4.2.4.P10
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We have seen that charged objects can attract neutral matter through the polarization of neutral matter – pushing the part of it that has the same charge slightly further away. At the molecular level, neutral molecules that have separated parts that are positive and negative can also attract one another by orienting properly. One example of this is hydrogen bonding of water molecules. This is the primary mechanism that creates surface tension in water (and a similar phenomenon plays a big role in a variety of biochemistry).
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The hydrogens in a water molecule are positive (+e) and the oxygen is negative (-2e). Electric forces and the quantum sharing of electrons hold the whole thing together. We won’t worry about the part inside the water molecule here but we will explore how the electric forces between water molecules properly arranged winds up being attractive.
| The angle between the hydrogen atoms in a water molecule is actually 104o, but in order to reduce your calculation for the purpose of this problem, we’ll treat them as if they were a right angle – 90o. In a water-water hydrogen bond the separation between the hydrogen in one molecule and the oxygen in the other is about twice the distance between the hydrogen and the oxygen in its own molecule. Our simplified model is sketched in the figure at the right. |
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A. Consider the “backbone” of charges ABD. A and D repel, but B and D attract. Who wins? Does (AB) attract or repel D? By how much? Express your answer as a multiple of the force between two charges, e, at a distance d, F0 = kce2/d2.
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B. Now consider the force of (AB) on the “arms” of the other molecule – charges (EF). Is the force of (AB) on (EF) attractive or repulsive? In this case, you don’t need to calculate the result exactly, but you have to be quantitative enough to be able to say convincingly which force is larger.
(Hint: Reason quantitatively about distances but qualitatively about angles. Feel free to measure.) |
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| C. The only piece we’ve omitted is the force C exerts on (DEF). Say whether you think this will be significant in the overall attraction-repulsion balance and explain why you think so (briefly). |
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Joe Redish 1/13/12
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