The first part of Old Main completed was what would later be the west wing. The chemistry rooms occupied the entire bottom floor of this wing after 1885.
The center portion of Old Main was completed in 1889. The large auditorium that formed the north wing (far right in photo) was completed in 1891. The library was located underneath the auditorium.
Chemical laboratories had their modest allotted space in the basement of Old Main, but for obvious reasons -- danger of fire being the foremost -- the need for a separate chemistry lab building was pointed out almost immediately. A Regents Report from December 1884 notes that "the noxious and disagreeable gases evolved in chemical work...unavoidably permeate other rooms." The entire lower floor of Old Main (i.e. what was later the west wing) was given over to the chemistry labs in 1885. The rooms were fitted with the latest equipment, including gas, water, hydrogen and oxygen connections, fume hoods, spectroscopes, balances, and assorted other appliances and instruments. But the ongoing problems of overcrowding, fumes, and a very real fire hazard argued strongly for a separate building for the Chemistry Department. 
View of the UT campus from the southwest in 1898. The Chemical Laboratory
is to the left of Old Main, and the stack of the first power plant (demolished 1910) can be seen between them. B Hall, prior to its 1900 expansion, is to the right.
(Photo courtesy of the Center for American History.)
Old Main, seen from the south. The date is probably 1905-10. The Chemical Laboratory is on the left, and the Engineering Building (present-day Gebauer Hall) is on the right. (The latter was completed in 1904, and is now the oldest building still standing on the Forty Acres.)
Old Main, looking north along University Avenue, 1914
Old Main, with new Littlefield Fountain in foreground, 1933.
Despite its lavish appearance, Old Main was not built to last. The auditorium was condemned for structural problems in 1914, and the north wing was torn down in 1931 to make way for the new library building, designed by Paul Cret. Despite much protest from nostalgic alumni, the remainder was razed in 1935 to allow new Main to be finished. The Tower, completed in 1937, soon became a symbol of UT -- and Old Main faded into memory.