Question

Acetylsalicylic acid \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) 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

There were approximately 5 grains of aspirin in the tablet.

Step-by-step solution

Calculate the number of moles of NaOH

First, we need to calculate the number of moles of NaOH using the formula: n = C * V. Here `n` is the number of moles, `C` is the molar concentration, and `V` is the volume. Remember we need to convert the volume from mL to L. So, n = 0.1466 mol/L * 0.01225 L = 0.0018 mol.

Determine the number of moles of acetylsalicylic acid

Since the ratio of neutralization is 1:1, the moles of acetylsalicylic acid will be same as the moles of NaOH. Therefore, the acetylsalicylic acid present in the solution is also 0.0018 mol.

Find the mass of acetylsalicylic acid

Next, knowing the molecular formula of acetylsalicylic acid i.e., C9H8O4, we calculate its molar mass. Molar mass = 9*12.01 g/mol (for C) + 8*1.01 g/mol (for H) + 4*16.00 g/mol (for O) = 180.158 g/mol. Multiply this with the number of moles to find the mass.\(Mass = moles * molar \ mass = 0.0018 \ mol * 180.158 \ g/mol = 0.324 \ g \).

Convert to grains

As the question asks for answer in grains, we convert this mass using the given conversion: 1 grain = 0.0648 g. Therefore, the number of grains = 0.324 g / 0.0648 g/grain = 5 grains.

Key concepts

Molar Concentration Calculation

Understanding how to calculate molar concentration is crucial when working with chemical solutions. It essentially tells us how much of a substance is present in a given volume of solution. In stoichiometry, this is the first step towards understanding the amount of reactants being used.

To calculate molar concentration, also known as molarity, you use the formula:
\( C = \frac{n}{V} \)
where \( C \) represents the molar concentration in moles per liter (mol/L), \( n \) is the number of moles of the solute, and \( V \) is the volume of the solution in liters.

For students, it's important to always ensure that the volume is in liters as this is the standard unit for molarity. If you're given volume in milliliters, it's essential to convert it to liters by dividing by 1000, which is often one of the first stumbling blocks.
Using the exercise as an example, the volume of the NaOH solution used was given in milliliters (mL) and needed to be converted to liters before the molarity calculation could be correctly performed. This conversion and subsequent molarity calculation are foundational to determining the number of moles of reactants in a solution.

Mole-to-Mass Conversion

Once you have the number of moles from the molarity calculation, the next step in stoichiometry is to convert moles to mass. This is an essential skill for chemists and students alike, especially when preparing for experiments or analyzing results.

To convert moles to grams, you need to multiply the number of moles by the molar mass of the compound, which can be calculated from its molecular formula. The formula for this is:
\( Mass = Moles \times Molar\;Mass \)
In simple terms, if you think of moles as a 'count' of molecules, the mole-to-mass conversion provides you with the actual weight of those molecules. This step is often where students must be vigilant, as using incorrect molar masses will skew the results.
In our aspirin example, after determining the moles of acetylsalicylic acid, we multiplied it by the molar mass of the compound to find the mass in grams. It’s a straightforward calculation but requires understanding of the mole concept and accurate molar mass for precision.

Molar Mass of Compounds

The molar mass of a compound is the weight in grams of one mole of that compound. It's calculated by adding up the atomic masses of all the atoms in its molecular formula. For students, this can initially seem daunting, but it becomes more manageable with practice.

To find the molar mass, you look at the periodic table for the atomic mass of each element, then multiply each by the number of times the element appears in the formula. Add up all of these values to get the total molar mass:
\( Molar\;Mass = \sum (Atomic\;Mass \times Number\;of\;Atoms) \)
In our exercise, we calculated the molar mass of acetylsalicylic acid (aspirin) by adding up the atomic masses of carbon (C), hydrogen (H), and oxygen (O) according to how many of each are in the formula \( C_9H_8O_4 \). Knowledge of how to calculate the molar mass is essential because it bridges the gap between the molecular and macroscopic worlds. Once molar mass is determined, it can be used for the mole-to-mass conversion as we did previously.