1. This is _____ a heavy chair that it is not easy to carry. (much, such) 2. I was ___ pleased about the letter that I ran to tell my mother. (so, very)
“Such” is correct, because it is a qualifying adverb modifying “heavy” – how heavy? Such that the chair is not easy to carry. “Much” is an adjective and (even though it looks like “such”) is not grammatically related.
“So” is correct because it is a qualifying adverb modifying “pleased” – how pleased? So pleased that I ran to tell my mother. “Very” is an adverb also, but not a “qualifying” adverb.
These small words are confusing to new language learners but can be explained grammatically. Native speakers have no trouble differentiating among them because they have heard them in speech patterns.