Problem 99
A pond with an initial oxygen content of zero is to be oxygenated by forming a tent over the water surface and filling the tent with oxygen gas at \(25^{\circ} \mathrm{C}\) and \(110 \mathrm{kPa}\). Determine the mole fraction of oxygen at a depth of \(0.8 \mathrm{~cm}\) from the surface after $24 \mathrm{~h}$.
Problem 100
A heated piece of steel, with a uniform initial carbon concentration of \(0.20\) percent by mass, was exposed to a carburizing atmosphere for an hour. Throughout the entire process, the carbon concentration on the surface was \(0.70\) percent. If the mass diffusivity of carbon in steel in this process was uniform at \(1 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}\), determine the percentage of mass concentration of carbon at \(0.2 \mathrm{~mm}\) and $0.4 \mathrm{~mm}\( below the surface after the process. Answers: \)0.428$ percent, \(0.268\) percent
Problem 102
What is diffusion velocity? How does it affect the mass-average velocity? Can the velocity of a species in a moving medium relative to a fixed reference point be zero in a moving medium? Explain.
Problem 103
What is the difference between mass-average velocity and mole-average velocity during mass transfer in a moving medium? If one of these velocities is zero, will the other also necessarily be zero? Under what conditions will these two velocities be the same for a binary mixture?
Problem 104
Define the following terms: mass-average velocity, diffusion velocity, stationary medium, and moving medium.
Problem 105
Consider one-dimensional mass transfer in a moving medium that consists of species \(A\) and \(B\) with \(\rho=\) \(\rho_{A}+\rho_{B}=\) constant. Mark these statements as being True or False. (a) The rates of mass diffusion of species \(A\) and \(B\) are equal in magnitude and opposite in direction. (b) \(D_{A B}=D_{B A^{-}}\) (c) During equimolar counterdiffusion through a tube, equal numbers of moles of \(A\) and \(B\) move in opposite directions, and thus a velocity measurement device placed in the tube will read zero. (d) The lid of a tank containing propane gas (which is heavier than air) is left open. If the surrounding air and the propane in the tank are at the same temperature and pressure, no propane will escape the tank, and no air will enter.
Problem 106
What is Stefan flow? Write the expression for Stefan's law and indicate what each variable represents.
Problem 107
A researcher is using a \(5-\mathrm{cm}\)-diameter Stefan tube to measure the mass diffusivity of chloroform in air at \(25^{\circ} \mathrm{C}\) and $1 \mathrm{~atm}\(. Initially, the liquid chloroform surface was \)7.00 \mathrm{~cm}\( from the top of the tube; after \)10 \mathrm{~h}$ elapsed, the liquid chloroform surface was \(7.44 \mathrm{~cm}\) from the top of the tube, which corresponds to \(222 \mathrm{~g}\) of chloroform being diffused. At \(25^{\circ} \mathrm{C}\), the chloroform vapor pressure is $0.263 \mathrm{~atm}$, and the concentration of chloroform is zero at the top of the tube. If the molar mass of chloroform is $119.39 \mathrm{~kg} / \mathrm{kmol}$, determine the mass diffusivity of chloroform in air.
Problem 108
A 1-in-diameter Stefan tube is used to measure the binary diffusion coefficient of water vapor in air at \(80^{\circ} \mathrm{F}\) and \(13.8\) psia. The tube is partially filled with water with a distance from the water surface to the open end of the tube of \(10 \mathrm{in}\). Dry air is blown over the open end of the tube so that water vapor rising to the top is removed immediately and the concentration of vapor at the top of the tube is zero. During 10 days of continuous operation at constant pressure and temperature, the amount of water that has evaporated is measured to be $0.0025 \mathrm{lbm}$. Determine the diffusion coefficient of water vapor in air at \(80^{\circ} \mathrm{F}\) and \(13.8\) psia.
Problem 109
Benzene is classified by the U.S. Department of cinogen. Exposure to benzene increases the risk of cancer and other illnesses in humans. The Occupational Safety and Health Administration (OSHA) has established that action should be taken when the benzene level in air reaches \(0.5 \mathrm{ppm}\). A lab technician has poured liquid benzene \((M=78.11 \mathrm{~kg} / \mathrm{kmol})\) into 10 test tubes with an inner diameter of \(25 \mathrm{~mm}\). Each test tube holds an equal amount of liquid benzene at a level of \(1 \mathrm{~cm}\) from the top. The benzene vapor pressure is \(10 \mathrm{kPa}\), and evaporation of benzene to the surrounding air is occurring at \(25^{\circ} \mathrm{C}\) and $1 \mathrm{~atm}$. The HVAC system for the laboratory is capable of keeping the air fresh, provided that the rate of benzene vapor being evaporated is below \(3 \mathrm{~g} / \mathrm{h}\). Determine whether or not the benzene evaporation rate from all 10 test tubes would present health risks to the people in the laboratory.
