Pronunciation of "a"

Question

My understanding is that the general rule regarding the pronunciation of "a" in Russian is that it is pronounced [a] (IPA notation). However, in certain cases, it can be pronounced as "и", for example in "Чапыгин" or "Чапаева".

My question is the following: does a rule exist about "a" being pronounced as "и"? If not, is there a list of words in which this is the case?

Answer 1

Yes, the rule exists and dictates that any vowel except for [у] that follows a soft consonant in an unstressed position is reduced to something between [э] and [и]:

часы́ [чисы]
яйцо́ [йийцо]
ле́чо [лече]
река́ [рика]
счастли́вый [щисливый]
её   [йийо]

Source: М.В. Пано́в. Ру́сская фоне́тика

In particular, this makes the words чистота́ (cleanliness) and частота́ (frequency) homophones while the respective adjectives чи́стый (clean) and ча́стый (frequent) have distinct pronunciations because the а in ча́стый is stressed.

In Russian [й], [ч] and [щ] are always soft. Other consonants are soft if followed by я, е, ё, и, ю, or ь. For the purposes of applying this rule we can ignore и (because it becomes a weak и but still an и), ю (because it gives the sound [у] which is an exception) and ь because its not a vowel. So practicality speaking we should be looking out for words containing unstressed я and е, including those at the beginning of a word.

The letter ё is almost always stressed. It can be unstressed in compound words e.g. трёхмерный (three-dimensional) which can be said without a secondary stress in which case the rule in question will apply.

Answer 2

Let's start with a small exercise. Say slowly, for instance, Чапаев, then Чипаев, Чепаев, then Чупаев, at last, say, Чопаев. Now say all these words again but quickly, like, very quickly - but actually casual speech can be very quick. See, the difference has gone, they all sound practically the same.

This phenomenon you've encountered (of vowels becoming almost indistinguishable from each other when pronounced quickly) is called vowel reduction and the vowel you have here is called an extra-short vowel and in some form it is a thing in many (but not all) languages.

Here's a quote from a Russian article on extra-short vowels:

В русском языке есть два вида сверхкратких гласных:

• Появились «из ниоткуда» на стыке большого количества согласных, чтобы это сочетание можно было удобнее произнести: «Мистер Твистер / Бывший минист(ъ)р…» (Самуил Маршак, знаком (ъ) отмечена явно прописанная в стихотворном размере редуцированная).
• Уменьшились из обычной безударной гласной — так, слово красота при определённом произношении редуцируется до красъта.

Your question falls into case #2.