Among the following reactions of hydrogen with halogens, the one that requires a catalyst is:

We recall the general order of chemical reactivity of the halogens toward molecular hydrogen. Experimental data and bond-dissociation energies tell us that the ease with which the reactions

$$H_2 + X_2 \longrightarrow 2HX$$

proceed in the gas phase decreases in the sequence

$$F_2 \; > \; Cl_2 \; > \; Br_2 \; > \; I_2.$$

This trend can be justified by comparing the bond strengths of the covalent bonds $$X\!-\!X$$ and $$H\!-\!X$$ along the group. The lighter halogens form weaker $$X\!-\!X$$ bonds but stronger $$H\!-\!X$$ bonds, making the overall enthalpy change more negative (that is, more exothermic) and the activation energy lower. As we go down the group, the $$X\!-\!X$$ bond becomes stronger relative to the $$H\!-\!X$$ bond that is to be formed, so the reaction becomes less spontaneous and increasingly sluggish.

Let us examine each option in the light of this trend.

(i) For $$H_2 + F_2$$ we have a violent, practically instantaneous reaction even in the dark at low temperatures because the driving force is very large. Therefore no catalyst is required.

(ii) For $$H_2 + Cl_2$$ the reaction is also fast, although it usually needs initiation by light (photochemical initiation) rather than a chemical catalyst. Again, no catalyst is necessary; mere exposure to light is enough.

(iii) For $$H_2 + Br_2$$ the reaction rate drops significantly. Ordinarily, gentle heating or strong light is supplied to accelerate the process, but a separate chemical species acting as a catalyst is still not indispensable.

(iv) For $$H_2 + I_2$$ the reaction is the slowest of all because the enthalpy change is almost thermoneutral and the activation energy is high. To obtain an appreciable rate at moderate temperature one introduces a catalyst such as finely divided platinum, palladium or moist red phosphorus. The catalyst provides an alternate pathway of lower activation energy by adsorbing both $$H_2$$ and $$I_2$$ on its surface, dissociating them into atoms, and allowing them to recombine as $$HI$$. Without this catalytic assistance the direct homogeneous reaction is practically negligible under ordinary laboratory conditions.

Consequently, among the four reactions listed, only

$$H_2 + I_2 \longrightarrow 2HI$$

unequivocally requires a catalyst to proceed at a reasonable rate. The others may need light or heat but not a chemical catalyst.

Hence, the correct answer is Option 2.