The Lagoon Nebula (?Fig. E18.24?) is a cloud of hydrogen gas located 3900 light-years from the earth. The cloud is about 45 light-years in diameter and glows because of its high temperature of 7500 K. (The gas is raised to this temperature by the stars that lie within the nebula.) The cloud is also very thin; there are only 80 molecules per cubic centimeter. (a) Find the gas pressure (in atmospheres) in the Lagoon Nebula. Compare it to the laboratory pressure referred to in Exercise 18.23. (b) Science-fiction films sometimes show starships being buffeted by turbulence as they fly through gas clouds such as the Lagoon Nebula. Does this seem realistic? Why or why not? Fig. E18.24 -13 18.23 .. Modern vacuum pumps make it easy to attain pressures of the order of 10? atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a -14 pressure of 9.00 X 10? atm and an ordinary temperature of 300.0 K, how many molecules are present in a volume of 1.00 cm? ? (b) How many molecules would be present at the same temperature but at 1.00 atm instead?
Solution 25E Step 1: According to the ideal gas equation, pv = nRT Where, p - Pressure of the gas v - volume of the gas n - Number of moles of the gas R - Universal gas constant T - Temperature of the gas Number of moles = total number of molecules/ Number of molecules in one mole n = N/N A