# Chemistry - Why is it considered acid rain with pH <5.6?

## Solution 1:

The $$\mathrm{pH}$$ of pure water (rain as well as distilled water) in equilibrium with the atmosphere ($$p_{\ce{CO2}}= 10^{-3.5}\ \mathrm{atm}$$) can be calculated as follows.

$$[\ce{H2CO3^*}]=K_\mathrm H\cdot p_{\ce{CO2}}$$

where $$[\ce{H2CO3^*}]$$ is the total analytical concentration of dissolved $$\ce{CO2}$$, i.e. $$[\ce{H2CO3^*}]=[\ce{CO2(aq)}]+[\ce{H2CO3}]$$, and
$$K_\mathrm H= 3.39\times10^{-2}\ \mathrm{mol\ l^{-1}\ atm^{-1}}$$ is Henry's law constant for $$\ce{CO2}$$.

\begin{align} \log[\ce{H2CO3^*}]&=\log K_\mathrm H+\log p_{\ce{CO2}}\\ &=-1.5-3.5\\ &=-5.0 \end{align}

The commonly used first acid dissociation constant of carbonic acid $$\mathrm pK_{\mathrm a1}=6.3$$ (at $$25\ \mathrm{^\circ C}$$) actually is a composite constant that includes both the hydration reaction $$\ce{H2O + CO2(aq) <=> H2CO3}$$ and the protolysis of true $$\ce{H2CO3}$$ $$\ce{H2CO3 <=> H+ + HCO3-}$$ For a weak acid \begin{align} \log[\ce{H+}]&\approx\frac12\left(\log K_\mathrm a+\log[\ce{H2CO3^*}]\right)\\ &=\frac12\left(-6.3-5.0\right)\\ &=-5.65\\ \mathrm{pH}&=5.65 \end{align}

Thus, pure rain in equilibrium with the atmosphere has about $$\mathrm{pH}=5.65$$. Any acid rain with lower $$\mathrm{pH}$$ would be caused by additional acids.

## Solution 2:

You are forgetting an important component of the air: carbon dioxide. When it dissolves in pure water (=rain water), it makes it acidic. It is not considered that harmful.

Acid rain has a negative connotation; it is mainly caused by anthropogenic activities. The low pH of acid rain is due to sulfur oxides and nitrogen oxides and it is indeed below 5.7.

IUPACs definition "Rain with pH values < about 5; commonly results from acids formed from pollutants. 'Pure' rain water equilibrated with atmospheric CO2 and naturally occurring acids in relatively clean air usually has a pH>5."

## Solution 3:

Under atmospheric pressure, dissolved carbon dioxide can reach an equilibrium state in water that yields a pH of as low as 5.7