I.E. of M + is equal to? (Electron gain enthalpy of M).

1. I.E. of M⁺ is equal to? (Electron gain enthalpy of M) +

Correct Answer

The magnitude is equal, but the sign is opposite.

Detailed Solution

Consider the ionization of a gaseous M⁺ ion:

M⁺(g) → M²⁺(g) + e⁻

The energy required for this process is the second ionization enthalpy of neutral M:

IE₂(M) = H[M²⁺] + H[e⁻] − H[M⁺]

Now consider electron gain by M⁺:

M⁺(g) + e⁻ → M(g)

This is the reverse process. Therefore, by the principle of energy conservation:

IE₂(M) = −Δ_egH(M⁺)

So, if the question literally means electron gain enthalpy of M⁺, then:

IE of M⁺ = − Electron Gain Enthalpy of M⁺

Important: If the question says only "Electron gain enthalpy of M" (neutral M), then it is not generally equal to the ionization enthalpy of M⁺. The species must be the same for the reverse-process relation.

Conceptual Shortcut

For a reversible pair:

M(g) + e⁻ → M⁻(g)

and

M⁻(g) → M(g) + e⁻

the enthalpy changes have the same magnitude but opposite signs. Thus:

Reverse reaction → same magnitude + opposite sign

For the exact question:

M⁺ + e⁻ ⇌ M

therefore:

IE₂(M) = −Δ_egH(M⁺)

30 Related MCQs with Solutions

1. Ionization of M⁺ produces:

A. M

B. M²⁺ + e⁻

C. M⁻

D. M + e⁻

Answer: B

2. Ionization enthalpy of M⁺ is actually:

A. IE₁(M)

B. IE₂(M)

C. Electron affinity of M

D. Zero

Answer: B. IE₂(M)

3. The reverse of M⁺ + e⁻ → M is:

A. M → M⁺ + e⁻

B. M⁺ → M²⁺ + e⁻

C. M + e⁻ → M⁻

D. M²⁺ → M⁺ + e⁻

Answer: A

4. For reverse reactions, enthalpy changes have:

A. Same sign

B. Opposite signs

C. Zero values

D. Random signs

Answer: B

5. IE₂(M) corresponds to removal of:

A. First electron from M

B. Electron from M⁺

C. Electron from M⁻

D. Neutron

Answer: B

6. If Δ_egH(M⁺) = −500 kJ mol⁻¹, IE₂(M) is:

A. −500 kJ mol⁻¹

B. +500 kJ mol⁻¹

C. 0

D. +1000 kJ mol⁻¹

Answer: B. +500 kJ mol⁻¹

7. Ionization enthalpy is generally:

A. Positive

B. Negative

C. Always zero

D. Undefined

Answer: A. Positive

8. Electron gain enthalpy may be:

A. Only positive

B. Only negative

C. Negative or positive depending on the process

D. Always zero

Answer: C

9. The process M⁺ + e⁻ → M represents:

A. Ionization

B. Electron gain by M⁺

C. Oxidation

D. Nuclear reaction

Answer: B

10. IE₂(M) and electron gain enthalpy of M⁺ are:

A. Equal with same sign

B. Equal in magnitude but opposite in sign

C. Always zero

D. Unrelated

Answer: B

11. Which equation represents IE₂(M)?

A. M → M⁺ + e⁻

B. M⁺ → M²⁺ + e⁻

C. M + e⁻ → M⁻

D. M²⁺ + e⁻ → M

Answer: B

12. Electron gain enthalpy of M⁺ represents:

A. M → M⁺

B. M⁺ + e⁻ → M

C. M²⁺ → M⁺

D. M → M²⁺

Answer: B

13. Which principle explains the sign reversal?

A. Hess's law

B. Energy conservation

C. Boyle's law

D. Hund's rule

Answer: B

14. If electron gain enthalpy of M⁺ is −800 kJ mol⁻¹, IE₂(M) is:

A. −800

B. +800

C. +400

D. 0

Answer: B. +800 kJ mol⁻¹

15. Which process is energetically opposite to M⁺ + e⁻ → M?

A. M → M⁺ + e⁻

B. M → M⁻

C. M²⁺ → M

D. M + e⁻ → M⁻

Answer: A

16. Which quantity is always an energy required to remove an electron?

A. Electron gain enthalpy

B. Ionization enthalpy

C. Electronegativity

D. Atomic radius

Answer: B

17. IE₂(M) involves:

A. Neutral atom only

B. A cation

C. An anion

D. A molecule only

Answer: B

18. Electron gain by M⁺ decreases its charge from:

A. +2 to +1

B. +1 to 0

C. 0 to −1

D. −1 to −2

Answer: B

19. Ionization of M⁺ increases its charge from:

A. 0 to +1

B. +1 to +2

C. +2 to +3

D. −1 to 0

Answer: B

20. The correct relation is:

A. IE₂(M) = Δ_egH(M⁺)

B. IE₂(M) = −Δ_egH(M⁺)

C. IE₂(M) = 0

D. IE₂(M) = 2Δ_egH

Answer: B

21. For an exothermic electron-gain process, Δ_egH is:

A. Positive

B. Negative

C. Zero

D. Infinite

Answer: B

22. If the reverse process is endothermic, its reverse electron-gain process is:

A. Endothermic

B. Exothermic

C. Always zero

D. Unrelated

Answer: B

23. Which pair is a reverse reaction pair?

A. M → M⁺ + e⁻ and M⁺ + e⁻ → M

B. M → M⁻ and M⁺ → M

C. M → M²⁺ and M → M⁻

D. None

Answer: A

24. The unit of ionization enthalpy is commonly:

A. kJ mol⁻¹

B. kg

C. metre

D. pascal

Answer: A

25. Which statement is correct?

A. Ionization is electron gain

B. Electron gain and ionization can be reverse processes for the same species pair

C. Both always have negative enthalpy

D. Both always have zero enthalpy

Answer: B

26. M⁺ + e⁻ → M is:

A. Reduction

B. Oxidation

C. Ionization

D. Sublimation

Answer: A. Reduction

27. M⁺ → M²⁺ + e⁻ is:

A. Reduction

B. Oxidation

C. Electron affinity

D. Neutralisation

Answer: B. Oxidation

28. If IE₂(M) = +600 kJ mol⁻¹, then Δ_egH(M⁺) is:

A. +600

B. −600

C. +300

D. 0

Answer: B. −600 kJ mol⁻¹

29. The reverse of an endothermic process is:

A. Endothermic

B. Exothermic

C. Always neutral

D. Always zero

Answer: B

30. For the exact species relationship, IE₂(M) equals:

A. Δ_egH(M)

B. −Δ_egH(M⁺)

C. Δ_egH(M⁻)

D. −IE₁(M)

Answer: B

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