - } \\\\M _ { a d s} ^ { + } \frac { k _ { 2 } } { \longleftarrow k _ { - 2 } } M _ { s o l } ^ { 2 + } + e ^ { - }\end{array}$$ .

-In the same mechanism, the faradaic impedance (Z_F) is given by $$i _ { F } = F \left[ k _ { 1 } ( 1 - \theta ) + k _ { 2 } \theta - k _ { - 2 } ( 1 - \theta ) C _ { M _ { \mathbf { sol } } ^ { +2 } } \right]$$

A) $$\left( Z _ { F } \right) ^ { - 1 } = F \left( b _ { 1 } k _ { 1 dc } \left( 1 - \theta _ { ss } \right) + b _ { 2 } k _ { 2 d { c } } \theta _ { ss } - b _ { - 2 } k _ { - 2 d c } C _ { M _ {sol } ^ { +2 } } \left( 1 - \theta _ { s s } \right) - \left( k _ { 1 d c } - k _ { 2 dc } + k _ { - 2 d c } C _ { M _ {sol} ^ {+ 2 } } \right) \frac { d \theta } { d E } \right)$$
B) $$\left( Z _ { F } \right) ^ { - 1 } = F \left( b _ { 1 } k _ { 1 d c } \left( 1 - \theta _ { ss } \right) + b _ { 2 } k _ { 2 d { c } } \theta _ { ss } - b _ { - 2 } k _ { - 2 d c } C _ { M _ {sol } ^ { +2 } } \left( 1 - \theta _ { s s } \right) - \left( k _ { 1 d c } - k _ { 2 dc } + k _ { - 2 d c } C _ { M _ {sol} ^ {+ 2 } } \right) \frac { d \theta } { d E } \right)$$
C) $$\left( Z _ { F } \right) ^ { - 1 } = F \left( b _ { 1 } k _ { 1 { dc } } \left( 1 - \theta _ { s s } \right) + b _ { 2 } k _ { 2 {dc } } \theta _ { ss } - \left( k _ { 1 { dc } } - k _ { 2 d { c } } + k _ { - 2 { dc } } C _ { M^{+2} _ { { sol } } } \right) \frac { d \theta } { d E } \right)$$
D) $$\left( Z _ { F } \right) ^ { - 1 } = F \left( b _ { 1 } k _ { 1 d c } \left( 1 - \theta _ { ss } \right) + b _ { 2 } k _ { 2 d { c } } \theta _ { ss } - b _ { - 2 } k _ { - 2 d c } C _ { M _ {sol } ^ { +2 } } \left( 1 - \theta _ { s s } \right) +\left( k _ { 1 d c } - k _ { 2 dc } + k _ { - 2 d c } C _ { M _ {sol} ^ {+ 2 } } \right) \frac { d \theta } { d E } \right)$$

Question 33

Consider the reaction given by $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { ads } ^ { + } + e ^ { - } \\\\M _ { a d s} ^ { + } \frac { k _ { 2 } } { \longleftarrow k _ { - 2 } } M _ { s o l } ^ { 2 + } + e ^ { - }\end{array}$$ .

-The complex plane plot of impedance spectra of the above reaction can exhibit at the most ______ loops

Question 34

Consider the reaction given by $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { ads } ^ { + } + e ^ { - } \\\\M _ { a d s} ^ { + } \frac { k _ { 2 } } { \longleftarrow k _ { - 2 } } M _ { s o l } ^ { 2 + } + e ^ { - }\end{array}$$ .

-For the above mechanism, the mid and low-frequency data, in the complex plane plot can exhibit

A) capacitive loop
B) inductive loop
C) Warburg behavior
D) none of the above

Question 35

Negative real values of impedance indicate that

A) there is a problem in the measurement
B) when a potential is applied, current flows in the opposite direction
C) when potential is increased, current decreases
D) the phase difference between the potential and current is 180 °

Question 36

The polarization plot of an electrochemical system is given below. An impedance spectrum is acquired at some dc bias and shows hidden negative impedance. The dc bias at which the spectrum was acquired could be

A) 0.4 V
B) 0.8 V
C) 1.2 V
D) none of the above

Question 37

Consider the reaction $$\begin{array} { l } P _ { s o l }\underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } }Q _ { - s o l } + e ^ { - } \\A _ { s ol } ^ { - } \underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } A _ { a d s } + e ^ { - } \\\end{array}$$


