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The reaction

$$\ce{2 H2S(g) + SO2(g) -> 2 H2O(l) + 3 S(s)}$$

goes in presence of a catalyst, usually $\ce{Al2O3}$ or $\ce{TiO2}$, but also just in presence of moist or water (YouTube video)

I don't understand the catalytic mechanism - why doesn't the reaction go without water and how exactly does presence of water help?

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Yes, hydrogen sulfide and sulfur dioxide reacts with each other in the presence of moisture. The reaction has been studied previously and was noted that the reaction did not proceed if there was no water vapor(dry gases). The mechanism of reaction was determined and was adsorption. The gases adsorped on the surface of water and collided with each other to deposit sulfur and water. The formation of water further catalysed the reaction. This is a excerpt from the paper which extensively studies the mechanism of the reaction.$\ce{^{[1]}}$

The results of experiment 3 are best explained by assuming that both the $\ce{H2S}$ and $\ce{SO2}$ are adsorbed and that reaction takes place only between these adsorbed molecules.

There is another paper which extensively discuss the mechanism of reaction. It says that both the gases react with a reaction to form a solution. This is called Wackenroeder solution which is a mixture of sulfur based acid(polythionic acids). These acids dissociate in aqueous solution and form and water. Have a good read at the paper:$\ce{^{[2]}}$

Volynskii proposed a mechanism for the reaction of $\ce{H2S}$ and $\ce{SO2}$ in aqueous solutions. The formation of sulfur follows the steps below.

$$\ce{H2S + SO2 -> HSSO2H }$$ $$\ce{HSSO2H -> S(OH)2 + S }$$ $$\ce{S(OH)2 + H2S -> 2H2O + 2S (or~S2) }$$

The overall equation for the three steps is reaction 2. The formation of polythionic acids results from the interaction of ionized $\ce{SO2}$ and monatomic or polyatomic sulfur, i.e.,

$$\ce{SO2 + H2O -> HSO3- + H+ }$$ $$\ce{HSO3- + S -> HS2O3- }$$ $$\ce{S_{x} + 2HSO3- -> S_{(x +1)}O6- + H2S }$$ $$\ce{S_{x} + 2HS2O3- ->S_{(x +2)}O6- + H2S }$$ $$\ce{S_{x} + HSO3- + HS2O3- -> S_{(x +3)}O6- + H2S }$$

where, x can range from 1 to 7. Tiwari believed that the reaction of $\ce{H2S}$ and $\ce{SO2}$ in dilute sulfuric acid (below 10 wt %) follows the scheme from (7) to (9). His kinetic data show that the reaction is first order with respect to both $\ce{H2S}$ and $\ce{SO2}$, consistent with the scheme because he assumed reaction 7 to be the rate-controlling

Reference

$\ce{^{[1]}}$ http://pubs.acs.org/doi/abs/10.1021/j150272a005

$\ce{^{[2]}}$ http://pubs.acs.org/doi/abs/10.1021/ie020275i

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