Chap24 solutions

Physical Chemistry

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Part 3: Change
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24 Molecules in motion Solutions to exercises Discussion questions E24.1(b) Diffusion is the migration of particles (molecules) down a concentration gradient. Diffusion can be interpreted at the molecular level as being the result of the random jostling of the molecules in a Fuid. The motion of the molecules is the result of a series of short jumps in random directions, a so-called random walk. In the random walk model of diffusion, although a molecule may take many steps in a given time, it has only a small probability of being found far from its starting point because some of the steps lead it away from the starting point but others lead it back. As a result, the net distance traveled increases only as the square root of the time. There is no net Fow of molecules unless there is a concentration gradient in the Fuid, alse there are just as many molecules moving in one direction as another. The rate at which the molecules spread out is proportional to the concentration gradient. The constant of proportionality is called the diffusion coef±cient. On the molecular level in a gas, thermal conduction occurs because of random molecular motions in the presence of a temperature gradient. Across any plane in the gas, there is a net Fux of energy from the high temperature side, because molecules coming from that side carry a higher average energy per molecule across the plane than those coming from the low temperature side. In solids, the situation is more complex as energy transport occurs through quantized elastic waves (phonons) and, in metals, also by electrons. Conduction in liquids can occur by all the mechanisms mentioned. At the molecular (ionic) level, electrical conduction in an electrolytic solution is the net migration of ions in any given direction. When a gradient in electrical potential exists in a conductivity cell there will be a greater Fow of positive ions in the direction of the negative electrode than in the direction of the positive electrode, hence there is a net Fow of positive charge toward the region of low electrical potential. Likewise a net Fow of negative ions in the direction of the positive electrode will occur. In metals, only negatively charged electrons contribute to the current. To see the connection between the Fux of momentum and the viscosity, consider a Fuid in a state of Newtonian Fow, which can be imagined as occurring by a series of layers moving past one another (²ig. 24.11 of the text). The layer next to the wall of the vessel is stationary, and the velocity of successive layers varies linearly with distance, z , from the wall. Molecules ceaselessly move between the layers and bring with them the x -component of linear momentum they possessed in their original layer. A layer is retarded by molecules arriving from a more slowly moving layer because they have a low momentum in the x -direction. A layer is accelerated by molecules arriving from a more rapidly moving layer. We interpret the net retarding effect as the Fuid’s viscosity.
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Chap24 solutions - Part 3: Change 24 Molecules in motion...

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