-The mass balance equation for fractional surface coverage of A_ads is given by

A) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } \left[ P _ { s d } \right] - k _ { - 1 } \left[ Q _ { s ol } \right] + k _ { 2 } \left[ A _ { s o l } ^ { - } \right] - k _ { - 2 } \theta$$
B) $$\Gamma \frac { d \theta } { d t } = k _ { 2 } \left[ A _ { s d } ^ { - } \right] ( 1 - \theta ) - k _ { - 2 } \theta$$
C) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } \left[ P _ { s o l } \right] ( 1 - \theta ) - k _ { - 1 } \left[ Q _ { s o l } \right] \theta + k _ { 2 } \left[ A _ { s o l } ^ { - } \right] ( 1 - \theta ) - k _ { - 2 } \theta$$
D) $$\Gamma \frac { d \theta } { d t } = k _ { 2 } \left[ A _ { s ol} ^ { - } \right] - k _ { - 2 } \theta$$

Question 38

Consider the reaction $$\begin{array} { l } P _ { s o l }\underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } }Q _ { - s o l } + e ^ { - } \\A _ { s ol } ^ { - } \underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } A _ { a d s } + e ^ { - } \\\end{array}$$


-In the same reaction, the equation for fractional surface coverage of A_ads is given by

A) $$\frac { k _ { 2 d c } \left[ A _ { s d } ^ { - } \right] } { k _ { 1 d \dot { k } } \left[ P _ { s o l } \right] - k _ { - 1 } \left[ Q _ { s o l } \right] + k _ { 2 d c } \left[ A _ { s o l } ^ { - } \right] + k _ { - 2 d c } }$$
B) $$\frac { k _ { 1 { dc} } \left[ P _ { s o l } \right] + k _ { 2 {dc } } \left[ A _ { sol } ^ { - } \right] } { k _ { 1 { dc } } \left[ P _ { s o l ] } \right] - k _ { - 1 } \left[ Q _ { s o l } \right] k _ { 2 { dc } } \left[ A _ { s ol } ^ { - } \right] + k _ { - 2 { dc } } }$$
C) $$\frac { k _ { 1 { dc } } \left[ P _ { s o l } \right] - k _ { - 1 } \left[ Q _ { s o l } \right] + k _ { 2{ dc } } \left[ A _ { s o l } ^ { - } \right] } { k _ { 1 \dot { k } } \left[ P _ { s o l } \right] - k _ { - 1 } \left[ Q _ { s o l } \right] + k _ { 2{dc } } \left[ A _ { s o l } ^ { - } \right] + k _ { - 2 { dc } } }$$
D) $$\frac { k _ { 2dc } \left[ A _ { s o l } ^ { - } \right] } { k _ { 2 dc } \left[ A _ { s o l } ^ { - } \right] + k _ { - 2 dc } }$$

Question 39

Consider the reaction $$\begin{array} { l } P _ { s o l }\underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } }Q _ { - s o l } + e ^ { - } \\A _ { s ol } ^ { - } \underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } A _ { a d s } + e ^ { - } \\\end{array}$$


-In the same reaction, the faradaic current is given by

A) $$i _ { F } = F \left\{ k _ { 1 } \left[ P _ { s o l } \right] ( 1 - \theta ) - k _ { - 1 } \left[ Q _ { s o l } \right] ( 1 - \theta ) + k _ { 2 } \left[ A _ { s o l } ^ { - } \right] ( 1 - \theta ) - k _ { - 2 } \theta \right\}$$
B) $$i _ { F } = F \left\{ k _ { 1 } \left[ P _ { s o l } \right] ( 1 - \theta ) - k _ { - 1 } \left[ Q _ { s o l } \right] \theta + k _ { 2 } \left[ A _ { s ol } ^ { - } \right] ( 1 - \theta ) - k _ { - 2 } \theta \right\}$$
C) $$i _ { F } = F \left\{ k _ { 1 } \left[ P _ { \text {sol } } \right] ( 1 - \theta ) - k _ { - 1 } \left[ Q _ { s o l } \right] ( 1 - \theta ) + k _ { 2 } \left[ A _ { s o l } ^ { - } \right] - k _ { - 2 } \theta \right\}$$
D) $$i _ { F } = F \left\{ k _ { 2 } \left[ A _ { s a l } ^ { - } \right] ( 1 - \theta ) - k _ { - 2 } \theta \right\}$$

