To determine the % mass of salicylic acid in the aspirin based on the titration with NaOH, we'll need to follow these steps:
1. Calculate the volume of NaOH solution used in the titration.
2. Determine the concentration of NaOH (which is not provided and is essential for calculations).
3. Use the stoichiometry of the reaction between salicylic acid and NaOH to find the number of moles of salicylic acid that reacted.
4. Calculate the mass of salicylic acid from the number of moles.
5. Finally, calculate the % mass of salicylic acid in the aspirin.
Given that the concentration of the NaOH solution is not provided, I will make an assumption to illustrate how the calculation would proceed. Let's assume that the NaOH solution has a concentration of 0.1 M (molar), a common concentration for titration problems.
Step 1: Calculate the volume of NaOH solution used in the titration.
Final volume of NaOH = 18.80 mL
Initial volume of NaOH = 15.90 mL
Volume of NaOH used = Final volume - Initial volume
= 18.80 mL - 15.90 mL
= 2.90 mL
To work in standard units, we convert the volume from mL to L:
Volume of NaOH used = 2.90 mL * (1 L / 1000 mL) = 0.00290 L
Step 2: Determine the concentration of NaOH. (We will use a concentration of 0.1 M in this example.)
Step 3: Calculate the moles of NaOH used in the titration.
Moles of NaOH = Volume (L) × Concentration (M)
= 0.00290 L × 0.1 M
= 0.000290 moles
The balanced chemical equation for the reaction is required to proceed. Salicylic acid reacts with sodium hydroxide (NaOH) in a 1:1 ratio, because it has one acidic hydrogen per molecule. This is a reasonable assumption for a typical acid-base titration.
Step 4: Use the stoichiometry of the reaction to find the number of moles of salicylic acid.
Since the ratio is 1:1,
Moles of salicylic acid = Moles of NaOH
= 0.000290 moles
Step 5: Calculate the mass of salicylic acid.
The molecular weight of salicylic acid is 138.12 g/mol. Using this, we can calculate the mass:
Mass of salicylic acid = Moles × Molecular weight
= 0.000290 moles × 138.12 g/mol
= 0.040056 g
Step 6: Calculate the % mass of salicylic acid in the aspirin.
% mass of salicylic acid = (Mass of salicylic acid / Mass of aspirin sample) × 100%
= (0.040056 g / 0.1000 g) × 100%
= 40.056%
Therefore, the % mass of salicylic acid in the aspirin is 40.056%, assuming the concentration of NaOH is 0.1 M. Note that this value will be different if the actual concentration of NaOH is different from the assumed value.
