Please find the number (in integers) of pills used for preparing the 250mL solution.

Question

Aspirin is a common drug for curing inflammation and fever. The active ingredient of aspirin is known as acetylsalicylic acid (C₉H₈O₄). It is a monoprotic acid and protonates according to the chemical equation below.

C₉H₈O₄ (ap)⇌ H⁺(aq) + C₉H₇O₄^- /(aq)

A nurse has prepared a solution with unknown number of aspirin pills dissolved in 250mL water. Each pill has a mass of 410mg. 50mL of solution requires 24.6mL 0.0925M sodium hydroxide (NaOH) to reach equivalence point.

(a) Please find the number (in integers) of pills used for preparing the 250mL solution.

Answer 1

Hi Jenny,

The reaction taking place for reaching equivalence is as follows:

C₉H₈O₄(aq) + NaOH(aq) ==> C₉H₇O₄Na + H₂O or you could look at it as ...

H⁺(aq) + C₉H₇O₄^- + NaOH ==> C₉H₇O₄^-Na⁺ + H₂O

Either way, note that it takes ONE mol NaOH for each ONE mol of acetylsalicylic acid

Now, the rest of the answer is involved, but stick with it, and follow the reasoning. It should make sense.

To neutralize (reach equivalence) 50 ml (out of the 250 mls), we have...

24.6 ml of 0.0925 M NaOH. We now find the mols of NaOH from this information.

24.6 mls x 1 L / 1000 ml x 0.0925 mol/L = 0.002276 mols NaOH used

This is then equal to 0.002276 mols of acetylsalicylic acid (see balanced equation and 1:1 mol ratio)

So, we have 0.002276 mols C₉H₈O₄ in the 50 mls. But this came from 250 mls originally. So, how many mols would be in the original 250 mls? It would be 5 times as many because 5 x 50 = 250.

So, mols C₉H₈O₄ in original sample = 5 x 0.002276 = 0.1138 mols

Now, we need to find how many gram or milligrams this is so that we can relate it to the number of aspirin pills used. To do this we use the molar mass of acetylsalicylic acid which is 180.2 g/mol (I looked it up, but you can just add up all the atomic masses of the elements present)

Grams C₉H₈O₄ present in original sample = 0.1138 mols x 180.2 g / mol = 20.5 g

milligrams present in original sample = 20.5 g x 1000 mg/g = 20,500 mg

Pills used = 20,500 mg x 1 pill / 410 mg = 50 pills were used