The Free Style

If one completely vaporizes a measured amount of a volatile liquid, the molecular weight of the liquid can be determined by measuring the volume, temperature, and pressure of the resulting gas. When one uses this procedure, one uses the ideal gas equation and assumes that the gas behaves ideally. However, if the sample is slightly above the boiling point of the liquid, the gas deviates from ideal behavior. Explain the postulates of the ideal gas equation, and explain why, when measurements are taken just above the boiling point, the calculated molecular weight of a liquid deviates from the true value. 

Restatement Explain ideal gas equation and why MW measurements taken just above boiling point deviate. 

The ideal gas equation, PV = nRT stems from three relationships known to be true for gases under ordinary conditions  

We obtain n, the symbol used for the moles of gas, by dividing the mass of the gas by the molecular weight. In effect, n = mass/molecular weight (n = m/MW). Substituting this relationship into the ideal gas law gives 

Real gas behavior deviates from the values obtained using the ideal gas equation because the ideal gas equation assumes that (1) the molecules do not occupy space and (2) there is no attractive force between the individual molecules. However, at low temperatures (just above the boiling point of the liquid), these factors become significant, and we must use an alternative equation, known as the van der Waals equation, that accounts for them. 

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In fertile areas, one or two people needed about a square mile to support themselves in desert or cold weather ones, 20 to 30 square miles were needed per person (Stavrianos). As the world population increased with the passage of thousands of years, consumption of food - the main energy source of the people at that time - grew faster than nature could provide for. Humanity, thus, reached its first major entropy watershed. A new energy source was needed Agriculture provided it. There is no doubt that people preferred the free style of the hunting life to the hard work of cultivating the earth. But they had no choice. It was a matter of survival. 

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