From their Lewis structures, determine the number of \(\sigma\) and \(\pi\) bonds in each of the following molecules or ions: (a) hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4}\) (b) hydrogen cyanide, HCN; (c) sulphur trioxide, \(\mathrm{SO}_{3} ;\) (d) ozone, \(\mathrm{O}_{3}\).

Draw the Lewis structures for hydrazine (N2H4), hydrogen cyanide (HCN), sulfur trioxide (SO3), and ozone (O3) For N2H4: H H \ / N - N / \ H H For HCN: H - C ≡ N For SO3: O || O - S - O For O3: O - O - O

Determine whether the bonds within each structure are single, double, or triple For N2H4: N-H bonds: single N-N bond: single For HCN: H-C bond: single C-N bond: triple For SO3: S-O bonds: double For O3: O-O bonds: single (between left and central O atoms) O-O bond: double (between central and right O atoms)

Count the number of \(\sigma\) and \(\pi\) bonds according to the following rules: - For single bonds, there is 1 \(\sigma\) bond - For double bonds, there is 1 \(\sigma\) bond and 1 \(\pi\) bond - For triple bonds, there is 1 \(\sigma\) bond and 2 \(\pi\) bonds For N2H4: - 4 N-H single bonds: 4 \(\sigma\) bonds - 1 N-N single bond: 1 \(\sigma\) bond Total: 5 \(\sigma\) bonds For HCN: - 1 H-C single bond: 1 \(\sigma\) bond - 1 C-N triple bond: 1 \(\sigma\) bond and 2 \(\pi\) bonds Total: 2 \(\sigma\) bonds and 2 \(\pi\) bonds For SO3: - 3 S-O double bonds: 3 \(\sigma\) bonds and 3 \(\pi\) bonds Total: 3 \(\sigma\) bonds and 3 \(\pi\) bonds For O3: - 1 O-O single bond: 1 \(\sigma\) bond - 1 O-O double bond: 1 \(\sigma\) bond and 1 \(\pi\) bond Total: 2 \(\sigma\) bonds and 1 \(\pi\) bond In conclusion: (a) Hydrazine (N2H4) has 5 \(\sigma\) bonds and no \(\pi\) bonds. (b) Hydrogen cyanide (HCN) has 2 \(\sigma\) bonds and 2 \(\pi\) bonds. (c) Sulphur trioxide (SO3) has 3 \(\sigma\) bonds and 3 \(\pi\) bonds. (d) Ozone (O3) has 2 \(\sigma\) bonds and 1 \(\pi\) bond.