这个英语句子对不对？帮我看一下，拜托，谢谢。

The air is polluted with a lot of black smoke by factories that burn coal.

建议把句子中的by前面加过去分词produced，这样produced by factories that burn coal 就作为后置定语，修饰 a lot of black smoke。这就避免了with短语和by短语都去修饰is polluted。