Question

Acetylsalicylic acid \(\left(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}\right)\) is a monoprotic acid commonly known as "aspirin." A typical aspirin tablet, however, contains only a small amount of the acid. In an experiment to determine its composition, an aspirin tablet was crushed and dissolved in water. It took \(12.25 \mathrm{~mL}\) of \(0.1466 \mathrm{M} \mathrm{NaOH}\) to neutralize the solution. Calculate the number of grains of aspirin in the tablet (one grain \(=0.0648 \mathrm{~g}\) ).

Short answer

The tablet contains approximately 4.99 grains of aspirin.

Step-by-step solution

Write the Neutralization Reaction

The reaction between acetylsalicylic acid (aspirin) and NaOH is:\[\mathrm{HC_9H_7O_4} + \mathrm{NaOH} \rightarrow \mathrm{C_9H_7O_4Na} + \mathrm{H_2O}\]Each mole of aspirin reacts with one mole of NaOH.

Calculate Moles of NaOH

Using the volume and molarity of NaOH, calculate the moles:\[\text{Moles of NaOH} = \text{Volume} \times \text{Molarity} = 0.01225 \text{ L} \times 0.1466 \text{ M} = 0.00179615 \text{ moles}\]

Calculate Moles of Aspirin

Since the reaction is 1:1, the moles of aspirin will be the same as the moles of NaOH:\[\text{Moles of Aspirin} = 0.00179615 \text{ moles}\]

Calculate Grams of Aspirin

Find the molar mass of aspirin, \(\mathrm{HC_9H_7O_4}\):\[(9\times12.01) + (8\times1.01) + (4\times16.00) = 180.17 \text{ g/mol}\]Calculate the grams of aspirin:\[\text{Grams of Aspirin} = 0.00179615 \text{ moles} \times 180.17 \text{ g/mol} = 0.3235 \text{ g}\]

Convert Grams to Grains

Convert grams of aspirin to grains using the given conversion:\[\text{Grains of Aspirin} = \frac{0.3235 \text{ g}}{0.0648 \text{ g/grain}} \approx 4.99 \text{ grains}\]

Key concepts

Moles of NaOH

In a neutralization reaction, it's essential to determine the number of moles of a reactant, such as sodium hydroxide (NaOH), to understand the reaction's stoichiometry. The moles of NaOH can be calculated using the formula:

• \(\text{Moles of NaOH} = \text{Volume} \times \text{Molarity}\)

In this particular problem, we use the given volume of NaOH (12.25 mL) and convert it to liters for our calculation, since molarity is typically given in moles per liter. The molarity is provided as 0.1466 M. Thus, we have:

• \(\text{Moles of NaOH} = 0.01225\, \text{L} \times 0.1466\, \text{M} = 0.00179615\, \text{moles}\)

This calculation gives us the exact amount of NaOH that participated in the reaction.

Moles of Aspirin

In a chemical reaction between aspirin (acetylsalicylic acid) and NaOH, the balanced equation reveals a 1:1 molar ratio. This means that one mole of aspirin will react with one mole of NaOH. Knowing this, we can determine the moles of aspirin involved simply by looking at the moles of NaOH calculated previously.

• Since the reaction is 1:1, \(\text{Moles of Aspirin} = \text{Moles of NaOH} = 0.00179615\, \text{moles}\)

Understanding this direct correlation is crucial as it allows us to predict the amount of reactants and products in the reaction using stoichiometry. It simplifies the process and ensures accuracy in further calculations.

Molar Mass of Acetylsalicylic Acid

To determine the number of grams of a substance from moles, we must first know its molar mass. Molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol).For acetylsalicylic acid (\(\mathrm{HC_9H_7O_4}\)), the molar mass is calculated by adding together the atomic masses of all the atoms in its formula:

• Carbon (C): 9 atoms \(\times 12.01\, \text{g/mol} = 108.09\, \text{g/mol}\)
• Hydrogen (H): 8 atoms \(\times 1.01\, \text{g/mol} = 8.08\, \text{g/mol}\)
• Oxygen (O): 4 atoms \(\times 16.00\, \text{g/mol} = 64.00\, \text{g/mol}\)

Adding these values together gives us the molar mass of acetylsalicylic acid:

• \(180.17\, \text{g/mol}\)

This molar mass is then used to convert moles of a substance to grams, a key step in many chemistry calculations.

Conversion of Grams to Grains

Sometimes, the measurements of substances might be required in different units for practical reasons. In chemistry, converting between units is a routine task. In this case, we need to convert grams to grains, a unit commonly used in pharmacology.We have already calculated the amount of aspirin in grams, which was:

• \(0.3235\, \text{g}\)

To convert grams to grains, we use the conversion factor provided:

• \(1\, \text{grain} = 0.0648\, \text{g}\)

Thus, the conversion is:

• \(\text{Grains of Aspirin} = \frac{0.3235\, \text{g}}{0.0648\, \text{g/grain}} \approx 4.99\, \text{grains}\)

Conversions like these are common, and understanding the process helps in various scientific calculations and real-world applications.