Problem 61 - Chemistry Matter and Change

Question

Challenge Aspirin is the world’s most-often used medication. The chemical analysis of aspirin indicates that the molecule is 60.00% carbon, 4.44% hydrogen, and 35.56% oxygen. Determine the empirical formula for aspirin.

Step-by-Step Solution

Answer

The empirical formula of aspirin is C2H2O based on the percentages of each element and their conversion to moles which results in a simplified whole number ratio of 2:2:1 for Carbon, Hydrogen, and Oxygen.

Step 1: Convert percentages to grams

We will assume a 100g sample of aspirin which makes the percentages equal to grams: Carbon: 60.00 g Hydrogen: 4.44 g Oxygen: 35.56 g

Step 2: Convert grams to moles

Next, we will convert the grams of each element to moles using their respective molar masses. The molar masses are approximately: C: 12.01 g/mol H: 1.01 g/mol O: 16.00 g/mol Carbon: \(\frac{60.00 \, g}{12.01 \, g/mol} = 4.996 \, moles\) Hydrogen: \(\frac{4.44 \, g}{1.01 \, g/mol} = 4.396 \, moles\) Oxygen: \(\frac{35.56 \, g}{16.00 \, g/mol} = 2.222 \, moles\)

Step 3: Find the smallest whole number ratio

Divide the moles of each element by the smallest number of moles to get the mole ratio: Carbon: \(\frac{4.996}{2.222} = 2.25\) Hydrogen: \(\frac{4.396}{2.222} = 1.98\) Oxygen: \(\frac{2.222}{2.222} = 1\) These mole ratios are close to whole numbers, so we will round them: Carbon: 2 Hydrogen: 2 Oxygen: 1 Therefore, the empirical formula of aspirin is C2H2O.

Key Concepts

Molar Mass

Molar mass is an essential concept in chemistry that helps us understand how to convert between grams and moles for a given substance. It's the mass of one mole of a substance and is usually expressed in grams per mole (g/mol). For example, in the case of aspirin, the molar masses for its elements are:

• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.01 g/mol
• Oxygen (O): 16.00 g/mol

By knowing these values, we can transform the given mass of an element (in grams) into moles, allowing us to perform calculations like determining an empirical formula.
To calculate the number of moles, we use the formula:\[\text{Moles} = \frac{\text{Mass in grams}}{\text{Molar Mass}}.\] This conversion is crucial for understanding the composition of compounds and performing stoichiometric calculations, which are the foundation of balancing chemical reactions.

Mole Ratio

The mole ratio is a fundamental concept that explains the relative amounts of reactants and products in a chemical reaction or the composition of a compound. It allows us to compare the number of moles of each element present in a compound.
In our aspirin example, after finding the moles of carbon, hydrogen, and oxygen, we calculated the mole ratio by dividing each by the smallest number of moles:

• Carbon: 2.25
• Hydrogen: 1.98
• Oxygen: 1.00

These values need to be whole numbers to represent the simplest ratio in the empirical formula, so rounding them off gives us integers that correspond to the final mole ratio. The use of mole ratios is vital in determining empirical formulas as it provides insight into the simplest representation of the compound's chemical formula.

Chemical Analysis

Chemical analysis involves techniques for determining the chemical composition of a substance, which is critical for validating the presence and proportions of elements in a compound. This process can be qualitative, which identifies the elements present, or quantitative, which determines the specific quantity of each element.
For aspirin, a quantitative chemical analysis was performed, revealing that the molecule is composed of 60.00% carbon, 4.44% hydrogen, and 35.56% oxygen. This step is critical as it forms the basis for calculating the empirical formula. It provides the detailed data needed to understand the structure and composition of a molecule.
The percentage values obtained from chemical analysis lay the groundwork for converting data into empirical formulas, showcasing the power and necessity of this process in the field of chemistry.

Percentage Composition

Percentage composition is a concept that describes the percent by mass of each element in a compound. It provides a close look at the makeup of a molecule, giving chemists insight into the molecular structure.
In the context of aspirin, the percentage composition is expressed as:

• Carbon: 60.00%
• Hydrogen: 4.44%
• Oxygen: 35.56%

Assuming a 100g sample facilitates the conversion of these percentages directly into grams, simplifying subsequent calculations. By finding the mass each element contributes to the molecule, one can deduce the proportional amounts of elements present, thus facilitating the calculation of the empirical formula.
Understanding percentage composition is useful not only in empirical formula calculations, but also in purity analysis of substances and in quality control environments where the specific makeup of a compound must be verified.