# By how many pH units does rain vs distilled water change a soil pH test?

Sources state that the concentration of $$\ce{H2CO3}$$ in rain is of a few µmol; I don't know if that's per ml. The buffering effect of most soils is >1000 µmol $$\ce{H+}$$/kg.

Is the difference from low acid rain water versus lab distilled water on a pH test for soil less than 0.1 in pH values?

Pure water (rain as well as distilled water) in equilibrium with the atmosphere ($$p_{\ce{O2}}=10^{-3.5}\ \mathrm{atm}$$) can be calculated to contain about \begin{align} \mathrm{pH}=-\log[\ce{H+}]&=5.65\\ -\log[\ce{HCO3-}]&=5.65\\ -\log[\ce{CO3^2-}]&=10.3\\ -\log[\ce{H2CO3^*}]&=5.0\\ -\log[\ce{CO2}]&=5.0\\ -\log[\ce{H2CO3}]&=7.8\\ \end{align}
Note that $$[\ce{H2CO3^*}]$$ is the total analytical activity of dissolved $$\ce{CO2}$$, i.e. $$[\ce{H2CO3^*}]=[\ce{CO2(aq)}]+[\ce{H2CO3}]$$. $$[\ce{H2CO3}]$$ is the concentration of true $$\ce{H2CO3}$$.
Thus, $$[\ce{H2CO3^*}]=10^{-5}$$ and $$c(\ce{H2CO3^*})=10^{-5}\ \mathrm{mol/l}$$; i.e. a few µmol/l.