Problem 103 - Chemistry An Atoms First Approach

Question

Acetylsalicylic acid is the active ingredient in aspirin. It took \(35.17 \mathrm{mL}\) of \(0.5065 \mathrm{M}\) sodium hydroxide to react completely with \(3.210 \mathrm{g}\) of acetylsalicylic acid. Acetylsalicylic acid has one acidic hydrogen. What is the molar mass of acetylsalicylic acid?

Step-by-Step Solution

Answer

The molar mass of acetylsalicylic acid is approximately \(180.34\,\mathrm{g/mol}\).

Step 1: Calculate the moles of sodium hydroxide

The moles of sodium hydroxide (NaOH) can be calculated using the volume and concentration: Moles of NaOH = Volume of NaOH × Concentration of NaOH Moles of NaOH = \(35.17\,\mathrm{mL}\) × \(0.5065\,\mathrm{M}\) Note: Make sure to convert the volume in mL to L by dividing by 1000. Moles of NaOH = \(0.03517\,\mathrm{L}\) × \(0.5065\,\mathrm{M}\) = \(0.0178\,\mathrm{mol}\)

Step 2: Calculate the moles of acetylsalicylic acid

Since acetylsalicylic acid reacts with sodium hydroxide in a 1:1 ratio, the moles of acetylsalicylic acid will be the same as the moles of sodium hydroxide. Moles of acetylsalicylic acid = Moles of NaOH = \(0.0178\,\mathrm{mol}\)

Step 3: Calculate the molar mass of acetylsalicylic acid

Now, we can use the moles of acetylsalicylic acid and its mass to find the molar mass: Molar mass of acetylsalicylic acid = Mass of acetylsalicylic acid ÷ Moles of acetylsalicylic acid Molar mass of acetylsalicylic acid = \(3.210\,\mathrm{g}\) ÷ \(0.0178\,\mathrm{mol}\) = \(180.34\,\mathrm{g/mol}\) The molar mass of acetylsalicylic acid is approximately \(180.34\,\mathrm{g/mol}\).

Key Concepts

Acetylsalicylic Acid

Acetylsalicylic acid, commonly known as aspirin, is a widely used medication known for its pain-relieving, anti-inflammatory, and fever-reducing properties. It is an organic compound with the chemical formula \( ext{C}_9 ext{H}_8 ext{O}_4 \). The presence of one acidic hydrogen atom makes it reactive, especially in neutralization reactions with bases like sodium hydroxide (NaOH).

Understanding the composition and structure of acetylsalicylic acid helps in exploring its chemical behavior and calculating its molar mass. Its molar mass is an essential property that helps in quantifying how much of the substance is required in reactions. Molar mass is calculated by adding up the atomic masses of all the atoms in the molecular formula. For acetylsalicylic acid, the molar mass calculation is vital in stoichiometry, which further helps chemists gauge the proportions needed for a complete reaction.

Stoichiometry

Stoichiometry is a branch of chemistry that involves calculating the reactants and products in chemical reactions. It is essential for predicting the quantities needed or produced in a chemical reaction based on balanced equations. In the case of acetylsalicylic acid reacting with sodium hydroxide, stoichiometry helps confirm the 1:1 mole ratio between the acid and the base in this particular reaction.

This means for every mole of acetylsalicylic acid, one mole of sodium hydroxide is required to completely neutralize it.

• This concept ensures that there are no leftover reactants, maintaining chemical efficiency.
• Stoichiometry is applied to calculate reactant quantities, and also to predict yields in industrial processes.

Understanding this stoichiometric relationship simplifies calculations, like finding out the molar mass, as it allows you to directly relate the moles of one substance to another.

Moles Calculation

Moles are a fundamental unit in chemistry used to quantify the amount of substance. Calculating moles is critical for determining how much of a reactant or product is involved in a chemical reaction. To find the number of moles, you can use the formula:

\[ \text{Moles} = \text{Concentration (Molarity)} \times \text{Volume (L)} \]

For instance, in the given problem, you calculated the moles of sodium hydroxide used by converting the volume from milliliters to liters and multiplying by its molarity. The calculation was:

• Convert 35.17 mL of NaOH to liters: 35.17 mL \( \div \) 1000 = 0.03517 L
• Use the formula: Moles of NaOH = 0.03517 L \( \times \) 0.5065 M = 0.0178 mol

Because acetylsalicylic acid and sodium hydroxide react in a 1:1 ratio, the moles of acetylsalicylic acid are the same, which allows for the calculation of its molar mass. Thus, understanding how to accurately compute moles using stoichiometry is integral to solving this exercise.