Since HI is a strong acid, it completely dissociates in water. However, because the concentration is so low, we must consider the water autoionization equilibrium. The reaction is
For this reaction
The equilibrium constant is related to the activities by
The charge balance equation for this solution is
with 
. Combining
these last two equations, we have
which we can rearrange to the quadratic equation
The positive root of this equation is
