Hot air balloons work by changing the density of the air within the balloon, which causes the balloon to rise. A new hot air balloon has a capacity of 218000 L and a maximum operating temperature of 120.0 °C. At its maximum temperature, the pressure in the balloon is 1.24 atm. a. Calculate the moles of air within the balloon at its maximum temperature and pressure. b. Calculate the density (in g/L) of the air in the balloon at its maximum temperature, assuming the molar mass of air is 28.97g/mol. c. Calculate the partial pressure of nitrogen in the balloon, assuming that air is 78% nitrogen.
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
Hot air balloons work by changing the density of the air within the balloon, which causes the balloon to rise. A new hot air balloon has a capacity of 218000 L and a maximum operating temperature of 120.0 °C. At its maximum temperature, the pressure in the balloon is 1.24 atm.
a. Calculate the moles of air within the balloon at its maximum temperature and pressure.
b. Calculate the density (in g/L) of the air in the balloon at its maximum temperature,
assuming the molar mass of air is 28.97g/mol.
c. Calculate the partial pressure of nitrogen in the balloon, assuming that air is 78% nitrogen.
d. Calculate the root-mean-square speed (Vrms) of the N2 molecules in the balloon.
e. Do you expect the O2 molecules to have a faster or slower Vrms than N2? Justify your answer with one or two complete sentances.
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