Q. increasing bond polarity

Goal: Determine how bond polarity changes and show an example ordering of bonds by increasing polarity.

Step 1: Understand the definition of bond polarity. Bond polarity is determined primarily by the difference in electronegativity between the two atoms forming the bond. The larger the absolute electronegativity difference the more polar the bond. In symbolic form the electronegativity difference is written as \( \Delta\chi = \chi_A – \chi_B \) and the relevant quantity for polarity is the absolute value \( \left\lvert \Delta\chi \right\rvert = \left\lvert \chi_A – \chi_B \right\rvert \).

Step 2: Recall typical Pauling electronegativity values that we will use in this example. The values are approximately \( \chi_{\mathrm{H}} = 2.20 \), \( \chi_{\mathrm{C}} = 2.55 \), \( \chi_{\mathrm{N}} = 3.04 \), \( \chi_{\mathrm{O}} = 3.44 \), and \( \chi_{\mathrm{F}} = 3.98 \).

Step 3: Compute the electronegativity differences for a common series of bonds H–X. Compute each absolute difference explicitly.

\( \left\lvert \Delta\chi_{\mathrm{H-C}} \right\rvert = \left\lvert \chi_{\mathrm{C}} – \chi_{\mathrm{H}} \right\rvert = \left\lvert 2.55 – 2.20 \right\rvert = 0.35 \)

\( \left\lvert \Delta\chi_{\mathrm{H-N}} \right\rvert = \left\lvert \chi_{\mathrm{N}} – \chi_{\mathrm{H}} \right\rvert = \left\lvert 3.04 – 2.20 \right\rvert = 0.84 \)

\( \left\lvert \Delta\chi_{\mathrm{H-O}} \right\rvert = \left\lvert \chi_{\mathrm{O}} – \chi_{\mathrm{H}} \right\rvert = \left\lvert 3.44 – 2.20 \right\rvert = 1.24 \)

\( \left\lvert \Delta\chi_{\mathrm{H-F}} \right\rvert = \left\lvert \chi_{\mathrm{F}} – \chi_{\mathrm{H}} \right\rvert = \left\lvert 3.98 – 2.20 \right\rvert = 1.78 \)

Step 4: Order the bonds by increasing electronegativity difference. Since bond polarity scales with \( \left\lvert \Delta\chi \right\rvert \), the bonds rank as H–C < H–N < H–O < H–F. This ordering gives increasing bond polarity from smallest to largest.

Step 5: Connect to dipole moment and note caveats. The molecular dipole moment \( \mu \) depends on the effective separated charge \( q \) and the distance between charges \( r \). The basic relation is

\[ \mu = q\,r \]

In many simple cases a larger electronegativity difference leads to larger effective \( q \) and thus a larger dipole moment, but the bond length \( r \) also matters. When comparing bonds between different pairs of atoms with similar bond lengths the electronegativity difference is the dominant factor. Exceptions occur when bond lengths differ substantially or when molecular geometry causes dipoles to cancel in polyatomic species.

Final statement: For the example series H–X with X equal to C, N, O, F the increasing bond polarity is H–C < H–N < H–O < H–F, because the absolute electronegativity differences are 0.35, 0.84, 1.24, and 1.78 respectively, and larger \( \left\lvert \Delta\chi \right\rvert \) corresponds to greater bond polarity.