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 for aspirin is \(C_9H_8O_4\).

Step 1: Convert Percentages to Grams

Assume you have a 100 g sample of aspirin. This assumption allows you to equate percentages to grams. Therefore, you have 60.00 g of carbon, 4.44 g of hydrogen, and 35.56 g of oxygen.

Step 2: Convert Grams to Moles

Use the atomic masses to convert grams of each element to moles. The atomic mass of carbon (C) is approximately 12.01 g/mol, hydrogen (H) is approximately 1.01 g/mol, and oxygen (O) is approximately 16.00 g/mol.\[\text{Moles of Carbon} = \frac{60.00 \text{ g}}{12.01 \text{ g/mol}} \approx 4.998 \text{ moles}\]\[\text{Moles of Hydrogen} = \frac{4.44 \text{ g}}{1.01 \text{ g/mol}} \approx 4.396 \text{ moles}\]\[\text{Moles of Oxygen} = \frac{35.56 \text{ g}}{16.00 \text{ g/mol}} \approx 2.222 \text{ moles}\]

Step 3: Calculate the Simplest Whole Number Ratio

Determine the simplest whole number ratio by dividing the number of moles of each element by the smallest number of moles calculated.\[\text{Ratio for Carbon} = \frac{4.998}{2.222} \approx 2.25\]\[\text{Ratio for Hydrogen} = \frac{4.396}{2.222} \approx 1.98 \approx 2.00\]\[\text{Ratio for Oxygen} = \frac{2.222}{2.222} = 1.00\]

Step 4: Adjust Ratios to the Whole Numbers

To convert the ratios to whole numbers, multiply each ratio by the same factor to eliminate fractions. For this case, multiplying by 4 works:\[\text{C} = 2.25 \times 4 = 9\]\[\text{H} = 2.00 \times 4 = 8\]\[\text{O} = 1.00 \times 4 = 4\]

Step 5: Write the Empirical Formula

The empirical formula is determined from the whole number ratios of each element:The empirical formula is \(C_9H_8O_4\).

Key Concepts

chemical composition

Chemical composition is essentially the recipe of a chemical compound that details each element’s presence in it. For aspiring chemists, understanding this is crucial. Every compound has a particular arrangement and quantity of elements in its structure, which is what defines its identity.

In the context of aspirin, its chemical composition involves carbon, hydrogen, and oxygen. Knowing the chemical composition allows scientists to explore how these elements interact and contribute to aspirin’s properties and effectiveness. A detailed breakdown is crucial as it can affect how the compound behaves in biological and chemical reactions.

It's important to note that the chemical composition determines the purity and characteristics of a compound. Any variation could significantly change the compound's effectiveness and use.

percentage composition

Percentage composition details how each element in a compound contributes to its total mass, described as a percentage. It is a stepping stone to calculate the empirical formula.

For instance, in aspirin:

• Carbon makes up 60.00% of aspirin.
• Hydrogen constitutes 4.44%.
• Oxygen accounts for 35.56%.

By knowing these percentages, chemists can better understand the proportion of each element in the compound, which is vital for making calculations such as the empirical formula. Plus, if you assume a 100 g sample, those percentages straightforwardly convert to grams making future calculations easier.

Understanding percentage composition is key to deriving more complex formulations in chemistry. It reflects how heavily each element weighs in the structure.

moles conversion

Moles conversion is a fundamental concept in chemistry, used to convert mass into moles to explore the absolute number of atoms or molecules in a sample. This process ensures chemists have a molecule count rather than just mass.

In the aspirin example, converting the grams to moles provided values such as approximately 4.998 moles of carbon, 4.396 moles of hydrogen, and 2.222 moles of oxygen. This step relies heavily on the atomic mass of each element and helps chemists move from the macro (grams) to the molecular level (moles).

This conversion is critical in deriving the empirical formula. It provides a consistent method for chemists to resonate with the atomic scale, ensuring accurate calculations and analyses, indispensable for rigorous chemical experimentation.

simplest whole number ratio

The simplest whole number ratio highlights the smallest integer ratio of elements in a compound, foundational in determining the empirical formula.

This ratio involves dividing the moles of each element by the smallest amount to derive uniformity. For aspirin, chemists divided the moles per element by 2.222 - the smallest amount - to arrive at approximate ratios of 2.25 for carbon, 2.00 for hydrogen, and 1.00 for oxygen. However, these numbers aren't always whole numbers, necessitating scaling, as seen when multiplying by 4 to reach whole numbers:

• 9 for Carbon
• 8 for Hydrogen
• 4 for Oxygen

Through this methodical conversion, we reach an empirical formula of \(C_9H_8O_4\). This calculation is crucial as it defines the simplest formula reflecting the most reduced form of the compound's composition.