Indirectly Measuring Diffusion of NO2 into Water
NO2 is a free stable radical, better express as $\ce{.NO2}$, and being a radical, does not directly react with H2O, or H+ or OH-.

The reaction mechanism likely proceed via a self-reaction creating nitrogen tetroxide:

$\ce{.NO2 + .NO2 &lt;=&gt; N2O4 }$

In a diluting medium of air, depending on the concentration of nitrogen dioxide, this reaction is kinetically expected to be slow.

When it does occur, it can be followed by:

$\ce{N2O4 +  H2O -&gt; HNO2 + HNO3 }$

Source: See Reactions (9) and (10) on Page 28 of this paper.

Now, one can ignore the intermediate reaction mechanics, for simplicity, however, this does present a problem for some, as yourselves, as clearly the rate determining step is not even cited. 

Also, if you review the paper, there are other reaction equilibriums that you may have to take into consideration. As a sidebar, what the paper does not mention is that aqueous nitrite is a photo-sensitive producing products, so you may wish to control the amount of lab light exposure as well.