The pairs among A = [ SO_3^2-, CO_3^2-], B = [ O_2^2-, F_2], C = [ CN^-, CO], D = [ NH_3, H_3 O^+] and E = [ MnO_4^2-, CrO_4^2-] that do not have…

Species with the same number of valence electrons and the same skeletal structure generally have similar Lewis dot structures (isoelectronic species).

For pair A: $\text{SO}_3^{2-}$SO32−​ has $6 + 3(6) + 2 = 26$6+3(6)+2=26 valence electrons. $\text{CO}_3^{2-}$CO32−​ has $4 + 3(6) + 2 = 24$4+3(6)+2=24 valence electrons. Since they have different numbers of valence electrons, they do not have similar Lewis dot structures ($\text{SO}_3^{2-}$SO32−​ has a lone pair on the central atom and is pyramidal, while $\text{CO}_3^{2-}$CO32−​ has no lone pair on the central atom and is trigonal planar).

For pair B: $\text{O}_2^{2-}$O22−​ has $2(6) + 2 = 14$2(6)+2=14 valence electrons. $\text{F}_2$F2​ has $2(7) = 14$2(7)=14 valence electrons. Both have a single bond and three lone pairs on each atom, so they have similar Lewis dot structures.

For pair C: $\text{CN}^-$CN− has $4 + 5 + 1 = 10$4+5+1=10 valence electrons. $\text{CO}$CO has $4 + 6 = 10$4+6=10 valence electrons. Both have a triple bond and one lone pair on each atom, so they have similar Lewis dot structures.

For pair D: $\text{NH}_3$NH3​ has $5 + 3(1) = 8$5+3(1)=8 valence electrons. $\text{H}_3\text{O}^+$H3​O+ has $6 + 3(1) - 1 = 8$6+3(1)−1=8 valence electrons. Both have three single bonds and one lone pair on the central atom, so they have similar Lewis dot structures.

For pair E: $\text{MnO}_4^{2-}$MnO42−​ has $7 + 4(6) + 2 = 33$7+4(6)+2=33 valence electrons. $\text{CrO}_4^{2-}$CrO42−​ has $6 + 4(6) + 2 = 32$6+4(6)+2=32 valence electrons. Since they have different numbers of valence electrons ($\text{MnO}_4^{2-}$MnO42−​ has an unpaired electron), they do not have similar Lewis dot structures.

Thus, pairs A and E do not have similar Lewis dot structures.

Answer: A and E