Steps involved in hydrogen evolution :- Theory :3
Step 1:
Diffusion of M⁺ or H₃0⁺ from bulk to the electrode - electrolysis interface.
Step 2:
Proton transfer from interface to cathode.
Step 3:
H⁺ + e⁻ →H atom (cathode reaction) discharge Reaction.
Step 4:
Catalytic action of the cathode in converting H atom to H₂ molecule.
Step 5:
H₂ gas bubble formation.
Theory 2:
Step 1:
Concentration to be slow step.
- This energy of activation for Diffusion process of the order of 1.5 kcl/mol whereas Ea for H₂ evolution process of the order of 10 - 20 kcal / mol. This shows that Diffusion of H⁺ can't be a slow step in H₂ evolution process at the cathode.
- The ηH₂ depends on the nature of the cathode used ( experimental fact) But if Diffusion is the slow step. It will not depend upon the nature of cathode. So step 1 is not the slow step.
Step 4 : - Bubble formation can be the slow step.
(1) This is also a physical process and it should have Ea of the order of 4 to 5 kcal /mol only. This doesn't agree with experimental Ea.
(2) Bubble formation is also independent of the nature of cathode. ηH₂ depends on nature of cathode.
(3) When the surface of cathode is coated with a detergent, the surface tension of cathode is altered. Hence it will after the velocity of formation of bubble But ηH₂ is not affected.
For these reasons bubble formation is not considered as slow step.
Theory 3 :
TAFEL'S THEORY FOR ηH₂
Catalytic action is considered as slow step.
(1) Metals like Ni, Pd and Pt are catalyst for the breaking of H-H bond. They will also be good catalyst for the formation of bond between hydrogen atoms.
Metal like Co, Hg don't function as catalyst for the formation of H₂ molecule (or) breaking for the formation of H₂ into H atoms. When these metals are used as cathode during electrolysis of acids and bases, higher ηH₂ is observed. This shows there is a direct correlation between the catalytic efficiency of cathode and observed ηH₂.
(2) As catalyst is ↓. This theory derives an expression for ηH₂ as
η = RT ln ( n )
F n₀
When η refers to number of hydrogen atoms adsorbed per square cm of the cathode and " no" refers to number of H atoms adsorbed per square cm in ⇔ with H₂ gas at 1 atm pressure. For an efficient catalyst, n value is greater than number based on this calculation, η obtained agrees with experimental value for platinised Pt electrode only.
TAFF'S EQUATION :
η = a + b log drift
This is derived from Butler - volmer equation after applying high field approximation. According to this equation η v log i should give a at line with slope equal to 6 and this value is found to be equal to 2.303 RT/2F = 0.059 = 0.029
2
This slope is obtained only with platinised Pt electrode. Hence this theory looks at right only for metals having low ηH₂ (or) having higher catalytic efficiency for the combination of H- atoms.
According to Tafel's equation :-
η = a + b log i drift which doesn't contain
[ H⁺] i.e ηH₂ is independent of [ H⁺ ] or PH and this areas with the experimental results.
The added catalytic poison like sulfide affects ηH₂ on platinised Pt electrode only. The catalytic poison has no effect on ηH₂ on electrodes having higher ηH₂ like Hg. This shows the catalytic action is not the slow step on metals having higher ηH₂.
Theory 4 :
SLOW STEP - DISCHARGE REACTION THEORY :-
H⁺ + e⁻ → H. atom
- Quantum mechanical treatment
(1) According to classical mechanics, the discharge reaction is considered to be an activation process.
But according to quantum mechanical principles, the discharge reaction doesn't involve an energy of activation. The e⁻ tunnels through the barrier and reaches H⁺. Quantum mechanics allows such e⁻ tunneling process.
(2) Using Fermi- Dirac statistics, the available e⁻ donate levels in metals are calculated.
Using Maxwell - Boltzmann statistics with quantum basics on the e⁻ acceptor levels in H⁺ are obtained. The e⁻ is transferred from the metal to H⁺ after matching the levels.
Based on quantum mechanical principles expression for Overpotential is derived.
η = constant + 2.303 RT log i drift
∝F
According to this equation a graph of η vs log i should give a straight line with slpoe
= 2.303 RT
∝F
where ∝ has a value between 0 and 1. For many metals ∝ ≈ 0.5
∴ slope = 0. 059 = 0.1180
Y₂
This agree with experimental value for metal having higher ηH₂
Limitations :-
1) The mathematical treatment is more complicated.
2) It doesn't explain the dependence of η on the nature of electrode.
Modification :-
Frumkin mathematical treatment
Erdy - Gruz - volmer - Smith - treatment.
This theory consider "Stern's model " for electrified interface to explain ηH₂.
ψ - Potential between electrode and OHP
ζ - Potential between OHP and bulk C (diifused Layer potential)
Using this model, the following expressions has linear derived.
η + ζ = constant + 2RT lni - RT ln [ H⁺]
F
According to this equation,
ζ ≠ constant - RT ln [ H⁺ ]
F
According to this equation, η depends on PH medium. It's observed in the electrolysis of alkaline solution with Ni electrodes or Hg Cathode coated with LaCl₃.
The above equation is rewritten as,
η = constant +. 2RT 2.303 log i and a length of η vs log i should be linear
Slope = 2.303 RT ×2
F
= 0.118
This agrees with experimental value for electrodes having higher ηH₂.
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