JEE Advanced · Chemistry · 17. Electrochemistry

The standard reduction potential data at $25 ° C$ is given below.
$E ^o\left( Fe ^{3+}, Fe ^{2+}\right)=+0.77 V ; $
$ E ^o\left( Fe ^{2+}, Fe \right)=-0 . 44 V $
$ E ^o\left( Cu ^{2+}, Cu \right)=+0.34 V ; $
$ E ^o\left( Cu ^{+}, Cu \right)=+0.52 V $
$ E ^o\left[ O _2(g)+4 H ^{+}+4 e ^{-} \rightarrow 2 H _2 O \right]=$ $+1.23~V $
$ E ^o\left[ O _2(g)+2 H _2 O +4 e^{-} \longrightarrow \text { 4OH}^{-}\right]=$ $+0.40~V $
$ E ^o\left( Cr ^{3+}, Cr \right)=-0.74 V ; $
$ E ^o\left( Cr ^{2+}, Cr \right)=-0.91 V$
Match E^o of the redox pair in List I with the values given in List II and select the correct answer using the code given below the lists :

List I List II

A. $E^{ο} ({Fe}^{3 +}, Fe)$ P. $- 0.18 V$

B. $E^{ο} (4 H_{2} O ⇌ 4 H^{+} + 4 {OH}^{-})$ Q. $- 0.4 V$

C $E^{ο} ({Cu}^{2 +} + Cu \to 2 {Cu}^{+})$ R. $- 0.04 V$

D. $E^{ο} ({Cr}^{3 +}, {Cr}^{2 +})$ S. $- 0.83 V$

A a-r;b-q;c-s;d-p;
B a-q;b-p;c-r;d-s;
C a-s;b-p;c-r;d-q;
D a-r;b-s;c-p;d-q;

Verified Solution

Answer & Solution

Correct Answer

(D) a-r;b-s;c-p;d-q;

Step-by-step Solution

Detailed explanation

P)
$Fe ^{3+}+ e ^{-} \longrightarrow Fe ^{2+} ;\quad \Delta G _{ I }^{ o }=-1 F(0.77) $
$ Fe ^{2+}+2 e ^{-} \longrightarrow Fe ;\quad \Delta G _{ II }^{ o }=-2 F(-0.44)$
Add $\quad Fe ^{3+}+3 e ^{-} \longrightarrow Fe \quad ; \Delta G _{\text {III }}^{ o }=$ $-3 F\left( E ^{ o }\right)_{ Fe ^{3+} / Fe }$

- 3 F {(E^{o})}_{{Fe}^{3 +} / Fe} = - 0.77 F + 0.88 F

0.11 F

E_{{Fe}^{3 +} / Fe}^{o} = - \frac{0.11}{3} = - 0.037 ≅ - 0.04 V

Q.)

2 H_{2} O ⟶ O_{2 (g)} + 4 H_{(aq)}^{+} + 4 e^{-}

(Oxidation half reaction)

E^{°} = - 1.23 V

O_{2 (g)} + 2 H_{2} O + 4 e^{-} ⟶ 4 {OH}_{(aq)}^{-}

(reduction half reaction)

E^{°} = + 0.40 V

It's an electrochemical cell, adding

4 H_{2} O ⇌ 4 H^{+} + 40 H^{-}

at equilibrium

E_{cell}^{o} = - 0.83 V

R.)

\begin{matrix} 2 {Cu}_{(s)} ⟶ 2 {Cu}^{+} + 2 e^{-} & E^{0} = - 0.52 V \\ {Cu}^{2 +} + 2 e^{-} ⟶ {Cu}_{(s)} & E^{0} = 0.34 V \end{matrix}

Adding

\begin{matrix} {Cu}^{2 +} + {Cu}_{(s)} ⟶ 2 {Cu}^{+} & E_{cell}^{0} = - 0.18 V \end{matrix}

\begin{matrix} {Cr}^{3 +} + 3 e^{-} ⟶ Cr & ; & Δ G_{I}^{0} = - 3 (F) (- 0.74) \\ {Cr}^{2 +} + 2 e^{-} ⟶ Cr & ; & Δ G_{II}^{0} = - 2 (F) (- 0.91) \end{matrix}

Subtracting
$Cr ^{3+}+ e ^{-}- Cr ^{2+} \longrightarrow 0 ; $
$ Cr ^{3+}+ e ^{-} \longrightarrow Cr ^{2+} ; \Delta G ^0=-1(F)$ $\left( E _{ Cr ^{3+} / Cr ^{2+}}^0\right) $
$ - F E _{\left( Cr ^{3+} / Cr ^{2+}\right)}^0= F (3 \times 0.74-2 \times 0.91) $
$ - E _{ Cr ^{3+} / Cr ^{2+}}^0= F (2.22-1.82) $
$ E _{ Cr ^{3+} / Cr ^{2+}}=-0.40 V$

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From JEE Advanced

Match List I with List II and select the correct answer using the codes given below the lists:

	$\text{List I}$		$\text{List II}$
a.	Boltzmann constant	p.	$\left[M L^2 T^{-1}\right]$
b.	Coefficient of viscosity	q.	$\left[M L^{-1} T^{-1}\right]$
c.	Planck constant	r.	$\left[M L T^{-3} K^{-1}\right]$
d.	Thermal conductivity	s.	$\left[M L^2 T^{-2} K^{-1}\right]$

JEE Advanced 2013 Easy

Three numbers are chosen at random, one after another with replacement, from the set $S=\{1,2,3, \ldots, 100\}$. Let $p_{1}$ be the probability that the maximum of chosen numbers is at least 81 and $p_{2}$ be the probability that the minimum of chosen numbers is at most 40 .
The value of $\frac{625}{4} p_{1}$ is

JEE Advanced 2021 Medium

Explore more questions on app

	List I		List II
A.	$E^{ο} ({Fe}^{3 +}, Fe)$	P.	$- 0.18 V$
B.	$E^{ο} (4 H_{2} O ⇌ 4 H^{+} + 4 {OH}^{-})$	Q.	$- 0.4 V$
C	$E^{ο} ({Cu}^{2 +} + Cu \to 2 {Cu}^{+})$	R.	$- 0.04 V$
D.	$E^{ο} ({Cr}^{3 +}, {Cr}^{2 +})$	S.	$- 0.83 V$

	\(\text{List I}\)		\(\text{List II}\)
a.	Boltzmann constant	p.	\(\left[M L^2 T^{-1}\right]\)
b.	Coefficient of viscosity	q.	\(\left[M L^{-1} T^{-1}\right]\)
c.	Planck constant	r.	\(\left[M L T^{-3} K^{-1}\right]\)
d.	Thermal conductivity	s.	\(\left[M L^2 T^{-2} K^{-1}\right]\)