Q. how to tell if a bond is polar or nonpolar

Goal. Determine whether a bond is polar or nonpolar, and explain the steps in detail.

Key idea. A bond is polar when the two atoms that form it pull on the shared electrons unequally. The usual practical test is to compare the electronegativities of the two atoms and then consider molecular geometry when deciding whether an entire molecule is polar.

Step 1. Identify the two atoms that form the bond. Write their symbols. For example, for hydrogen chloride write H and Cl. For a bond inside a molecule, identify the specific pair of bonded atoms you are testing.

Step 2. Look up the electronegativities on the Pauling scale for each atom. Common values you may use include: H = 2.20, C = 2.55, O = 3.44, N = 3.04, Cl = 3.16, F = 3.98, Br = 2.96, S = 2.58, Na = 0.93, K = 0.82. Use a consistent table for accuracy.

Step 3. Compute the absolute electronegativity difference. Use the formula

\[
\Delta \chi \;=\; \lvert \chi_A – \chi_B \rvert
\]

where \( \chi_A \) and \( \chi_B \) are the Pauling electronegativities of the two atoms.

Step 4. Compare the value of \( \Delta \chi \) to approximate classification ranges. These ranges are approximate and may vary slightly between sources. A commonly used guideline is:

If \( \Delta \chi \approx 0 \) the bond is nonpolar covalent. If \( \Delta \chi \lesssim 0.4 \) treat the bond as essentially nonpolar. If \( 0.4 \) < \( \Delta \chi \) < \( 1.7 \) the bond is polar covalent. If \( \Delta \chi \gtrsim 1.7 \) the bond has large ionic character and is often treated as ionic. These are rules of thumb only.

Step 5. Interpret the result physically. A polar bond has a bond dipole moment because one atom is more electronegative and pulls electron density toward itself, creating partial charges \( \delta^- \) on the more electronegative atom and \( \delta^+ \) on the other atom. A nonpolar bond has no significant bond dipole.

Step 6. If you need to decide whether an entire molecule is polar or nonpolar, consider molecular geometry. Bond dipoles are vectors. Add the bond dipole vectors. If they sum to zero because of symmetry, the molecule is nonpolar overall even if the individual bonds are polar. If they do not sum to zero, the molecule is polar overall.

Worked examples, shown step by step.

Example 1. HCl bond.

Electronegativities: \( \chi_{\mathrm{H}} = 2.20 \), \( \chi_{\mathrm{Cl}} = 3.16 \).

\[
\Delta \chi \;=\; \lvert 3.16 – 2.20 \rvert \;=\; 0.96
\]

Interpretation: \( \Delta \chi = 0.96 \) lies in the polar covalent range. Therefore the H–Cl bond is polar. The chlorine end carries a partial negative charge \( \delta^- \) and hydrogen carries \( \delta^+ \).

Example 2. H2 bond.

Electronegativities: \( \chi_{\mathrm{H}} = 2.20 \), \( \chi_{\mathrm{H}} = 2.20 \).

\[
\Delta \chi \;=\; \lvert 2.20 – 2.20 \rvert \;=\; 0
\]

Interpretation: \( \Delta \chi = 0 \) so the H–H bond is nonpolar covalent.

Example 3. CO2 molecule.

Bond-level: For each C–O bond, \( \chi_{\mathrm{C}} = 2.55 \), \( \chi_{\mathrm{O}} = 3.44 \).

\[
\Delta \chi_{\mathrm{C-O}} \;=\; \lvert 3.44 – 2.55 \rvert \;=\; 0.89
\]

Each C–O bond is polar. Molecular-level: CO2 is linear with two equal C–O bond dipoles pointing in opposite directions. The bond dipole vectors cancel, so the net dipole moment of the molecule is zero. Therefore CO2 is nonpolar overall despite having polar bonds.

Example 4. H2O molecule.

Bond-level: For each O–H bond, \( \chi_{\mathrm{O}} = 3.44 \), \( \chi_{\mathrm{H}} = 2.20 \).

\[
\Delta \chi_{\mathrm{O-H}} \;=\; \lvert 3.44 – 2.20 \rvert \;=\; 1.24
\]

Each O–H bond is polar. Molecular-level: Water has a bent geometry, so the two O–H bond dipoles do not cancel. Their vector sum points toward the oxygen, so water has a net dipole moment and is a polar molecule.

Summary checklist you can use quickly.

1. Identify bonded atoms. 2. Get electronegativities. 3. Compute \( \Delta \chi = \lvert \chi_A – \chi_B \rvert \). 4. Use approximate thresholds to classify the bond. 5. For molecular polarity, add bond dipole vectors according to the molecular geometry and check whether they cancel.