Step 1. Start with the balanced equation.
I'll write the molar masses above the formulas for easy access.
#M_r:color(white)(ll)138.12color(white)(mmml)102.09#
#color(white)(mml)underbrace("C"_7"H"_6"O"_3)_color(red)("salicylic acid") + underbrace("C"_4"H"_6"O"_3)_color(red)("acetic anhydride") → underbrace("C"_9"H"_8"O"_4)_color(red)("aspirin") + underbrace("C"_2"H"_4"O"_2)_color(red)("acetic acid")#
Now let's rewrite the equation for easier typing.
#"Sal" + "Ac"_2"O" → "Asp" + "HOAc"#
Step 2. Calculate the moles of #"Sal"#.
#"Moles of Sal" = 2.182 color(red)(cancel(color(black)("g Sal"))) × "1 mol Sal"/(138.12 color(red)(cancel(color(black)("g Sal")))) = "0.015 798 mol Sal"#
Step 3. Calculate the moles of #"Ac"_2"O"#.
#"Moles of Ac"_2"O" = "0.015 798" color(red)(cancel(color(black)("mol Sal"))) × ("1 mol Ac"_2"O")/(1 color(red)(cancel(color(black)("mol Sal")))) = "0.015 798 mol Ac"_2"O"#
Step 4. Calculate the mass of #"Ac"_2"O"#.
#"Mass of Ac"_2"O" = "0.015 798" color(red)(cancel(color(black)("mol Ac"_2"O"))) × ("102.09 g Ac"_2"O")/(1 color(red)(cancel(color(black)("mol Ac"_2"O")))) = "1.6128 g Ac"_2"O"#
Step 5. Calculate the volume of #"Ac"_2"O"#.
#"Volume of Ac"_2"O" = 1.6128 color(red)(cancel(color(black)("g Ac"_2"O"))) × ("1 mL Ac"_2"O")/(1.08 color(red)(cancel(color(black)("ml Ac"_2"O")))) = "1.49 mL Ac"_2"O"#
