Chemical Kinetics using Integrated Rate Laws

Question

Some reactions are so rapid that they are said to be 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 1.3×10^11M−1s−1 at 25∘C. If equal volumes of 4.0 M HCl and 4.0 M NaOH are mixed instantaneously, how much time is required for 99.999% of the acid to be neutralized?

Express your answer using two significant figures.

I have tried the above problem nearly 20 times, and every time I have used the integrated rate law for a 2nd order reaction and gotten the answer 1.9*10^-7 seconds, which is wrong. What am I doing incorrectly? I am plugging in 0.00004 for At, 4 for A0 and the given rate constant for k into the 2nd order integrated rate law. Please advise!

Answer 1

When you mix equal volumes of two solutions, all initial concentrations are diluted by a factor of 2. Formally concentration A after mixing = concentration A before mixing * V_A/(V_A+V_B)

Your calculation is fine, you just have to start with 2 Molar rather than 4M