Is it possible to calculate solubility of salicylic acid using this data? 1 gram of salicylic acid was dissolved in 20 grams of ethanol (99%). This was then titrated using 1 mol sodium hydroxide, end point was reached using 9.53ml.
No. A compound will be soluble up to its solubility limit in any solvent. The analysis just tells you how much is in the solution, which should correspond to the amount that you put in to the known amount of solvent. It cannot be used in any way to predict or calculate the solubility.
Solubility can only be determined by adding increments of the solute until it no longer dissolves. Analyzing the concentration of the solute in a SATURATED solution (where some of the solute is undissolved) WILL give you an accurate value for the solubility, as it will be the maximum soluble quantity.