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Fundamentos de Transferencia de Momento, Calor y Masa - Welty, Limusa-Wiley, 2a. Ed. 26.11 La celda de Arnold descrita en el problema 26.10 se va a operar como una celda en estado pseudo permanente. Si el tubo estuviera inicialmente lleno de etanol hasta la boca del tubo, ¿cuánto tardaría el nivel del etanol en descender? a) 2 cm. b) 4 cm. c) 10 cm 26.15 Se extrae amoniaco, NH,, en forma selectiva, de una mezcla de aire y NH, mediante la absorción en agua. En este proceso en estado permanente, el amoniaco se difunde a través de una película de gas estancado de 2 cm de espesor y después a través de una capa de agua estancada de 1 cm de espesor. La concentración de amoniaco en la frontera externa de la capa de gas es de 4.5% por volumen y la concentración de amoniaco en la frontera exterior de la capa de agua es, esencialmente, igual a cero. La temperatura del sistema es de 15" C y la presión total sobre el mismo es de 1 atm. La concentración en la interfase entre el gas y las fases líquidas está dada por los siguientes datos de equilibrio: Datos de equilibrio correspondientes al amoniaco en aire sobre soluciones acuosas P NH3 (mmHg) 5 10 15 20 15 30 C NH3 (mol/cm3)(10^6) 6,1 11,9 20.0 32.1 53.6 84. Determine la rapidez de difusión del amoniaco 26.18 Una capa de etanol de 0.05 in de grosor se mantiene a 75" F en contacto con aire seco a 75" F y 1 atm. La gravedad específica del etanol es de 0.789. Suponiendo que la vaporización se lleva a cabo por difusión molecular a través de una película de gas de 0.15 in de espesor, calcule el tiempo necesario que debe transcurrir para que el etanol se evapore totalmente. Transferencia de Masa - Fundamentos y Aplicaciones- Hines & Maddox. Prentice-Hall, 1a. Ed. 1.10 An ideal solution containing 0.1 x10-^3 m^3 of methanol and 9.0 x10-^3 m^3 of^ benzene moves at a molar average velocity of 0,12 m/s. if the molar flux of benzene relative to the mass average velocity is - 1. kgmol/m^2 * s, what is the total molar flux of methanol, N A, and the mass average velocity? Methanol A Benzene B M A = 32,04 kg/kgmol M B = 78.12 kg/kgmol P A = 792 kg/m3 P B = 879 kg / m 3.25 Solute A diffuses from a liquid phase I, where its molar concentration is C AI, into liquid II where it reacts. The reaction is first order with respect to the solute A. The molar flux at a depth L in liquid II falls to the one-fourth of its value at the liquid-liquid inter-face: 𝑁𝐴𝑍|𝑍= 0 = 4 𝑁𝐴𝑍|𝑍=𝐿 Obtain an expression for (a) the concentration of A in liquid II as a function of the depth from the surface, and (b) the molar flux at the liquid-liquid interface. Assume that the process is carried out at steady state. The process is shown in figure 3-15.
Principles and modern applications of mass transfer operations- Jaime Benitez, Ed. John Wiley and Sons 1.26 Ammonia, NH3, is being selectively removed from an air–NH3 mixture by absorption into water. In this steady-state process, ammonia is transferred by molecular diffusion through a stagnant gas layer 5 mm thick and then through a stagnant water layer 0.1 mm thick. The concentration of ammonia at the outer boundary of the gas layer is 3.42 mol% and the concentration at the lower boundary of the water layer is essentially zero. The temperature of the system is 288 K and the total pressure is 1 atm. The diffusivity of ammonia in air under these conditions is 0.215 cm2/s and in liquid water is 1.77 × 10–5 cm2/s. Neglecting water evaporation, determine the rate of diffusion of ammonia, in kg/m2·h. Assume that the gas and liquid are in equilibrium at the interface. The equilibrium data for ammonia over very dilute aqueous solution at 288 K and 1 atm can be represented by (Welty et al., 1984)
Where s is the concentration of substrate in the sludge layer (gmol cm-^3 ) and k 1 is the first-order rate constante (s-^1 ). The effective diffusivity of substrate in sludge is DSe. Obtain a differential equation relating s and z. Hint: Area A is constant for flat-plate geometry and can be cancelled from all terms of the mass- balance equation. b) External mass-transfer effects at the liquid-sludge interface are negligible. What are the boundary for this problem? c) The differential equation obtained in (a) is solved by making the substitution: 𝑠 = 𝑁𝑒𝑝𝑧 where N and p are constants. i. Substitute this expression for s into the differential equation derived in (a) to obtain an equation for p. (Remember that √𝑝^2 = 𝑝 𝑜𝑟 − 𝑝.) ii. Because there are two possible values of p, let: 𝑠 = 𝑁𝑒𝑝𝑧^ + 𝑀𝑒−𝑝𝑧 Apply the boundary condition at z=0 to this expression and obtain a relationship between N and M. iii. Use the boundary condition at z=L to find N and M explicity. Obtain an expression for s as a function of z. iv. Use the definition of cosh x: cosh 𝑥 =
𝑒𝑥^ + 𝑒−𝑥
to prove that: 𝑠 𝑠𝑏
cosh (𝑧√ (^) 𝐷𝑘^1 𝑆𝑒
cosh (𝐿√
𝐷𝑆𝑒^ )
d) At steady state, rate of substrate consumption must be equal to the rate at which substrate enters the sludge. As substrate enters the sludge by diffusion, the overall rate of reaction can be evaluated using Fick’s law: 𝑟𝐴,𝑜𝑏𝑠 = 𝐷𝑆𝑒𝐴
Where 𝑑𝑠 𝑑𝑧
Use the equation for s from © to derive an equation for 𝑟𝐴,𝑜𝑏𝑠. Hint: the derivative of cosh ax= a sinh ax where a is a constant and: sinh 𝑥 =
𝑒𝑥^ − 𝑒−𝑥
e) Show from the result of (d) that the internal effectiveness factor is given by the expression: 𝜂𝑖𝑙 = tanh 𝜙 1 𝜙 1 Where 𝜙 1 = 𝐿√^
And tanh 𝑥 = sinh 𝑥 cosh 𝑥
f) Plot the concentration profiles through a sludge layer of thickness 2 cm for the following sets of conditions: (1) (2) (3) K 1 (s -^1 ) 4,7x10-^8 2,0 x10-^7 1,5 x10-^4 DSe (cm^2 s-^1 ) 7,5 x10-^7 2,0 x10-^7 6,0 x10-^6 Take sb to be 10 -^5 gmol cm-^3. Label the profiles with corresponding values of 𝜙 1 and 𝜂𝑖𝑙. Comment on the general relationship between 𝜙 1 , the shape of the concentration profile, and the value of 𝜂𝑖𝑙.
