Question 1

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 (Rt) is given by

Accepted Answer

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

Question 2

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 kS1U1B110S1U1B0 = 10S1U1P1-9 S1S1P0mol cmS1U1P1-2S1S1P0 sS1U1P1-1S1S1P0, bS1U1B11S1U1B0 = 10 VS1U1P1-1S1S1P0, g = 15, $\beta$S1U1B11S1U1B0 = -0.5 , kS1U1B120S1U1B0 = 10S1U1P1-8S1S1P0 mol cmS1U1P1-2S1S1P0 sS1U1P1-1S1S1P0, $\beta$S1U1B12S1U1B0 = +0.5 and $\varGamma$ = 10S1U1P1-8S1S1P0 mol cmS1U1P1-2S1S1P0.
-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 ____

Accepted Answer

3 (exact)

Question 3

Consider the reaction $$\begin{array} { l } 
M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds } ^ { + } + e ^ { - } \
M + M _ { a d s } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { a d s } ^ { + } + M _ { s o l } ^ { + } + e ^ { - } \
M _ { a d s } ^ { + } \stackrel { k _ { s } } { \longrightarrow } M _ { s o l } ^ { + }
\end{array}$$
-For the above mechanism, the number of electrical elements (including polarization resistance) required to model the Faradaic impedance is _____

Accepted Answer

3(exact)

Question 4

Consider the reaction $$\begin{array} { l } 
M \stackrel { k _ { 1 } } { \longrightarrow } M _ { a ds } ^ { + } + e ^ { - } \
M + M _ { a d s } ^ { + } \stackrel { k _ { 2 } } { \longrightarrow } M _ { a d s } ^ { + } + M _ { s o l } ^ { + } + e ^ { - } \
M _ { a d s } ^ { + } \stackrel { k _ { s } } { \longrightarrow } M _ { s o l } ^ { + }
\end{array}$$
-If EIS is acquired for the above mechanism, the maximum number of loops that can manifest in a complex plane plot is _____

Accepted Answer

The answer of Consider the reaction \[\begin{array} { l }...

Question 5

The polarization plot of an electrochemical system is given below.
  
-If an impedance spectrum is acquired at Edc = 0.7 V vs. OCP, then the polarization resistance is expected to be.

Accepted Answer

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

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 current is given by

Accepted Answer

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)  $$i _ { F } = F \left[ k _ { 1 } ( 1 - \theta ) - k _ { - 1 } \theta - k _ { 2 } \theta \right]$$ 
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 7

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 (ZF) is given by

Accepted Answer

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)  $$\left( Z _ { F } \right) ^ { - 1 } = F \left( b _ { 1 } k _ { 1 d \dot { c} } \left( 1 - \theta _ { s s } \right) - b _ { - 1 } k _ { - 1 \dot { dc } } \theta _ { ss } + \left( k _ { 1 d \dot { c} } + k _ { - 1 d \dot {c } } \right) \frac { d \theta } { d E } \right)$$ 
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 8

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 kS1U1B110S1U1B0 = 10S1U1P1-5 S1S1P0cm sS1U1P1-1S1S1P0, bS1U1B11S1U1B0 = 20 VS1U1P1-1S1S1P0, kS1U1B120S1U1B0 = 10S1U1P1-6S1S1P0 cm sS1U1P1-1S1S1P0, bS1U1B12S1U1B0 = 20 VS1U1P1-1S1S1P0, kS1U1B1-20S1U1B0 =10S1U1P1-6S1S1P0 mol cmS1U1P1-2S1S1P0 sS1U1P1-1S1S1P0 , bS1U1B1-2S1U1B0 = -18 VS1U1P1-1S1S1P0 and $\varGamma$ = 10S1U1P1-8S1S1P0 mol cmS1U1P1-2S1S1P0. Solution species concentrations are given by [PS1U1B1solS1U1B0] = [QS1U1B1solS1U1B0] =[
 $$A _ { s o l } ^ { - }$$ ] = 100 mM.
-At the same potential (Edc = 0.25 V vs. OCP), the total Faradaic current is given by,
iF-dc = ______________ mA cm-2

Accepted Answer

6.13 (from

Question 9

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 kS1U1B110S1U1B0 = 10S1U1P1-S1S1P0S1U1P19S1S1P0S1U1P1 S1S1P0mol cmS1U1P1-2S1S1P0 sS1U1P1-1S1S1P0, bS1U1B11S1U1B0 = 10 VS1U1P1-1S1S1P0, kS1U1B1-1S1U1B0S1U1B10S1U1B0 = 10S1U1P1-S1S1P0S1U1P18S1S1P0 mol cmS1U1P1-S1S1P0S1U1P12S1S1P0 sS1U1P1-1S1S1P0, bS1U1B1-1S1U1B0 = -10 VS1U1P1-1S1S1P0, kS1U1B120S1U1B0 = 10S1U1P1-8S1S1P0 mol cmS1U1P1-2S1S1P0 sS1U1P1-1S1S1P0, bS1U1B12S1U1B0 = 10 VS1U1P1-1S1S1P0 and$\varGamma$ = 10S1U1P1-8S1S1P0 mol cmS1U1P1-2S1S1P0.
-At Edc = 0.1 V vs. OCP, the fractional surface coverage of Mads is given by,
$\theta$ss = _________

