18B.6. Two-bulb experiment for measuring gas diffusivity-quasi-steady-state analysis (Fig. 18B.6). One way of measuring gas diffusivities...

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18B.6. Two-bulb experiment for measuring gas diffusivity-quasi-steady-state analysis“ (Fig. 18B.6). One way of measuring gas diffusivities is by means of a two-bulb experiment. The left bulb and the tube from z = -L to z = 0 are filled with gas A. The right bulb and the tube from z = 0 to z = +L are filled with gas B. At time t = 0 the stopcock is opened, and diffusion begins; then the concentrations of A in the two well-stirred bulbs change. One measures x, as a function of time, and from this deduces D. We wish to derive the equations describing the diffusion. Since the bulbs are large compared with the tube, x and x, change very slowly with time. Hence the diffusion in the tube can be treated as a quasi-steady-state problem, with the boundary conditions that xA = x, and z = -L, and that xA = xA at z = +L. (a) Write a molar balance on A over a segment Az of the tube (of cross-sectional area S), and show that NA C, a constant. (b) Show that Eq. 18.0-1 simplifies, for this problem, to dxA NA- (18B.6-1) dz (c) Integrate this equation, using (a). Call the constant of integration C2. (d) Evaluate the constant by requiring that xA (e) Next set xA = xà (or 1 – x;) at z = x at z = +L. || -L, and solve for NA to get finally c AB G – x)- NA- (18B.6-2) (f) Make a mass balance on substance A over the right bulb to obtain dx Vc (Yx – )s dt CDAB (1813.6-3) %3! L (g) Integrate the equation in (f) to get an expression for x which contains DAR: SDARt In (18B.6-4) LV 2 (h) Suggest a method of plotting the experimental data to evaluate DAn. 18B.6. Two-bulb experiment for measuring gas diffusivity-quasi-steady-state analysis“ (Fig. 18B.6). One way of measuring gas diffusivities is by means of a two-bulb experiment. The left bulb and the tube from z = -L to z = 0 are filled with gas A. The right bulb and the tube from z = 0 to z = +L are filled with gas B. At time t = 0 the stopcock is opened, and diffusion begins; then the concentrations of A in the two well-stirred bulbs change. One measures x, as a function of time, and from this deduces D. We wish to derive the equations describing the diffusion. Since the bulbs are large compared with the tube, x and x, change very slowly with time. Hence the diffusion in the tube can be treated as a quasi-steady-state problem, with the boundary conditions that xA = x, and z = -L, and that xA = xA at z = +L. (a) Write a molar balance on A over a segment Az of the tube (of cross-sectional area S), and show that NA C, a constant. (b) Show that Eq. 18.0-1 simplifies, for this problem, to dxA NA- (18B.6-1) dz (c) Integrate this equation, using (a). Call the constant of integration C2. (d) Evaluate the constant by requiring that xA (e) Next set xA = xà (or 1 – x;) at z = x at z = +L. || -L, and solve for NA to get finally c AB G – x)- NA- (18B.6-2) (f) Make a mass balance on substance A over the right bulb to obtain dx Vc (Yx – )s dt CDAB (1813.6-3) %3! L (g) Integrate the equation in (f) to get an expression for x which contains DAR: SDARt In (18B.6-4) LV 2 (h) Suggest a method of plotting the experimental data to evaluate DAn.