You determine the acetic acid (HOAc) content of vinegar by
titrating with a sodium hydroxide standard solution to a
phenolphthalein (an indicator) end point. An approximately 5-mL
sample of vinegar is weighed on an analytical balance in a weighing
boat and this is found to be 5.0268 g. The standard deviation in
making a single weighing is 0.2 mg. The sodium hydroxide must be
accurately standardised (this means its concentration must be
accurately determined) by titrating known mass of high-purity
potassium hydrogen phthalate, and three such titrations give molar
concentrations of 0.1167, 0.1163 and 0.1164 mol L-1. A volume of
36.78 mL of sodium hydroxide is used to titrate each sample. The
standard deviation of the burette used is 0.02 mL. Calculate the
percentage of acetic acid in the vinegar and its standard
deviation.