Why does the Torah add the word "Chayim"?
Ramban #1 (citing the Ibn Ezra): To clarify that it was the Voice of Hashem that they heard and not that of an angel, who is sometimes referred to as 'Elohim'. 1
Ramban #2: Because someone who hears the Voice of Hashem - Who is the source of life - clings to the source and no longer lives a regular physical life. 2