Calculate the theoretical yield of aspirin to be obtained in this experiment, starting with 2.0 g of salicylic acid and 5.0 ml of acetic acid anhydride (density = 1.08 g/ml).

Writ the equation for salicylic acid + acetic anhydride to produce ASA.

This is a limiting reagent problem.
2a. Convert 2.0 g salicylic acid to mols.
2b. convert 5.0 mL to grams by density, then to mols.

3. Convert to mols ASA (aspirin)
a. Convert mols salicylic acid to mols ASA (1:1 ratio).
b. Convert mols acetic anhydride to mols ASA (1:1 ratio).
c. Choose the smaller number of mols ASA produced. The reagent producing this result is the limiting reagent.

4. Convert mols ASA in 2c to grams. That is the theoretical yield.

Post your work if you get stuck BUT tell me what you don't understand about the next step.

(5.0ml)x(2.0g/1.08g/ml)x(1 mole S/138g S) x (1 mole Aspirin/1 mole S)x (180g Aspirin/ 1 mole Aspirin) = 12.077 g Aspirin

I don't get those numbers. Apparently you are using acetic anhydride as the limiting reagent. Unless I made a goof in my calculations, and I may have done that, salicylic acid is the limiting reagent. If you will show your calculations I can check it better.

3.42g

how did you get 3.42g?

2.52 grams

But then the weight of the synthesized aspirin obtained what is the use of it. I mean the weight of the aspirin you get after subtracting the weight of filter paper from the weight of filter paper+aspirin product.