Chapter 20, Problem 20.63E

At room temperature $\left(22°\text{C}\right)$, the rate constant for proton transfer between water molecules in solution is about $1\times {10}^{11}{\text{s}}^{-1}$, which is one of the fastest known reactions in a condensed phase. If the activation energy for this process equals one-half of the $\text{O}-\text{H}$ bond strength of $498\text{kJ}/\text{mol}$, what is the pre-exponential factor $A$ for this reaction?