The mass of a gas is related to the number of moles

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Unformatted text preview: he volume of the lungs increases resulting in a decrease in pressure inside the lungs. Because there is an open airway keeping the lungs in contact with the open air, fresh air will rush into the lungs to equilibrate the pressure. As one contracts her/his diaphragm, the volume of the lungs decreases, thereby increasing the pressure inside the lungs. Now air will Dakota State University Page 128 of 232 Experiment 10: Gas Laws General Chemistry I and II Lab Manual rush out of the lungs in order to equilibrate the pressure. How quickly the air will rush through the airways is a function of the radius of those passages and the pressure difference between the two ends. This is Poiseuille’s Law. Poiseuille determined empirically in 1840 that the mass of air Q= π∆p 4 r 8νl that will flow through a tube per unit time can be determined by Here, Q is the mass of air that can flow through a tube per unit time (such as, for instance, g/sec), ∆p is the difference in pressure between one end of the tube and the other (without a pressure difference, there would be no flow), ν is the viscosity of the air (the higher the viscosity, the greater the resistance to flow; for instance, water has a low viscosity, honey has a high viscosity), l is the length of the tube, and r is the radius of the tube. The mass of a gas is related to the number of moles of gas through the average molecular weight of the gas, n=Q/M, where n is the number of moles and M is the average molecular weight of the gas. The volume of the gas is directly related to the number of moles of gas, V=nRT/P where V is the volume, R is the Universal Gas constant, T is temperature and P is the pressure of the gas. Thus, we find that V= πRT ∆p 4 r 8νlMP V=QRT/MP, or Q=VMP/RT. Thus, we can substitute for Q, and on rearrangement, we find is the volume of air flow per unit time. Of course, π , R and 8 are all constant, and typically we can take T, ν , l and M to be constant as well. Therefore, typically we adjust the pressure difference to get the volume per unit time that we want through a tube of radius r. Consider a patient with emphysema. The condition causes a constriction of the airways, such that the radius of the airways decreases. Poiseuille tells us that all else being the same, this constriction will decrease the amount of air they can g per second (since the length and air et viscosity is constant). In fact, because it is a fourth power relationship (r4 =r*r*r*r), the amount of air the patient can get is greatly diminished. Poiseuille also tells us that the patient will try to make up for this deficit by increasing the pressure difference between the atmosphere and their lungs. Boyle tells us that this can be accomplished by increasing the volume of the lungs more drastically, which will greatly decrease the pressure inside the lungs, thereby creating a greater pressure difference when compared with the atmosphere. Therefore, the patient will breath harder in order to more greatly increase the volume of their...
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