What is the chemical formula for acid raid?

Pure rainwater is already acidic due to carbon dioxide (#"CO"_2#) in the air dissolving in the rainwater and reacting according to the following equation.

#"H"_2"O" + "CO"_2 rightleftharpoons "H"_2"CO"_3^#

Acid rain is caused additionally by having large amounts of sulfur dioxide (#"SO"_2#) and nitrogen oxides (#"NO"_x#) from the atmosphere dissolve into the rainwater.

Sulfur dioxide is produced primarily from burning of fossil fuels that contains sulfur. It gets oxidized by molecular oxygen present in air to produce sulfur trioxide (#"SO"_3#), according to the following reaction.

#2"SO"_2 + "O"_2 -> 2"SO"_3#

The sulfur trioxide produced then dissolves in the rainwater.

#"SO"_3 + "H"_2"O" rightleftharpoons "H"_2"SO"_4#

The overall reaction is given by combining the two steps.

#2"SO"_2 + "O"_2 + 2"H"_2"O" rightleftharpoons 2"H"_2"SO"_4#

Nitrogen dioxide results from combustion using air (which 99% is made up of #"N"_2# and #"O"_2#) as oxidants. It reacts in water to form a equimolar nitrous (#"HNO"_2#) and nitric acid (#"HNO"_3#) solution.

#2"NO"_2 + "H"_2"O" rightleftharpoons "HNO"_2 + "HNO"_3#

However, nitrous acid decomposes rapidly to regenerate nitrogen dioxide and water, while at the same time producing nitric oxide (#"NO"#).

#2"HNO"_2 -> "NO" + "NO"_2 + "H"_2"O"#

The nitric oxide produced can be oxidized by atmospheric oxygen back into nitrogen dioxide, although this happens at a relatively slower rate.

#2"NO" + "O"_2 -> 2"NO"_2#

So when we combine the 3 reactions, the overall equation is

#4"NO"_2 + "O"_2 + 2"H"_2"O" rightleftharpoons 4"HNO"_3#

All the acids produced in the above reaction will dissociate in water to give #color(red)("H"_3"O"^{+})#, which is why the pH decreases.

#"H"_2"CO"_3 + "H"_2"O" rightleftharpoons "HCO"_3^{-} + color(red)("H"_3"O"^{+})#

#"HNO"_3 + "H"_2"O" -> "NO"_3^{-} + color(red)("H"_3"O"^{+})#

#"H"_2"SO"_4 + "H"_2"O" -> "HSO"_4^{-} + color(red)("H"_3"O"^{+})#