# Kinetics of Decomposition of HI

## Kinetics of Decomposition of HI

2HI ---h𝜈→ H_{2}+ I

_{2}

The possible mechanism of the above reaction is-

i. HI + h𝜈 ---k

_{1}→ H + I

ii. H + HI ---k

_{2}→ H

_{2}+ I

iii. I + I ---k

_{3}→ I

_{2}

where, k

_{1}, k

_{2}and k

_{3}are rate constants.

The rate of formation of decomposition of HI is given by-

−d[HI]/dt = k

_{1}I

_{abs}+ k

_{2}[H][HI] -----Equation-1

d[H]/dt = k

_{1}I

_{abs}+ k

_{2}[H][HI] Applying SSA we get-

0 = k

_{1}I

_{abs}+ k

_{2}[H][HI]

k

_{2}[H][HI] = k

_{1}I

_{abs}-----Equation-2

Substituting the value of k

_{2}[H][HI] in equation-1 we get-

−d[HI]/dt = 2k

_{1}I

_{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)/k

_{1}I

_{abs}

or, Φ = 2k

_{1}I

_{abs}/k

_{1}I

_{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 + I

_{2}---k

_{4}→ HI + I

becomes significant.

If this reaction is also induced in the mechanism, then the steady state approximation for [H] gives-

d[H]/dt = k

_{1}I

_{abs}− k

_{4}[H][I

_{2}] = 0 -----Equation-4

[H] = k

_{1}I

_{abs}/(k

_{2}[HI] + k

_{4}[I

_{2}]) -----Equation-5

Substituting the value of [H] in equation-1 from equation-5 we get-

As the reaction proceeds, [I

_{2}] increases and hence the quantum yield decreases.

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