Question 40

Consider the reaction $$\begin{array} { l } P _ { s o l }\underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } }Q _ { - s o l } + e ^ { - } \\A _ { s ol } ^ { - } \underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } A _ { a d s } + e ^ { - } \\\end{array}$$


-In the same reaction, the expression for $$\frac { d \theta } { d E }$$
is given by

A) $$\frac { d \theta } { d E } = \frac { b _ { 2 } k _ { 2dc } \left[ A _ { so l } ^ { - } \right] - b _ { - 2 } k _ { - 2 dc} } { k _ { 2 dc } \left[ A _ { s ol } ^ { - } \right] + k _ { - 2 { dc} } + j \omega \Gamma }$$
B) $$\frac { d \theta } { d E } = \frac { b _ { 2 } k _ { 2 dc } \left[ A _ { s ol } ^ { - } \right] \left( 1 - \theta _ { ss } \right) - b _ { - 2 } k _ { - 2 dc } \theta _ { s s } } { k _ { 2 d c} \left[ A _ { so l } ^ { - } \right] \left( 1 - \theta _ { s s } \right) + k _ { - 2 dc } \theta _ { ss } + j \omega \Gamma }$$
C) $$\frac { d \theta } { d E } = \frac { b _ { 2 } k _ { 2dc } \left[ A _ { s o l } ^ { - } \right] \left( 1 - \theta _ { s s } \right) - b _ { - 2 } k _ { - 2 dc } \theta _ { s s } } { k _ { 2 dc } \left[ A _ { s o l } ^ { - } \right] + k _ { - 2 dc } + j \omega \Gamma }$$
D) $$\frac { d \theta } { d E } = \frac { b _ { 2 } k _ { 2 dc } \left[ A _ { s o l } ^ { - } \right] - b _ { - 2 } k _ { - 2 d c } } { k _ { 2 d \dot { } } \left[ A _ { s o l } ^ { - } \right] \left( 1 - \theta _ { s s } \right) + k _ { - 2 d c } \theta _ { s s} + j \omega \Gamma }$$

Question 41

Consider the reaction $$\begin{array} { l } P _ { s o l }\underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } }Q _ { - s o l } + e ^ { - } \\A _ { s ol } ^ { - } \underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } A _ { a d s } + e ^ { - } \\\end{array}$$


-In the same mechanism, the charge transfer resistance (R_t) is given by

A) $$\left( R _ { t } \right) ^ { - 1 } = F \left\{ b _ { 1 } k _ { 1 { d c} } \left[ P _ { s o l } \right] \left( 1 - \theta _ { s s } \right) - b _ { - 1 } k _ { - 1 { dc } } \left[ Q _ { s o l } \right] \left( 1 - \theta _ { s s } \right) \right\}$$
B) $$\left( R _ { t } \right) ^ { - 1 } = F \left\{ \begin{array} { l } b _ { 1 } k _ { 1 dc } \left[ P _ { so l } \right] \left( 1 - \theta _ { s s } \right) - b _ { - 1 } k _ { - 1 { dc} } \left[ Q _ { s o l } \right] \left( 1 - \theta _ { ss} \right) \\+ b _ { 2 } k _ { 2 { dc } } \left[ A _ { s o l } ^ { - } \right] \left( 1 - \theta _ { s s } \right) - b _ { - 2 } k _ { - 2 { dc } } \theta _ { s s }\end{array} \right\}$$
C) $$\left( R _ { t } \right) ^ { - 1 } = F \left\{ b _ { 1 } k _ { 1 d c} \left[ P _ { s ol } \right] - b _ { - 1 } k _ { - 1 dc} \left[ Q _ { s o l } \right] + b _ { 2 } k _ { 2 dc } \left[ A _ { s o l } ^ { - } \right] - b _ { - 2 } k _ { - 2 d c } \right\}$$
D) $$\left( R _ { t } \right) ^ { - 1 } = F \left\{ b _ { 2 } k _ { 2 { dc} } \left[ A _ { s ol } ^ { - } \right] \left( 1 - \theta _ { s s } \right) - b _ { - 2 } k _ { - 2 { dc} } \theta _ { ss } \right\}$$

