Research: Science & Education
Why Does a Stream of Water Deflect in an Electric Field? G. K. Vemulapalli and S. G. Kukolich Department of Chemistry, University of Arizona, Tucson, AZ 85721
A demonstration that is often performed in a class (1, 2) shows bending of a thin stream of water in an electric field. The static field is readily created by charging a comb, balloon, or plastic rod through friction. This experiment attracts the students’ immediate attention. Like many striking demonstrations, the experiment illustrates an important property—the polar nature of water— but also raises many interesting questions for a thoughtful student. What is the strength of the electric field? Does the experiment work with every polar compound? Since nonpolar compounds acquire an induced dipole moment in an electric field, do they also deflect in an electric field? The statement found in most textbooks, that polar molecules do and nonpolar molecules do not, is too simplistic; it misses the most interesting aspects of the demonstration. We give a more complete explanation of this phenomenon here. We will also describe a simple experiment that answers the questions raised above. The Force on Molecules in an Electric Field An external electric field exerts force on a polar molecule and tends to align its dipole moment along the field direction. This occurs because the positive and negative poles at the opposite ends of the sample dipole are attracted to negative and positive sides of the electric field. If the field is uniform, the force on the negative pole will be equal and opposite to the force on the positive pole. In that case the molecule will not move in the field direction but rotates around its center of mass. Hence we must have a nonuniform electric field for the displacement of a stream of polar molecules. This is analogous to another phenomenon we introduce to the students: separation of atoms with magnetic dipole moments in a nonuniform magnetic field, first investigated by Stern and Gerlach. Electric fields not only orient dipolar molecules but also induce dipole moments in them. Since thermal agitation tends to disorient molecules, only partial orientation in the field direction is achieved under normal experimental conditions. Hence the property that is significant in describing the electric fields effects is not the actual dipole moment but the average net dipole moment, . It is the sum of (i) the induced dipole moment and (ii) the averaged component of the permanent dipole moment along the field direction. Both these quantities (3–5) depend on the electric field, %:
µ net
µ 2% = α% + 3kT
(1)
In this expression the first term on the right-hand side containing polarizability, α, is the induced dipole moment. The second term is the component of the permanent dipole moment, µ, along the field direction. Here k and T are the Boltzmann constant and temperature, respectively. The second term in the above expression is derived from the Boltzmann distribution law as shown elsewhere (3–5).
For nonpolar molecules µ = 0 and the orientation term vanishes. Now the energy of a molecule in an electric field is given by %
µ netd% = α +
E= o
µ2 %2 3kT 2
(2)
Since force is the derivative of energy, we have: µ2 f x, elec = – dE = – α + % d% dx dx 3kT
(3)
where we have designated the field direction by the subscript x. We see from this that the force depends on both the electric field and its gradient. Polar and nonpolar molecules alike experience no force along the field direction in a uniform electric field. If the force of electric field is of the same magnitude as the force of gravity, drops of falling liquid show deflection in an electric field. The force of gravity is given by the familiar formula: f = mg (4) where m is the mass and g, the gravitational acceleration. We will now show how the interplay of these two forces bends a falling stream of water molecules. Quantitative Estimate of Forces for Water Molecules For an estimate of the electrical force, we observed the droplets falling from a burette in a nonuniform electric field (Fig. 1). The field was generated by applying a potential (V) to a sharp tip of a metallic probe while the liquid in the burette was kept at the ground potential (G.P.). The tip was located 5 mm below the burette. At 1.0 × 103 V the centers of the drops were approximately 1.5 mm from the tip. The horizontal displacement of the drop toward the tip is between 1 and 2 mm. The following procedure was used for estimating the field strength. We considered the tip as a sphere of 0.5-mm radius (ro). The effective charge at the center of the probe is then given by
q(eff ) = φr = (1 3 10 3 V) (5 3 10 –4 m) 4πε 0
(5)
Hence the electric field at 1.5 mm from the tip is given by
%=
q(eff ) = 2 3 10 5 V m –1 4πε 0 r 2d
(6)
where rd (1.5 mm) is the distance between the tip and the center of the drop. Therefore the field gradient is:
Vol. 73 No. 9 September 1996 • Journal of Chemical Education
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Research: Science & Education
at ambient temperature. As this is twenty times larger than the polarizability contribution, we are justified in saying that the orientation of the water dipoles and the electric force on them in a nonuniform electric field causes the deflection. Water is an opportune choice for these experiments since the mass of water molecules is relatively low. Molecules much heavier than water, but with the same dipole moment, will not show the effect unless we use significantly larger fields. Benzene: A Nonpolar Molecule
Figure 1. Experimental arrangement for observing deflection of water and benzene in an electric field. (See text for discussion.)
