[biostu]

The diffusion coefficient D of an ion is related to its ionic mobility u by

D = uRT / zF

The ionic mobilities of H+ and OH- are 3.63x10-7 m2 V-1 s-1 and 2.06 x 10-7 m2 V-1 s-1 at 25°C.  What is the rate constant for the following reaction?

H+ + OH- -> H20

The reaction radius is 0.75 nm, because once the proton is this close the reaction can proceed very rapidly by quantum mechanical tunneling.  The electrostatic factor f is 1.70.

-------------------------------

I know the formula for this problem is k = 4piDRN (1000 L /m^3), where D = uRT/ zF and N is Avogadro.  I'm guessing R is the reaction radius.  I'm pretty sure z is +1 since the molecules are moving together and F is Faraday constant, although I'm not sure on which units to use.  The electrostatic factor I'm guessing is some kind of correction factor to be used at the end.

I was absent the day we went over this and so I am lost as to how to incorporate the ion mobilities to solve for this problem.

I know the answer is 1.4 x 10^11 L/mol/s from the answer key.

Any help would be much appreciated.  Thank you.