Question 42

Consider the reaction
-If EIS is acquired for the above mechanism, the maximum number of loops that can manifest in a complex plane plot is _____

Question 43

Consider the reaction
-For the above mechanism, the number of electrical elements (including polarization resistance) required to model the Faradaic impedance is _____

Question 44

Consider the reaction
-The minimum number of dc potentials at which EIS must be acquired to avoid an infinite number of solutions is ______

Question 45

Consider the reaction $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds } ^ { + } + e ^ { - } \\M + M _ { a d s } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { a d s } ^ { + } + M _ { s o l } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + } \stackrel { k _ { s } } { \longrightarrow } M _ { s o l } ^ { + }\end{array}$$

-The mass balance equation for fractional surface coverage of $$M _ { a d s} ^ { + }$$
is given by

A) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { 2 } \theta ( 1 - \theta ) + k _ { 3 } \theta$$
B) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { 2 } \theta ( 1 - \theta )$$
C) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { 2 } \theta ( 1 - \theta ) - k _ { 3 } \theta$$
D) $$\Gamma \frac { d \theta } { d t } = k _ { 1 } ( 1 - \theta ) - k _ { 3 } \theta$$

Question 46

Consider the reaction $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds } ^ { + } + e ^ { - } \\M + M _ { a d s } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { a d s } ^ { + } + M _ { s o l } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + } \stackrel { k _ { s } } { \longrightarrow } M _ { s o l } ^ { + }\end{array}$$

-In the same reaction, the equation for fractional surface coverage of A_ads is given by

A) $$\frac { k _ { 1 { dc } } } { k _ { 1 { dc} } + k _ { 2 dc } + k _ { 3 {dc } } }$$
B) $$\frac { k _ { 1 d c } } { k _ { 1 dc} + k _ { 3 d c } }$$
C) $$\frac { k _ { 3 { dc } } } { k _ { 1 { dc } } + k _ { 2 d \dot { } } + k _ { 3 { dc } } }$$
D) $$\frac { k _ { 3 { dc } } } { k _ { 1 {dc } } + k _ { 3 d c} }$$

Question 47

Consider the reaction $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds } ^ { + } + e ^ { - } \\M + M _ { a d s } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { a d s } ^ { + } + M _ { s o l } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + } \stackrel { k _ { s } } { \longrightarrow } M _ { s o l } ^ { + }\end{array}$$

-In the same reaction, the faradaic current is given by

A) $$i _ { F } = F \left\{ k _ { 1 } ( 1 - \theta ) + k _ { 2 } \theta ( 1 - \theta ) \right\}$$
B) $$i _ { F } = F \left\{ k _ { 1 } ( 1 - \theta ) + k _ { 2 } \theta ( 1 - \theta ) + k _ { 3 } \theta \right\}$$
C) $$i _ { F } = F \left\{ k _ { 1 } ( 1 - \theta ) - k _ { 2 } \theta ( 1 - \theta ) - k _ { 3 } \theta \right\}$$
D) $$i _ { F } = F \left\{ k _ { 1 } ( 1 - \theta ) - k _ { 3 } \theta \right\}$$

Question 48

Consider the reaction $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds } ^ { + } + e ^ { - } \\M + M _ { a d s } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { a d s } ^ { + } + M _ { s o l } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + } \stackrel { k _ { s } } { \longrightarrow } M _ { s o l } ^ { + }\end{array}$$

-In the same reaction, the expression for $$\frac { d \theta } { d E }$$
is given by