d% = 2 q(eff ) = 3 3 10 8 V m –2 dx 4πεr 3d
(7)
The dipole moment of water (6) is 1.85 D = 6.16 × 10–30 C m and its polarizability is 1.45 × 10–30 m3 = 1.61 × 10–40 C2 J–1 m2. From these numbers and eq 3 we estimate that the electrical force on a water molecule is 2 × 10–25 N. (We compute the force per molecule, since the horizontal and downward forces are both proportional to the number of molecules.) The downward force is computed from eq 4 to be 3 × 10–25 N. We see from these estimates that the two forces are approximately equal, as expected. We made no effort to measure the angle of deflection accurately. Considering that polarizability is not uniform across the droplet and that we are using the polarizability data from the gas phase, we could only hope for orderof-magnitude estimates. A more quantitative study should take into account other factors such as the actual field strength inside the liquid droplet, the shape of the droplet, and the orientation of dipoles due to flow. These factors, however, are not important enough to change our qualitative conclusion: the deflection is a result of the balance between the gravitational and electrical forces in a nonuniform field. For water,
µ2 = 3.06 3 10 –39 C 2J –1m 2 3kT
888
(8)
Many chemistry textbooks state that only molecules with a dipole moment deflect in an electric field. Unfortunately this statement is not correct. Since nonpolar molecules acquire induced dipole moments, they should also show deflection at appropriate field strengths. Consider for example the benzene molecule. Its polarizability is 1.15 × 10–39 C2 J–1 m2, which is a third of the total polarizability (due to induction and orientation) of water. The mass of benzene is four times that of water. Hence felec has to be 12 times that for water for a comparable deflection. Since felec is proportional to both the electric field and its gradient, we should observe this when the potential is 3.5 times that used for water. Indeed, we observe the deflection of benzene to the same extent as in water when the potential on the tip is 3.6 kV, all other conditions being the same. From these experiments we conclude that: • Deflection of molecules in an electric field depends on both the field strength and the gradient of the field. In case of water these quantities are of the order of 105 V m–1 and 108 V m–2. • The effect is readily observed with water because of its lighter mass. • Because they acquire a dipole moment in an electric field, nonpolar molecules also show deflection. Since induced dipole moments are generally weaker than permanent moments, we need larger field strengths to deflect nonpolar molecules. Literature Cited 1. Atkins, P. W.; Beran, J. A. General Chemistry, 2nd ed.; Scientific American Books: New York, 1992; p 330. 2. Umland, J. B. General Chemistry; West: Minneapolis, 1993; p 329. 3. Vemulapalli, G. K. Physical Chemistry; Prentice-Hall: Englewood Cliffs, NJ, 1993. 4. Hill, T. L. An Introduction to Statistical Thermodynamics; Addison-Wesley: Reading, MA, 1960. 5. McClelland, B. J. Statistical Thermodynamics; Chapman and Hall: London, 1973. 6. Handbook of Chemistry and Physics, 71st ed.; CRC: Baton Rouge, LA, 1990.
Journal of Chemical Education • Vol. 73 No. 9 September 1996
