Academica X w 2130 homework 4 (fall/ x VA 2130 homework 4 (fall/ x * [Solved] Two atoms col X Average acceleration o x [Solved] Two atoms col x + X ( - C webassign.net/web/Student/ Assignment-Responses/last?dep=30229534 Capillaries are the narrowest elements in the blood transport system of animals. They connect the arteries (the vessels that carry blood away from the heart) to the veins (the vessels that carry blood back to the heart). They are the place where the chemicals that the blood is carrying are taken from source regions (lungs for air, intestines for food, glands for hormones) and delivered to the cells that need them. They are pretty small-about 5 um in diameter. One of the interesting questions about this process is: how do oxygen molecules know where to go? For example, Wikipedia says that red blood cells "take up oxygen in the lungs or gills and release it while squeezing through the body's capillaries." In order to consider this let's make an oversimplified model in which oxygen diffuses into the blood stream in the lungs, is carried by fluid flow out to the cells where it diffuses out. (In reality, the oxygen is bound to hemoglobin, carried, and released, but the beginning and end processes are as described here.) A. Consider a capillary in an alveolus in the lung. The density of oxygen inside the capillary is 0.3 million molecules/(um) and in the air outside is about 5 million molecules/(um). Capillaries Arteriole Venule Artery Vein capillaries Tissue cells Source: Wikimedia commons Which way will be the net flow of oxygen across the membrane? O into the capillary O out of the capillary O equal flows into and out of the capillary B. Consider an individual molecule in the air outside the alveolus. Capillary beds Connective tissue Oct 7 2:00 A 3Academica X w 2130 homework 4 (fall/ x VA 2130 homework 4 (fall/ x * [Solved] Two atoms col X Average acceleration o' X *[Solved] Two atoms col x + X C webassign.net/web/Student/Assignment-Responses/last?dep=30229534 B. Consider an individual molecule in the air outside the alveolus. Capillary beds Connective tissue Alveolar sacs Alveolar duct Mucous gland Mucosal lining Pulmonary vein Alveoli Pulmonary artery Atrium Source: Wikimedia commons How is it moving? O moving within the capillary O moving out of the capillary into the muscle cell O moving in random directions C. Now consider a capillary inside a muscle. The muscle has done work and used up its oxygen. The density of oxygen inside the capillary is 1 million molecules/(um) and in the fluid surrounding the muscle is 0.3 million molecules/(um) 3. Which way will the net oxygen flow be across the membrane? O out of the muscle cell into the capillary O into the muscle cell out of the capillary O equally in both directions Oct 7 2:01 A 3Academica X w 2130 homework 4 (fall/ x VA 2130 homework 4 (fall/ x * [Solved] Two atoms col X Average acceleration o' X *[Solved] Two atoms col x + X C webassign.net/web/Student/Assignment-Responses/last?dep=30229534 O moving in random directions C. Now consider a capillary inside a muscle. The muscle has done work and used up its oxygen. The density of oxygen inside the capillary is 1 million molecules/(um) and in the fluid surrounding the muscle is 0.3 million molecules/(um)3. Which way will the net oxygen flow be across the membrane? O out of the muscle cell into the capillary O into the muscle cell out of the capillary O equally in both directions D. Consider an individual molecule in the capillary in part C (after is has been released by the hemoglobin). How is it moving? O remaining within the capillary O in random directions O into the muscle cell E. Fick's Law tells us how a concentration difference drives flow: J = -DAn/Ax. If the membrane in the alveolus (parts A and B) is 7 nm thick, and the diffusion constant, D, for oxygen through the membrane is 6 x 10-3 (um)2/s, calculate the rate of flow through the alveolar membrane. molecules/Jm2/s. M Oct 7 2:01 A 4Two atoms collide while moving in a gas. The larger atom has a mass M, = 6 Daltons and a speed v1 = 244 m/s, while the smaller has a mass M2 = 1 Daltons (D). During the collision both atoms simply bounce off each other. They do not change their speeds, but after the collision they each reverse their directions, bouncing straight back. (You may express your results using the mass unit "Daltons". 1 Dalton is approximately equal to the mass of a proton or neutron and is defined as one-twelfth the mass of a single neutral carbon-12 atom in its ground state.) M1 M2 A. What is the magnitude of the change in the momentum, Apj, of mass M,? 2928 D m/s B. If the collision took place over a time interval of 2 ns, what is the average acceleration experienced by the atom M,? (Note: 1 ns = 1 x 109 s. You can enter your answer in scientific notation using e, like 1.2e3 for 1200.) m/s/s( Express powers of 10 with a small "e". So for 1200 write 1.2e3. Give your answer to 2 significant figures.) A. A common small-molecular weight (and therefore fast diffusing for an organic molecule) ingredient in perfumes is vanillin, the primary component of vanilla bean extract (molecular weight = 152). The D for vanillin in air is 0.114 cm /s. If I open a bottle of vanilla on the other side of the room 3 meters away, and the air is still so there is no convection, about how long would I have to wait before I could expect to smell the vanilla? seconds B. The diffusion constant for glucose in water is 0.70 x 10-5 cm-/s. About how much time would it take to get significant diffusion across the following structures? Assume that glucose diffuses through cells and membranes as fast as it does through water. across a cell membrane 8 nm thick seconds from the center of a eukaryotic cell 6um in radius to the cell membrane seconds across the wall of the human heart 2.5 cm in thickness seconds from the cells in the center of the cactus to the photosynthetic cells on the surface of a barrel cactus if the cactus has a radius of 12 cm secondsOur molecular model of matter describes a fluid as consisting of lots of little particles [atoms or molecules) moving around very fast. Collisions between the molecules makes the particles of the fluid change directions and speeds often and randomly. We've talked about two different phenomena that depend on these random molecular interactions: viscosity and diffusion. Viscosity is the way collisions with other parts of the fluid slow down fasteramoVing bits of fluid, and diffusion is the way collisions spread out concentrations of molecules. Let's see if they could they be related. Let's consider how the viscosity and diffusion coefficients might depend on the properties of the fluid by dimensional analysis. (a) First, determine the dimensionality {in terms of M, L, and T) of the viscosity coefcient {1, and the diffusion coefaent D. Recall that they are dened by the equation for viscous force WWII! _ madam * '6"ng and Fick's law for diffusion d_n ctr J=D where} is the number of molecules crossing a unit area per unit time and n is the concentration. Use dimensional analysis of these equations to determine the dimensionality of pi and Din terms of M, L, and T. Dimensionality of pi = Dimensionality of D = (b) Now let's consider what they might depend on. Since what is controlling both of them are the molecules of the fluid colliding with each other, here are some parameters they might depend on: the mass density of the fluid [9) the average speed of the molecules of the uid (V) how far the molecules travel between collisions (the mean free path A). If we are going to use only these three parameters, nd combinations of these three parameters that give you the correct dimensionality for pi and D. (b) Now let's consider what they might depend on. Since what is controlling both of them are the molecules of the fluid colliding with each other, here are some parameters they might depend on: the mass density of the fluid (p) the average speed of the molecules of the fluid (v) how far the molecules travel between collisions (the mean free path 1). If we are going to use only these three parameters, find combinations of these three parameters that give you the correct dimensionality for u and D. Write an equation that shows how u might depend on p, v, and A: LL= Write an equation that shows how D might depend on p, v, and 1: D= AV (c) From the dimensionality of each, construct a plausible relation between u and D (i.e., an equation relating u and D). U =