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A very thin layer of oil floats on top of water. A drop of dye is placed at the center of the oil. The dye diffuses through the oil in all directions equally with a diffusion constant D0. Since the layer of oil is thin, we can assume the diffusion is two-dimensional. After a time T0 has passed, the dye has diffused a distance of 5 mm. If the dye had a diffusion constant of D0/3 what distance would the dye have diffused after a time T0/4? Give your answer in units of mm. (Round your answer to two decimal places.)
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- (a) Find the average time required for an oxygen molecule to diffuse through a 0.200-mm-thick tear layer on the cornea. (b) How much time is required to diffuse 0.500 cm3 of oxygen to the cornea if its surface area is 1.00 cm2?The small capillaries in the lungs are in close contact with the alveoli. A red blood cell takes up oxygen during the 0.5 s that it squeezes through a capillary at the surface of an alveolus. What is the diffusion time for oxygen across the 1-μm -thick membrane separating air from blood? Assume that the diffusion coefficient for oxygen in tissue is 2×10^−11 m2/s. Give your answer to 1 significant figure.Bacteria have a density that is about the same as water. Their average velocity is 10^-3 m/s. A bacterium with a radius of 1 um should have a diffusion coefficient of about 2.2x10^-13 m^2/s. (a) Find the random-walk step size (b) How long does it take for an average walk to reach 1 mm in seconds and days? Note that we are considering the diffusion away from the starting point and are calculating the distance through three dimensions. Show your work
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- Many entertainers have facial tattoos. Assuming the ink is in the extracellular space, how long would it take to diffuse (or blur) 10mm? Assume the diffusion coefficient of the ink is 2.5*10-8 cm2/s and that 2 dimensional diffusion occurs in the skin. (hint: use similar units for the variables) 29 days 116 days 231 days 58 daysA typical sugar cube has an edge length of 1 cm. If you had a cubical box that contained a mole of sugar cubes, what would its edge length be?Let us consider a bacterial cell that depends on chemical reactions using oxygen to produce energy. The cell needs to obtain molecular oxygen from the extra-cellular medium by diffusion through the cell membrane. We model the cell as a water-filled sphere of radius 1 µm. This means that we neglect the presence of the internal structures of the cell: nucleus, nutrients, etc. The oxygen diffusion coefficient (O2) in water at 25°C is 1.0x10-5 cm².s'. Figure 1: Transmission electron microscope Reminder: The distance travelled by diffusion can be picture of a bacterium. [from Wikipedia: written as L(t) = V6Dt, where D is the diffusion coefficient and t the diffusion time. "Transmission Electron Microscopy"| 2. Diffusion as a function of time People have measured the distance travelled by the oxygen molecule in water as a function of time. The results are given in the table below. 0.1 t(s) L (x10-“m) log1o(t) log10(L) 0.001 0.005 0.01 0.05 2.45 5.4 7.7 17.3 25.5 Draw the plot of L as a…
- A food coloring has a diffusion constant in water of 10 x 10–10 m2/s. A difference of food coloring concentration of 20 g/m3 is maintained between the ends of a cylinder with a cross-sectional area of 5 cm2 and a length of 8 cm. How much mass of food coloring diffuses though the cylinder in 20 minutes? A.1.5 x 10-10 kg B.1.5 x 10-8 kg C.1.5 x 10-6 kg D.1.5 x 10-4 kg E.1.5 x 10-2 kgThe most dangerous particles in polluted air are those with diameters less than 2.5 μm because they can penetrate deeply into the lungs. A 15-cm-tall closed container holds a sample of polluted air containing many spherical particles with a diameter of 2.5 μm and a mass of 1.4 x 10-14 kg. How long does it take for all of the particles to settle to the bottom of the container?A 2.0-cmcm-diameter, 0.50-mmmm-thick spherical plastic shell holds carbon dioxide at 2.0 atm pressure and 25•C. CO2 molecules diffuse out of the shell into the surrounding air, where the carbon dioxide concentration is essentially zero. The diffusion coefficient of carbon dioxide in the plastic is 2.5x10-12 m2/s. a. What is the diffusion rate in molecules/s of carbon dioxide out of the shell? Express your answer in molecules per second. b. If the rate from part A is maintained, how long in hours will it take for the carbon dioxide pressure to decrease to 1.0 atm? The actual rate slows with time as the concentration difference decreases, but assuming a constant rate gives a reasonable estimate of how long the shel will contain the carbon dioxide. Express answer in hours.
