A prototype sports ball for a new game is precisely inflated to a pressure of 7.3 psi at 25 degrees C. The ball is spherical with an inner bladder diameter of 22.8 cm. It is filled with air (Mw=28.97 g/mol). Not Avogadro’s number is 6.022 x 10^23 atom/mol. A. Calculate the number of moles of air in the ball at the specified temperature and pressure. Consider the air in the ball to follow the ideal gas law. PV=nRT Where P is the absolute pressure of the air in atm, V is the volume of the ball, T is the absolute temperature in K, and R is the ideal gas constant.
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.
A prototype sports ball for a new game is precisely inflated to a pressure of 7.3 psi at 25 degrees C. The ball is spherical with an inner bladder diameter of 22.8 cm. It is filled with air (Mw=28.97 g/mol).
Not
A. Calculate the number of moles of air in the ball at the specified temperature and pressure. Consider the air in the ball to follow the
PV=nRT
Where P is the absolute pressure of the air in atm, V is the volume of the ball, T is the absolute temperature in K, and R is the ideal gas constant.
B. How many oxygen atoms compose the air in the ball? Assume that the mole fraction of N2 in the air is 0.79 and the remainder of the air is 02(oxygen).
This problem is based on ideal gas equation. The detailed solution is given below.
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