To gain a much more molecular understanding of diffusive motion, it is instructi
ID: 773735 • Letter: T
Question
To gain a much more molecular understanding of diffusive motion, it is instructive to compute the "jump distance" of a diffusing molecule. This can be estimated using the Einstein-Smoluchowski relationship which says that diffusion governed by diffusion coefficient D can be related to jump length lambda and time between jumps tau as D = lambda2/2 pi Consider a spherical molecule of diameter 4.00 Angstroms diffusing in water with viscosity of 1.00 cP. What is the jump time tau in ps if the jump distance lambda equals one molecular diameter. (In other words, how often does the particle have to jump with step sizes of one diameter to diffuse at the rate governed by its D value in water?) Calculate the diffusion coefficient for the protein cytochrome c in aqueous solution assuming sphericity and using the Stokes-Einstein equation at 25 degree C. The hydrodynamic radius is R =18.9 Angstroms. The viscosity of water is 1.00 cP = 0.00100 kg/m-s. Dcytc = m2 /s. If the critical reaction distance is the sum of their radii, what value is expected for the Smoluchowski theory second order rate constant for a diffusion controlled reaction between two cytochrome c's? kd = L mol-1s-1 What would be the rate constant if the protein had twice the radius? kd = L mol-1-s-1 You should be able to explain this surprising result. The rate of decomposition of a sample of gaseous A, can be written as: Suppose at a certain temperature, the rate of decomposition of A, initially at a pressure of 530 Torr, was 1.07 Torr s-1 when 5.0 per cent had reacted and 0.76 Torr s-1 when 20.0 per cent had reacted. Determine the order a of the reaction, and then determine the rate constant with Torr and seconds in the units. determine the half-life of a starting from initial pressure 530 Torr sExplanation / Answer
12.given jump distance = diameter = 4 A ,
then 2T = Lamda^2/D , time T = (4x10^-10)^2 /2D ,
but D = RT/(N x 6 x3.14 x n x r) , where N- avagadro number , r= radius of molecule in m ,
n- viscocity in poise = 1/100 =0.01 ,
D = (8.314 x298)/(6.023 x10^ 23 x 6 x3.14 x 0.01 x 2 x10^ -10) = 1.091 x10^ -10 m/s ,
now time T = 16 x10^ -20/ (1.091 x10^ -10) = 1466 x 10^ -12 seconds = 1466 ps