The standard reduction potential ($E^\circ$) for the $Mn^{3+}/Mn^{2+}$ couple is highly positive ($+1.57\text{ V}$), whereas it is negative for the $Cr^{3+}/Cr^{2+}$ couple. Why?

The standard reduction potential (E°) for the Mn³⁺/Mn²⁺ couple is highly positive (+1.57 V), whereas it is negative for the Cr³⁺/Cr²⁺ couple. Why? +

Correct Answer

Mn³⁺ → Mn²⁺ is highly favourable because Mn²⁺ has a particularly stable 3d⁵ half-filled configuration, whereas Cr³⁺ → Cr²⁺ requires destroying the stable 3d³ arrangement of Cr³⁺.

Electronic Configurations

For manganese:

Mn: [Ar] 3d⁵4s²
Mn²⁺: [Ar] 3d⁵
Mn³⁺: [Ar] 3d⁴

Thus:

Mn³⁺(3d⁴) + e⁻ → Mn²⁺(3d⁵)

The product Mn²⁺ has a half-filled 3d⁵ configuration, which has extra stability due to exchange energy and symmetrical distribution of electrons. Therefore, Mn³⁺ has a strong tendency to accept an electron. Hence:

E°(Mn³⁺/Mn²⁺) = +1.57 V

What happens in Chromium?

Chromium has:

Cr: [Ar] 3d⁵4s¹
Cr³⁺: [Ar] 3d³
Cr²⁺: [Ar] 3d⁴

The reduction reaction is:

Cr³⁺(3d³) + e⁻ → Cr²⁺(3d⁴)

Cr³⁺ has a relatively stable 3d³ configuration. Reduction to Cr²⁺ gives 3d⁴, which does not gain the special half-filled d⁵ stability. Therefore, Cr³⁺ is less willing to accept an electron and the reduction is less favourable. Consequently:

E°(Cr³⁺/Cr²⁺) < 0

Why is the Difference So Large?

The standard reduction potential is determined by the overall free-energy change of the redox process. Electronic configuration is a major factor, but it is not the only factor. For Mn:

3d⁴ → 3d⁵

This produces a particularly stable half-filled d-subshell. For Cr:

3d³ → 3d⁴

This does not produce an especially stable half-filled or fully filled configuration. Thus the thermodynamic driving force for reduction is much greater for Mn³⁺ than for Cr³⁺.

JEE-Level Shortcut

Remember:

