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One factor that plays a role in the separation of oil and water (and in the formation of membranes) is the electrical force between water molecules and oil molecules. Let's do a small piece of that analysis here. The strongest attraction between a water molecule and an oil molecule arises from the charges on the oxygen ion polarizing the oil molecule as shown in the figure at the right. The oxygen's two negative charge pushes away electrons on the oil resulting in excess positives being nearer to the water and excess negatives farther away. The biggest effect is at the point on the molecule closest to the oxygen ion and decreases as we go farther away.
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A. Let's model the interaction between the water molecule and the oil with a simple 5-charge model as shown at the right. (Note that the figure is rotated 90o from the one above.) The two charges at the left represent the polarization charge in the oil and a simplified version of the water molecule (for ease of calculation) is shown at the right. One box is 100 pm (= 0.1 nm).
Write an expression for the electric force that the oxygen ion exerts on the two polarization charges on the oil (the two leftmost charges in the figure at the right). Treat each charge (or ion) as a point. Express your answer in terms of kC, the Coulomb constant, and e, the magnitude of the charge on the electron. Use those symbols in your answer; don't put in values for them. But put in the correct numbers for distances and pay attention to the signs. Put a box around your final expression. (Use a standard coordinate system: x represents horizontal with + to the right and y represents vertical with + upward.) |
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B. Do you expect the force of the two hydrogen ions on the two polarization charges of the oil to be greater or less in magnitude than the force you calculated in part A? Is the net force between the water molecule and the polarization charges in the oil attractive or repulsive? Explain.
C. Write an expression for the force between the two hydrogen ions in the water molecule and the polariza-tion charges of the oil. In your expression use the symbols kC and e, but evaluate the relevant distances needed explicitly. Put a box around your final answer. Show your work.