Some reactions are so rapid that they are diffusion controlled; that is, the rea
ID: 1006231 • Letter: S
Question
Some reactions are so rapid that they are diffusion controlled; that is, the reactants react as quickly as they can collide. An example is the neutralization of H3O+ by OH- ,which has a second-order rate constant of 1.3 x 10^11 M^-1 s^-1 at 25C.
(a) If exactly equal volumes of 2.0M HCl and 2.0M NaOH are mixed instantaneously, how much time is required for 99.999% of the acid to be neutralized?
(b) Under normal laboratory conditions, would you expect the rate of the acid-base neutralization to be limited by the rate of the reaction or by the speed of mixing?
Explanation / Answer
(a): Since neutralization reaction is a 2nd order reaction, the rate law can be written as
rate = kx[H3O+]x[OH-]
where k = 1.3x1011 M-1s-1
Given initial concentration for both the reactant are same and equals to 2.0 M i.e
[H3O+] = [OH-] = [A]0 = 2.0 M
When the reaction is 99.999% completed, the final concentration of both the reactants are
[H3O+] = [OH-] = [A]t = 2.0 M x (0.001/100) = 2.0x10-5 M
the integrated rate law canbe written as
kt = 1/[A]t - 1/[A]0
=> 1.3x1011 M-1s-1 x t = 1/(2.0x10-5 M) - 1/(2.0 M)
=> 1.3x1011 M-1s-1 x t = 49999.5 M-1
=> t = 3.85x10-7 s (answer)
(b):Since the rate of the acid-base neutralization is very high and very less time is required the completion of the reaction, rate of the acid-base neutralization cannot be limited by the rate of the reaction.
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