Mn³⁺ → Mn²⁺: 3d⁴ → 3d⁵ → half-filled stability → high +E°

Cr³⁺ → Cr²⁺: 3d³ → 3d⁴ → no special extra stability → low/negative E°

30 Related MCQs with Solutions

1. The electronic configuration of Mn²⁺ is:

A. 3d³

B. 3d⁴

C. 3d⁵

D. 3d⁶

Answer: C. 3d⁵

2. The configuration of Mn³⁺ is:

A. 3d³

B. 3d⁴

C. 3d⁵

D. 3d⁶

Answer: B. 3d⁴

3. Mn³⁺ reduction gives:

A. 3d³

B. 3d⁴

C. 3d⁵

D. 3d⁶

Answer: C. 3d⁵

4. Mn²⁺ is particularly stable because of:

A. 3d²

B. 3d³

C. 3d⁵

D. 3d¹⁰

Answer: C. Half-filled 3d⁵

5. The standard reduction potential of Mn³⁺/Mn²⁺ is approximately:

A. −1.57 V

B. −0.26 V

C. +1.57 V

D. 0 V

Answer: C. +1.57 V

6. A positive E° for Mn³⁺/Mn²⁺ indicates:

A. Reduction is favourable

B. Oxidation is impossible

C. No redox reaction occurs

D. Mn²⁺ is unstable

Answer: A

7. Cr³⁺ has which d-electron configuration?

A. 3d²

B. 3d³

C. 3d⁴

D. 3d⁵

Answer: B. 3d³

8. Cr²⁺ has:

A. 3d²

B. 3d³

C. 3d⁴

D. 3d⁵

Answer: C. 3d⁴

9. Which ion has a half-filled d-subshell?

A. Cr³⁺

B. Mn²⁺

C. Cr²⁺

D. Mn³⁺

Answer: B. Mn²⁺

10. The half-filled d⁵ configuration is stabilised by:

A. Exchange energy

B. Zero electron density

C. Low nuclear charge

D. Large atomic radius

Answer: A. Exchange energy

11. Reduction of Mn³⁺ involves:

A. Loss of electron

B. Gain of electron

C. Loss of proton

D. Gain of neutron

Answer: B. Gain of electron

12. Reduction of Cr³⁺ gives:

A. Cr⁺

B. Cr²⁺

C. Cr⁴⁺

D. Cr⁵⁺

Answer: B. Cr²⁺

13. Which reduction is more favourable?

A. Mn³⁺ → Mn²⁺

B. Cr³⁺ → Cr²⁺

C. Both equally

D. Neither

Answer: A

14. The unusually high E° of Mn³⁺/Mn²⁺ is mainly associated with formation of:

A. 3d³

B. 3d⁴

C. 3d⁵

D. 3d¹⁰

Answer: C. 3d⁵

15. Which configuration is especially stable among the following?

A. d⁴

B. d⁵

C. d⁶

D. d⁷

Answer: B. d⁵

16. Cr³⁺ is comparatively stable because of its:

A. d³ configuration

B. d⁵ configuration

C. d¹⁰ configuration

D. d¹ configuration

Answer: A. d³

17. Cr³⁺ → Cr²⁺ changes:

A. d³ → d²

B. d³ → d⁴

C. d⁴ → d⁵

D. d⁵ → d⁴

Answer: B

18. Which statement is correct about E°?

A. More positive E° generally means greater tendency for reduction

B. More positive E° means oxidation is always spontaneous

C. E° has no relation to redox tendency

D. E° is always zero

Answer: A

19. Mn²⁺ has how many unpaired d-electrons in the free-ion picture?

A. 1

B. 2

C. 3

D. 5

Answer: D. 5

20. Which configuration has maximum exchange energy among these?

A. d⁴

B. d⁵

C. d⁶

D. d⁸

Answer: B. d⁵

21. The standard reduction potential of Cr³⁺/Cr²⁺ is:

A. Highly positive

B. Negative

C. Exactly +1.57 V

D. Always zero

Answer: B. Negative

22. The reduction potential depends on:

A. Only electronic configuration

B. Overall thermodynamics of the redox process

C. Only atomic mass

D. Only colour

Answer: B

23. Mn³⁺ is a strong:

A. Reducing agent

B. Oxidising agent

C. Neutral molecule

D. Ligand

Answer: B. Oxidising agent
Its high positive reduction potential means it readily accepts an electron.

24. Cr²⁺ tends to act as a:

A. Strong reducing agent

B. Strong oxidising agent only

C. Noble gas

D. Non-redox species

Answer: A. Strong reducing agent

25. The stable configuration of Mn²⁺ is:

A. d²

B. d³

C. d⁵

D. d⁸

Answer: C. d⁵

26. Which transition-metal ion is strongly associated with a half-filled d-subshell?

A. Mn²⁺

B. Cr³⁺

C. Cu²⁺

D. Ni²⁺

Answer: A. Mn²⁺

27. Which change gives a half-filled d-subshell?

A. Mn³⁺ + e⁻ → Mn²⁺

B. Cr³⁺ + e⁻ → Cr²⁺

C. Fe³⁺ + e⁻ → Fe²⁺

D. Cu²⁺ + e⁻ → Cu⁺

Answer: A

28. A highly positive standard reduction potential indicates:

A. Strong tendency to gain electrons

B. Strong tendency to lose electrons

C. No electron transfer

D. Metallic bonding only

Answer: A

29. The unusual E° values of Cr and Mn are related to:

A. d-electron configurations and their relative stability

B. Only atomic size

C. Only density

D. Only melting point

Answer: A

30. The best explanation for the difference between Mn³⁺/Mn²⁺ and Cr³⁺/Cr²⁺ is:

A. Mn³⁺ reduction produces stable d⁵, whereas Cr³⁺ reduction produces d⁴

B. Both produce d⁵

C. Cr³⁺ has no d-electrons

D. Mn²⁺ has d¹⁰

Answer: A

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