I am not sure why the answer is missing a very essential point which is teaching the student Le Châtelier's principle . Maybe this is not a grade 12 question!!!!
The student could easily deduce that since the #[I_2]=0M# the equilibrium will shift toward the direction of making #I_2# and therefore to the left and in this case, the ICE table is written as follows:
#" " " " " " " " " "H_2(g)+I_2(g)rightleftharpoons 2HI(g)#
#Initial" " " " " "8M" " "0M" " " " "2.4M#
#"Change" " " " " " "+x" +x" " " " "-2x#
#Equilibrium" "8+x" " x" " " "2.4-2x #
In this case, ONLY #color(green)("positive")# values of #x# will be accepted.
However, the way the answer is written is that he will assume that the equilibrium is shifting to the right and in this case #x# will be #color(green)("positive")#, however, if his assumption is wrong, #x# will be #color(red)("negative")# and this is the case, that is why the #[HI]# dropped from #2.4M# to #2.2M#.
