Order in the increasing order of acidity:HCl, H2SO4, HF, HCl, HI, HBr, HNO3, HBrO, HClO, HClO3, HClO4, H2S, H3PO4(?)

Well, you should know seven of these at least roughly...

...and for the rest, why don't you use the acid dissociation constants your book provides? Higher #K_a# = stronger acid.

The seven common strong acids are:

#"HClO"_4#, #" "" "K_a ~~ 10^10#
#"HI"#, #" "" "" "" "K_a = 3.2 xx 10^9#
#"HBr"#, #" "" "" "K_a = 1.0 xx 10^9#
#"HCl"#, #" "" "" "K_a = 1.3 xx 10^6#
#"H"_2"SO"_4#, #" "" "K_(a1) = 10^3#
#"HNO"_3#, #" "" "K_a = 24#
#"HClO"_3#, #" "" "K_a ~~ 10#

Of these, the binary acids are some of the strongest, with one exception being #"HClO"_4#.

We explain after-the-fact that in general,

• a more electronegative central atom pulls electron density towards itself.
• a larger atom makes a longer (weaker) bond with the #"H"#;

Whatever trends there are follow from those two observations.

As examples,

• #"HI"# is a stronger acid than #"HBr"#; the primary reason is that #"I"# is larger than #"Br"#, and makes a weaker bond with #"H"# (there is a counteracting electronegativity trend, which is not significant here). Weaker bond = stronger acidity.
• #"HNO"_3# is a stronger acid than #"HClO"_3#; the primary reason is that #"N"# is more electronegative than #"Cl"#, so it pulls electron density towards itself better. Thus, the #"H"#, attached to an outer #"O"#, gets less of it and thus the #"O"-"H"# bond is weakened. Weaker bond = stronger acidity.

Setting aside the ones we picked, the remaining ones are:

#"H"_3"PO"_4#, #" "" "K_(a1) = 7.52 xx 10^(-3)#
#"HF"#, #" "" "" "K_a = 7.2 xx 10^(-4)#
#"H"_2"S"#, #" "" "" "K_(a1) = 9.1 xx 10^(-8)#
#"HClO"#, #" "" "K_a = 3.0 xx 10^(-8)#
#"HBrO"#, #" "" "K_a = 2.0 xx 10^(-9)#

Of these, the only ones that are conceptually reasonable to explain are #"HClO"# vs. #"HBrO"#.

• In direct contrast with #"HCl"# vs. #"HBr"#, #"HClO"# is a stronger acid than #"HBrO"#, because #"Cl"# is more electronegative, which dominates over the size difference between #"Cl"# and #"Br"# due to the presence of the oxygen.

Therefore, the #"H"-"Cl"# bond is weakened more from more uneven sharing of electrons, and weaker bond = stronger acidity.