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.
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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.