Why Molecules Have Shapes

Chapter 3 Shape and electronegativity

Polar and nonpolar molecules

A molecule is polar when its bond dipoles fail to cancel. That takes two things: bonds between atoms of different electronegativity, and a shape without the symmetry to balance them.

7 min read · 5 interactive figures · 3 questions

Carbon dioxide, straight: each C=O bond dipole (blue arrow, pointing toward the more electronegative oxygen) is matched by an equal one pointing the other way, and their sum, drawn below the molecule, is zero. Drag an oxygen, or use the slider, to bend the molecule and watch a sum appear. The dashed lines mark the angle measured in the real molecule. Choose other atoms to compare water, sulfur dioxide, hydrogen sulfide and oxygen difluoride.

A polar molecule has a positive end and a negative end; a nonpolar molecule does not. Two conditions make a molecule polar: it must have polar bonds, between atoms that attract electrons unequally, and its shape must not cancel them out[1]. Carbon dioxide has two strongly polar bonds but is straight, so they cancel and its measured dipole moment is zero. Water's two polar bonds meet at 104.5°, so they add, and water has a dipole moment of 1.86 debye[2]. Shape is the difference.

This chapter takes the two conditions in turn, then tests the simple picture against measured dipole moments. It passes the test that matters most, deciding polar from nonpolar, and fails some others in ways worth seeing.

Bond polarity and electronegativity

In a bond between two identical atoms, the shared electrons are shared equally. Between different atoms they are not: one atom pulls harder. The measure of that pull is electronegativity, χ. Linus Pauling defined the first scale in 1932 from bond energies[3]; the values in use today are Allred's 1961 revision of it[4], which reach their maximum, 3.98, at fluorine, the most electronegative element. This site takes them from PubChem's periodic table[5]. established

Figure 1 The Pauling electronegativity scale, with hydrogen and oxygen selected: Δχ = 1.24, so the electrons of an O–H bond lean toward oxygen, which becomes slightly negative (δ−) and leaves hydrogen slightly positive (δ+). The strip at the bottom places Δχ on OpenStax’s rough guide to bond type. Choose any two elements.#

The difference Δχ between two bonded atoms sets the bond's polarity. OpenStax gives a rough guide: below 0.4 the bond is close to nonpolar, between 0.4 and 1.8 it is polar covalent, and above 1.8 it is largely ionic, while warning that the guide has "many exceptions"[6]. Carbon and hydrogen differ by only 0.35, which is why hydrocarbons behave as nonpolar; C=O differs by 0.89, O–H by 1.24.

A polar bond is drawn as an arrow along the bond, pointing toward the negative end, with a small cross at the positive end. Its strength is the bond's dipole moment, measured in debye (D). A molecule's dipole moment is the vector sum of the dipoles of all its parts.

Adding bond dipoles

Return to the figure at the top of the page. It starts as carbon dioxide: two C=O bond dipoles of the same size, pointing in exactly opposite directions. Their sum is zero, and so is CO2's measured dipole moment[2]. Bend the molecule and the two arrows no longer line up; their sideways parts still cancel, but their downward parts add. For two equal bond dipoles of size d at an angle θ, the sum is

|sum| = 2 d cos(θ/2)(3.1)

zero at 180°, growing as the angle closes. Choose water's atoms (O with two H) and drag to its measured angle, 104.5°: the sum points toward oxygen, the molecule's negative end. Choose sulfur dioxide: the same story at 119.5°. Shape decides whether polar bonds make a polar molecule, and VSEPR decides the shape. established

Symmetry cancels

The same cancellation works in three dimensions. Three identical bonds at 120° in a plane, as in boron trifluoride, cancel. The question is what happens when the bonds point out of a plane.

Question 1 Prediction: carbon tetrachloride#
Figure 2 Carbon tetrachloride with its four bond dipoles (blue) and, beneath them, their sum, which is zero. Choose other molecules to compare: water, ammonia and chloroform have sums; carbon dioxide, boron trifluoride, phosphorus pentachloride, sulfur hexafluoride and xenon tetrafluoride do not. The sentence under the model gives the measured dipole moment where one is known. Drag to turn.#

The cancellation is general. Four identical bonds of a tetrahedron, five of a trigonal bipyramid, six of an octahedron and the four of a square plane all add to zero[1]: any shape in which every bond is matched by symmetry gives zero.

