The number of hydroxyl Groups is 3.
The reaction of an alcohol with #"CH"_3"COCl"# is
#"RO-H" + "CH"_3"CO-Cl" → "RO-COCH"_3 + "HCl"#
Assume that the compound #"X"# has a molecular mass of #x " u"#.
For each #"OH"# group that reacts, #"X"# loses #1 " H"# atom (1.008 u) to form an #"RO"# group.
The mass of the #"RO"# group is #(x –1.008)" u"#.
The #"RO"# group then adds a #"CH"_3"CO"# unit (43.04 u).
So the mass of the product is #(x -1.008 + 43.04)" u" = (x+ 42.03)" u#
#"X"# gains 42.03 u of mass for every OH group that reacts.
So #"42.03 u gained" = "1 OH group"#.
We can create a conversion factor by dividing each side of the equation by #"42.03 u gained"#:
#"1 OH group"/"42.03 u gained" = 1#.
Then
#126 cancel("u gained") × "1 OH group"/(42.03 cancel("u gained")) = "3.00 OH groups" ≈ "3 OH groups"#.
The compound contains 3 OH groups.
