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I know the meaning of despair but I can't understand what the phrase much to his despair means in the following sentence.
His friend went back on his word much to his despair.
Could anybody please help me understand the meaning of this phrase in a way that I will be able to use it in my own writing in future.
Regarding the usage of to:
to
preposition
2 b —used as a function word to indicate the result of an action or a process
// broken all to pieces
// go to seed
// to their surprise, the train left on time
(M-W)
to
preposition
2.2 Governing a phrase expressing someone's reaction to something.
‘to her astonishment, he smiled’
‘Much to his surprise, this small film has turned out to have wide appeal.
(Lexico)
Regarding the usage of much:
much
determiner
a large amount or to a large degree:
• Much to our surprise, (= we were very surprised that) they accepted our offer.
(Cambridge Dictionary)
So much to his despair means that "he" suffered despair to a great extent (much despair) due to the friend's going back on his word. I personally don't believe it is clear who "he/his" is (who suffered the despair), but presumably it is the first friend (not the one who went back on his word).
Notice that this is not an isolated usage of much to. A common usage is much to someone's surprise:
much to someone's surprise
idiom
Definition of much to someone's surprise
—used to say that someone is very surprised by something
// Much to our surprise, she refused.
(M-W)
The phrase "much to his despair" is a variation of the phrase "be the despair of". This sentence is saying that because this person's friend went back on his word (going back on your word is when you break a promise or you fail to uphold a commitment you made), it caused this person's friend despair. In this sentence, "despair" is referring to unhappiness or sadness that this person's friend is experiencing because he broke a promise or failed on an important commitment he made to his friend. Thus, "much to his despair" is saying that because the person's friend broke his promise, the friend now feels despair, presumably because of the disappointment he caused by breaking his promise.
"In a way that caused him to feel despair." The friend's going back on his word is the reason for his despair, and so (by definition) it contributes much to that feeling.
Much to his surprise and much to his dismay are also common variations on the same formula, as well as their plainer versions without "much": to his surprise and to his dismay.
Edit: There should be a comma after "word", which could be the reason for your confusion:
His friend went back on his word, much to his despair.