Lone pairs are what usually break the symmetry. Ammonia's lone pair makes it a pyramid, so its three N–H dipoles do not cancel (measured 1.48 D). Sulfur tetrafluoride's lone pair makes it a seesaw (0.63 D), and xenon tetrafluoride's two lone pairs, placed opposite each other, leave a perfectly symmetric square that cancels[2][1]. Different atoms break it too: chloroform has the shape of a tetrahedron but not its symmetry, because one corner is hydrogen.

Against measured dipole moments, the rule "polar bonds plus an unsymmetric shape" is right for every molecule in the figure above that has a measurement, zero or not[2]. That is the result most people need, and the bond-dipole model gets it from nothing but a Lewis structure and a table of electronegativities.

Where the arrows get the numbers wrong

The model is less good at saying how polar. Try it on the chloromethanes, the series from methane to carbon tetrachloride in which chlorines replace hydrogens one at a time.

Question 2 Prediction: which chloromethane is most polar?#
Figure 3 Chloroform, CHCl₃, with its bond dipoles and their sum. The chart sets the model’s sum (Δχ units) for all five chloromethanes above their measured dipole moments (debye, NIST CCCBDB). Change the number of chlorine atoms with the − and + buttons. Drag the model to turn it.#

Both rows of the chart agree that CH4 and CCl4 are zero, and that the other three are polar. They disagree about the order. The arrows treat each bond as a fixed, independent dipole, and by symmetry that makes CH3Cl and CHCl3 nearly equal (exactly equal on a perfect tetrahedron) and CH2Cl2 larger. The measurements say each added chlorine makes the molecule less polar[2]. Real bonds are not independent: each atom's pull changes the electrons around its neighbours, and the arrow model has no way to say so.

Two more cases where the arrows mislead. Ozone, O3, has three identical atoms, so every Δχ is zero and the model calls it nonpolar; its measured dipole moment is 0.53 D[2]. Its central atom carries a different share of the electrons from the end atoms (its Lewis structure gives it a formal charge of +1), which no electronegativity difference captures. And nitrogen trifluoride has the same pyramid shape as ammonia and bonds about as polar (Δχ 0.94 against 0.84), pointing the other way, yet its dipole moment is only 0.24 D against ammonia's 1.48 D[2]: the lone pair, which carries no arrow in the model, matters. established

What polarity does

Polarity matters because it decides how molecules hold on to each other. The positive end of one polar molecule attracts the negative end of the next: a dipole–dipole attraction. Every molecule, polar or not, also feels dispersion forces, attractions between momentary, fleeting dipoles in its electron cloud, and these grow with the size of the molecule: larger, heavier molecules with more easily distorted electron clouds attract each other more strongly[8]. Hydrogen bonded to nitrogen, oxygen or fluorine adds a third, stronger attraction, the hydrogen bond[8]. established

Question 3 Prediction: chloroform or carbon tetrachloride?#
Figure 4 Normal boiling points (NIST Chemistry WebBook) against measured dipole moments (NIST CCCBDB) for six small molecules, with the chloromethanes highlighted (the points are separate molecules, not a curve): each added chlorine raises the boiling point, even when the molecule becomes less polar. Use Compare to pair molecules with the same number of electrons instead.#

Compare molecules of the same size and the effect of polarity is clear. Tetrafluoromethane and dichloromethane both have 42 electrons; the nonpolar one boils at −128 °C, the polar one at 40 °C[9]. Methane and water both have 10; water, polar and hydrogen-bonded, boils 262 degrees higher. But across the chloromethanes size wins, and carbon tetrachloride, with no dipole at all, boils highest. OpenStax notes the same pattern down the periodic table: increasingly strong dispersion forces can dominate increasingly weak dipole–dipole attractions[8].

That is the chain this site set out to follow. Electron domains repel, and their number, read off a Lewis structure, fixes a molecule's shape. The shape, with the electronegativities of the atoms, decides whether the bond dipoles cancel. And whether they cancel helps decide how the molecules cling together: whether a liquid boils at −128 °C or 40 °C, and why water, small as it is, is liquid at room temperature.