why phosphoric acid is preferred to H2SO4 to prepare HI in situ
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Answer:
The synthesis of alkyl halides from the corresponding aliphatic alcohols using concentrated hydrohalogen acids was investigated by Klein, Zhang and Jiang.[1] They note:
[W]e found that the reflux of 1-butanol ($\pu{2.34 g}, \pu{31.5 mmol}$) with $48~\%$ hydrogen bromide ($\pu{7 mL}$) for $\pu{4 h}$ on a $\pu{120 °C}$ oil bath only gave low yield of 1-bromobutane ($54~\%$) and moderate purity ($93~\%$). The yield of 1-bromobutane was improved to $82~\%$ with $90~\%$ purity by adding additional sulfuric acid ($98~\%, \pu{1 mL}$). Interestingly, we found that 1-iodobutane could be directly synthesized using 1-butanol and hydriodic acid ($\ce{HI}, 57~\%$) by reflux without adding an additional acid in $80~\%$ yield with $98~\%$ purity.
They do not offer any reasoning why switching from $\ce{HBr}$ to $\ce{HI}$ gives better yields. However, we may use our chemical reasoning to deduce the reason. As has been pointed out and explained multiple times on this site, the acidity of hydrohalogen acids increases from fluorine to iodine: $\ce{HI}$ is a stronger acid than $\ce{HBr}$ is. This means that hydrogen iodide should protonate a greater percentage of alcohol molecules than hydrogen bromide — and it requires the collision of a protonated alcohol and the halide anion for the reaction to proceed ($\mathrm{S_N2}$ mechanism)