Problem 192 - Chemistry Matter and Change

Question

Skunks Analysis of skunk spray yields a molecule with \(44.77 \% \mathrm{C}, 7.46 \% \mathrm{H}\) and 47.76\(\% \mathrm{S}\) . What is the chemical formula for this molecule found in the spray from skunks that scientists think is partly responsible for the strong odor?

Step-by-Step Solution

Answer

The empirical formula for the molecule is \( C_5H_{10}S \).

Step 1: Convert Percentages to Grams

Assume you have 100 grams of the compound. This allows us to directly convert the percentage of each element into grams. Therefore, there are 44.77 grams of Carbon (C), 7.46 grams of Hydrogen (H), and 47.76 grams of Sulfur (S).

Step 2: Find Moles of Each Element

To find the moles of each element, divide the mass of each element by its molar mass. The molar mass of Carbon is approximately 12.01 g/mol, Hydrogen is approximately 1.01 g/mol, and Sulfur is approximately 32.07 g/mol.\[\text{Moles of C} = \frac{44.77 \text{ g}}{12.01 \text{ g/mol}} \approx 3.73 \text{ mol} \\text{Moles of H} = \frac{7.46 \text{ g}}{1.01 \text{ g/mol}} \approx 7.39 \text{ mol} \\text{Moles of S} = \frac{47.76 \text{ g}}{32.07 \text{ g/mol}} \approx 1.49 \text{ mol}\]

Step 3: Determine the Simplest Ratio

Divide each element's mole value by the smallest number of moles calculated in the previous step, which is 1.49 moles from Sulfur.\[\frac{3.73}{1.49} \approx 2.50, \\frac{7.39}{1.49} \approx 4.96, \\frac{1.49}{1.49} = 1\]Since these are not perfectly whole numbers, they suggest the ratio needs to be multiplied by 2 to convert them to approximate whole numbers: \(2.50\) becomes \(5\), and \(4.96\) becomes \(10\).

Step 4: Write the Empirical Formula

Using the ratio derived in Step 3, the simplest whole number ratio of the atoms is approximately C:S:H = 5:1:10. Therefore, the empirical formula is \( C_5H_{10}S \).

Key Concepts

Mole Concept

The mole concept is foundational in chemistry and helps us bridge the gap between the atomic world and the real-world quantities we can measure. A mole, also known as Avogadro's number, is a basic counting unit. It represents approximately \(6.022 \times 10^{23}\) particles, which can be atoms, molecules, or ions. It's akin to a dozen, but instead of twelve, it's a massive number that corresponds to the amount of substance in grams equivalent to its atomic or molecular weight.

Understanding the mole concept is crucial because it allows chemists to work with and convert between atoms and grams with ease. For example, one mole of carbon atoms weighs about 12.01 grams. This understanding is pivotal in quantifying how atoms and molecules come together to form compounds during chemical reactions, which, in this case, helps us find the empirical formula of a compound based on its composition.

Chemical Analysis

Chemical analysis is a process used to identify and quantify the chemical components of a substance. In the context of determining an empirical formula, chemical analysis involves breaking down a substance to find out its elemental composition. This often requires precise measurement techniques and calculations to translate the data into meaningful results.

When analyzing a compound like skunk spray, the percentage composition of each element is determined. These percentages indicate how much of each element by mass is present in the sample. By converting these percentages to grams, assuming a sample size of 100 grams of the compound, we can then use molar masses to figure out the number of moles of each element. This quantitative form of analysis is a cornerstone of chemistry that helps in deducing the structure and identity of a chemical compound based on the empirical data.

Percentage Composition

Percentage composition refers to the percent by mass of each element present in a compound. It provides a formula or direct insight into the makeup of the compound. To determine this, one typically assumes a certain amount of the compound, such as 100 grams, to make the math straightforward.

For example, if a molecule consists of \(44.77\%\) carbon, \(7.46\%\) hydrogen, and \(47.76\%\) sulfur, as in the case of skunk spray, these values tell us how much mass of each element is contained per 100 grams of the compound. Calculating the percentage composition is the first step in finding the empirical formula, as it provides the basis to convert the element's mass into moles, which can then be used to determine the simplest ratio and structure of the molecule.

Skunk Spray Chemistry

Skunk spray, notorious for its strong and repugnant odor, is an interesting subject of chemical analysis. The specific molecule responsible for the smell is composed of carbon, hydrogen, and sulfur, which are common components that can combine in several ways to create odorous compounds.

The chemistry behind skunk spray involves understanding the specific combination and arrangement of these elements. In the laboratory, scientists determine the percentage composition and use this data to identify or synthesize the chemical formula. This involves breaking down the skunk spray into its basic elements, determining the mass percentage of each, and finally using these values to construct an empirical formula that represents the structure of the molecule.

Through empirical formula determination, we come closer to understanding how nature constructs organic molecules with strong fragrances, such as those found in skunk spray. This knowledge not only contributes to a scientific interest but also aids in developing methods to neutralize or replicate these chemical structures for various practical applications.