Kinetics of Decomposition of HI

Kinetics of Decomposition of HI

2HI ---h𝜈→ H₂ + I₂
The possible mechanism of the above reaction is-
i. HI + h𝜈 ---k₁→ H + I
ii. H + HI ---k₂→ H₂ + I
iii. I + I ---k₃→ I₂
where, k₁, k₂ and k₃ are rate constants.
The rate of formation of decomposition of HI is given by-
−d[HI]/dt = k₁I_abs + k₂[H][HI] -----Equation-1
d[H]/dt = k₁I_abs + k₂[H][HI] Applying SSA we get-
0 = k₁I_abs + k₂[H][HI]
k₂[H][HI] = k₁I_abs -----Equation-2
Substituting the value of k₂[H][HI] in equation-1 we get-
−d[HI]/dt = 2k₁I_abs -----Equation-3
The quantum yield of the reaction is given by-
Φ = Rate of disappearance of HI/Rate of absorption of light
or, Φ = (−d[HI]/dt)/k₁I_abs
or, Φ = 2k₁I_abs/k₁I_abs
or, Φ = 2
In this case, Φ decreases as the reaction proceeds. This is due to the fact that as iodine accumulates, the thermal reaction
H + I₂ ---k₄→ HI + I
becomes significant.
If this reaction is also induced in the mechanism, then the steady state approximation for [H] gives-
d[H]/dt = k₁I_abs − k₄[H][I₂] = 0 -----Equation-4
[H] = k₁I_abs/(k₂[HI] + k₄[I₂]) -----Equation-5
Substituting the value of [H] in equation-1 from equation-5 we get-

As the reaction proceeds, [I₂] increases and hence the quantum yield decreases.

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