Dipole Moments

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You can actually measure dipole moments of molecules in the laboratory with some simple experiments. The measurements originate in the electrical "capacitance", C, of two charged plates where the capacitance is the amount of charge (per unit area) divided by the voltage across the gap between the plates. A reference measurement is taken for Co, the capacitance with a vacuum between the charged plates. If you then place a sample of a pure chemical liquid or gas, for example, between the plates, the measured capacitance changes because the dipoles of the molecules tend to line up with their positive ends towards the negative plate and vice versa so that the charge-to-voltage ratio between the plates is reduced. However, the molecules are in thermal motion so that the alignment is not perfect as shown in the figure below.

 Click figure to "freeze" motion. As the temperature of the sample is raised, the random thermal agitation of the molecules increases and the misalignment becomes more and more appreciable reducing the effect caused by the sample between the charged plates. Peter Debye cleverly showed that the temperature dependence of the measured capacitance could be used to determine the dipole moment of the individual molecule according the the theoretical formula

In this equation, NAvog is Avogadro's number, k is a constant (the Boltzmann constant), and T is the absolute temperature in kelvin at which the capacitance measurement C is made. You should now recognize that a graph of 3(C-Co)/(C+2Co) versus 1/T will give a straight line, the slope of which involves known quantities (such as Avogadro's number and Boltzmann's constant) and, the square of a molecule's dipole moment, which can be consequently calculated. Debye's method is one of a number of ways in which the dipole moment can be determined.

 On the left is some sample data. Note that there is no dependence of the measured effect on temperature for methane (CH4) and carbon tetrachloride indicating these have zero dipole moment.

Incidentally, the "constant" inside the braces in Debye's equation also has physical significance for the molecule. It is a measure of how easily the electron cloud of a molecule can be distorted when the molecule is in the electric field potential between the plates. The constant is referred to as the molecule's "polarizability". You can see from the figure with data that extrapolation to 1/T = 0 corresponding to the intercept of the Debye equation indicates that methane, for example, with no dipole moment, still affects the measured capacitance because the charge plates of the apparatus can polarize (distort) the valence electron clouds from their normal distribution.