What is the probability that the ends of a polyethene chain of molar mass \(65 \mathrm{~kg} \mathrm{~mol}^{-1}\) are 10nm apart when the polymer is treated as a onedimensional freely jointed chain?

Text Transcription:

65 kg mol^-1

Gases Deviation from Ideal Behavior Deviations from Ideal Behavior All real gasses fail to obey the ideal gas law to varying degrees The ideal gas law can be written as: For a sample of 1.0 mol of gas, n = 1.0 and therefore: Plotting PV/RT for various gasses as a function of pressure, P: The deviation from ideal behavior is large at high pressure The deviation varies from gas to gas At lower pressures (<10 atm) the deviation from ideal behavior is typically small, and the ideal gas law can be used to predict behavior with little error Deviation from ideal behavior is also a function of temperature: As temperature increases the deviation from ideal behavior decreases As temperature decreases the deviation increases, with a maximum deviation near the temperature at which the gas becomes a liquid Two of the characteristics of ideal gases included: The gas molecules themselves occupy no appreciable volume The gas molecules have no attraction or repulsion for each other Real molecules, however, do have a finite volume and do attract one another At high pressures, and low volumes, the intermolecular distances can become quite short, and attractive forces between molecules becomes significant o Neighboring molecules exert an attractive force, which will minimize the interaction of molecules with the container walls. And the apparent