A) $$\frac { d \theta } { d E } = \frac { b _ { 1 } k _ { 1 d c } \left( 1 - \theta _ { s s } \right) - b _ { 2 } k _ { 2 { dc } } \theta _ { ss } \left( 1 - \theta _ { s s } \right) } { k _ { 1 { dc } } + k _ { 2 d c} + j \omega \Gamma }$$
B) $$\frac { d \theta } { d E } = \frac { b _ { 1 } k _ { 1 dc } \left( 1 - \theta _ { s s } \right) - b _ { 2 } k _ { 2 { dc } } \theta _ { ss } \left( 1 - \theta _ { s s } \right) } { k _ { 1 dc } + k _ { 2 d c} + k _ { 3 } + j \omega \Gamma }$$
C) $$\frac { d \theta } { d E } = \frac { b _ { 1 } k _ { 1 dc } \left( 1 - \theta _ { ss} \right) } { k _ { 1dc } + k _ { 3 } + j \omega \Gamma }$$
D) $$\frac { d \theta } { d E } = \frac { b _ { 1 } k _ { 1 dc } \left( 1 - \theta _ { s s } \right) - b _ { 2 } k _ { 2 dc } \theta _ { s s } } { k _ { 1 dc } + k _ { 2 dc } + k _ { 3 } + j \omega \Gamma }$$

Question 49

Consider the reaction $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds } ^ { + } + e ^ { - } \\M + M _ { a d s } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { a d s } ^ { + } + M _ { s o l } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + } \stackrel { k _ { s } } { \longrightarrow } M _ { s o l } ^ { + }\end{array}$$

-In the same mechanism, the charge transfer resistance (R_t) is given by

A) $$\left( R _ { t } \right) ^ { - 1 } = F \left\{ b _ { 1 } k _ { 1 dc } \left( 1 - \theta _ { ss } \right) - b _ { 2 } k _ { 2 dc } \left( 1 - \theta _ { s s } \right) \theta _ { s s } \right\}$$
B) $$\left( R _ { t } \right) ^ { - 1 } = F \left\{ b _ { 1 } k _ { 1 dc} \left( 1 - \theta _ { ss } \right) + b _ { 2 } k _ { 2dc } \left( 1 - \theta _ { s s } \right) \theta _ { s s } \right\}$$
C) $$\left( R _ { t } \right) ^ { - 1 } = F \left\{ b _ { 1 } k _ { 1 d c } \left( 1 - \theta _ { s s } \right) + b _ { 2 } k _ { 2 dc } \theta _ { s s } \right\}$$
D) $$\left( R _ { t } \right) ^ { - 1 } = F \left( b _ { 1 } k _ { 1 d c } \left( 1 - \theta _ { s s } \right) - b _ { 2 } k _ { 2 dc } \theta _ { s s } \right\}$$

Question 50

Consider the reaction
-If EIS is acquired for the above mechanism, the maximum number of loops that can manifest in a complex plane plot is _____

Question 51

Consider the reaction
-For the above mechanism, the number of electrical elements (including polarization resistance) required to model the Faradaic impedance is _____

Question 52

Consider the reaction
-The minimum number of dc potentials at which EIS must be acquired to avoid an infinite number of solutions is ______

Question 53

Consider the reaction $$\begin{array} { l } M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds } ^ { + } + e ^ { - } \\M + M _ { a d s } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { a d s } ^ { + } + M _ { s o l } ^ { + } + e ^ { - } \\M _ { a d s } ^ { + } \stackrel { k _ { s } } { \longrightarrow } M _ { s o l } ^ { + }\end{array}$$

-Choose the mechanism(s), which, for appropriate values of kinetic parameters and dc potentials, can yield negative differential impedance.

A) $$\begin{array} { l } M \rightarrow M _ { a ds } ^ { + } + e ^ { - } \\\\M _ { a ds} ^ { + } \rightarrow M _ { a d s} ^ { 2 + } + e ^ { - } \\\\M _ { a ds } ^ { + } \rightarrow M _ { so l } ^ { 2 + }\end{array}$$
B) $$P _ { s ol } \stackrel { k _ { 1 } } { \underset { k _ { - 1 } } { \rightleftarrows } } Q _ { s o l } + e ^ { - }$$
C) $$\begin{array} { l } M \rightarrow M _ { ad s } ^ { + } + e ^ { - } \\\\M _ { a ds } ^ { + } \rightarrow M _ { \text {sol } } ^ { 2 + } + e ^ { - }\end{array}$$
D) $$\begin{array} { l } P _ { s o l } \underset { k _ { - 1 } } { \stackrel { k _ { 1 } } { \rightleftarrows } } Q _ { - s o l } + e ^ { - } \\A _ { s ol } ^ { - } \underset { k _ { - 2 } } { \stackrel { k _ { 2 } } { \rightleftarrows } } A _ { a d c } + e ^ { - } \\\end{array}$$