Accepted Answer

106 (betwe

Question 10

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 (Rt) is given by

Accepted Answer

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)  $$\left( R _ { t } \right) ^ { - 1 } = F \left\{ b _ { 2 } k _ { 2 { dc} } \left[ A _ { s ol } ^ { - } \right] \left( 1 - \theta _ { s s } \right) - b _ { - 2 } k _ { - 2 { dc} } \theta _ { ss } \right\}$$ 
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 11

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

Accepted Answer

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)  $$i _ { F } = F \left\{ k _ { 2 } \left[ A _ { s a l } ^ { - } \right] ( 1 - \theta ) - k _ { - 2 } \theta \right\}$$ 
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 12

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.

Accepted Answer

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

Question 13

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 _________

Accepted Answer

2 (exact),

Question 14

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

Accepted Answer

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)  $$2 F \left\{ k _ { 1 } + k _ { - 1 } \left[ M _ { s o l } ^ { 2 + } \right] \right\}$$ 
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 15

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 Aads is given by

Accepted Answer

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)  $$\Gamma \frac { d \theta } { d t } = k _ { 2 } \left[ A _ { s ol} ^ { - } \right] - k _ { - 2 } \theta$$ 
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 16

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

Accepted Answer

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??}}}$ 
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 17

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

Accepted Answer

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)  $$\theta _ { ss } = \frac { k _ { 1 \dot { dc } } - k _ { - 1 \dot { dc } } } { k _ { 1 \dot { dc } } + k _ { - 1 \dot { dc } } + k _ { 2 } + k _ { - 2 } C _ { M _ { 2a i } ^ { 2+ } } }$$ 
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)  $$\theta _ { ss } = \frac { k _ { 1 \dot { dc } } - k _ { - 1 \dot { dc } } } { k _ { 1 \dot { dc } } + k _ { - 1 \dot { dc } } + k _ { 2 } + k _ { - 2 } C _ { M _ { 2a i } ^ { 2+ } } }$$

Question 18

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 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 k1dc = ___________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.

Accepted Answer

1e-7(exact), 4.03e-5 (from 4e-

Question 19

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

Accepted Answer

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

Question 20

A unique method of representing impedance spectrum is

Accepted Answer

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

Consider the reaction M + M+ ++ -In the same mechanism, the charge transfer resistance (R_t) is given by

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

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

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.

Consider a reaction given by M + . -In the same mechanism, the faradaic current is given by

Consider a reaction given by M + . -In the same mechanism, the faradaic impedance (Z_F) is given by

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

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

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

Consider the reaction + + -The mass balance equation for fractional surface coverage of A_ads is given by

Consider the reaction given by M + + . -In the same mechanism, the value of $\frac { d \theta } { d E }$ is given by

Consider a reaction given by M + . -In the same mechanism, the steady-state fractional surface coverage of the intermediate is given by

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 unique method of representing impedance spectrum is

Introduction

Experimental Aspects

Data Validation

Data Analysis Equivalent Electrical Circuits

Eis Other Physical Phenomena

Nonlinear Eis

Filters

Exam 5: Mechanistic Analysis

Consider the reaction M + M+ ++ -In the same mechanism, the charge transfer resistance (Rt) is given by

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

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

The polarization plot of an electrochemical system is given below. -If an impedance spectrum is acquired at Edc = 0.7 V vs. OCP, then the polarization resistance is expected to be.

Consider a reaction given by M + . -In the same mechanism, the faradaic current is given by

Consider a reaction given by M + . -In the same mechanism, the faradaic impedance (ZF) is given by

Consider the reaction + + -In the same mechanism, the charge transfer resistance (Rt) is given by

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

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

Consider the reaction + + -The mass balance equation for fractional surface coverage of Aads is given by

Consider the reaction given by M + + . -In the same mechanism, the value of dθdE\frac { d \theta } { d E }dEdθ​ is given by

Consider a reaction given by M + . -In the same mechanism, the steady-state fractional surface coverage of the intermediate is given by

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 unique method of representing impedance spectrum is

Introduction

Experimental Aspects

Data Validation

Data Analysis Equivalent Electrical Circuits

Eis Other Physical Phenomena

Nonlinear Eis

Filters

Consider the reaction M + M+ ++ -In the same mechanism, the charge transfer resistance (R_t) is given by

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.

Consider a reaction given by M + . -In the same mechanism, the faradaic impedance (Z_F) is given by

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

Consider the reaction + + -The mass balance equation for fractional surface coverage of A_ads is given by

Consider the reaction given by M + + . -In the same mechanism, the value of $\frac { d \theta } { d E }$ is given by