Question

P160.4 A lump of sucrose of mass 10.0g is suspended in the middle of a spherical flask of water of radius 10 cm at 25°C. What is the concentration of sucrose at the wall of the flask after (a) 1.0 h, (b) 1.0 week. Take D= 5.22 10-'m's

Answer 1

a lump of sucrose and it is suspended in no so this exercise we have the middle of a spherical Ilars of water. . We have to answer what is the concentration of sucrose at the wals of the flask after thank and week. 1. To solve this we need to use aquation for 3-dimensional diffusion- ccat) - LOOF 312 e 4ot where, C (e,t) = concentration of sucrose at distance. no = number of moles of sucrose. t = time D = Diffusion coefficient for sucrose D = m²ls. 5.22 x 10 r Radius of spherical flash = loom = olm * Mass of sucrose is given as log, convert this to moles. (Moliwt of sucrose : 342.3g/mol) molesing = wt lesing - mot ut = 342.39 a 100g = 2.9x102 mol. * Now lets calculate I = 4.5 x 10 mls - -V2 4.5xió pels = 4.8x106Sec. substitute these values into the equation c (2,7) = 0 132 qot » c(x, t) = 2.9810?mos 48x1ots 8 X 5.22x10'215xt <(x, t) = 5.5 x16°mo lm3 -4.8x10sec - (+) 312 Here t is the only variable that needs to be substituted to get the concentration at time t.

a. In this case we have to answer what is the concentration of sucrose at the Wall of the flask after lohr. t = lar conversion (Because = 3600 sec all other time units are in sec is minst) , D= 5.22x10 tom²/s substitute all the values on the right side an eqo Ime é e os 5.5x10 mollins -4.84106s I rea Top=4.8 x 106 sims no = 2.9x10 mos t = 3600 sec c(10cm, iour) = (3600g) 312 1 2.5x18 mollm3 r 8.7 xio 580 - 580 = ~ Omollme sucrose diffusion is close to zero. so, at the wall after one hows Thr I t= 604800S (6) In this case we have to answer what is the concentration of sucrose at the wall of the flask after one week. Firstly convert time from week to sec 1 t = week = week . 7 days . 84h. 36005 = 6088005 1 week Iday use all the values on the right side in eqo clroom, week) = 5.5x10 mot lims -4.8x100s 0 25.22x1070 m² ls 1 r2 =4.8x10° slm = 117 mol/m3 (3.5 7 x704) = 4.18810? mot lm3 l So, at the wall after I week, sucrose diffusion concentration 1. & 4.188102 mol ) m3. (6048005) 312 e 604800s/ No: 2.9 4102 mol