It is implied early on the acid rains are somehow linked to climate change. However, they are not; they are due to emissions of sulfur dioxide and nitrogen oxide, mostly due to the burning of coal and oil and agriculture. Due to air pollution regulation starting in the 80s, acid rains are not a big problem anymore in several continents like Europe or North America, even though it is still ongoing in Russia or China.
Actual acid rains do not impact the environment the way they do in the movie. Even severe acid rains with a pH of 2, capable of damaging structures, do not have immediate effect, nor do they burn human beings or melt cars.
It is never explained how or why the acid rains take over the planet. In real life, they are due to several kinds of air pollution, particles which move around so the acid rains could happen hundreds of miles away from the emission site, but not across oceans.
The BFMTV news channel lower third misspells "pH" as "PH".