Question

Calculate the empirical formula for each natural flavor based on its elemental mass percent composition. $$ \begin{array}{l}{\text { a. methyl butyrate (component of apple taste and smell): } \mathrm{C} 58.80 \% \text { , }} \\ {\text { H } 9.87 \%, \mathrm{O} 31.33 \%}\end{array} $$ $$ \begin{array}{l}{\text { b. vanillin (responsible for the taste and smell of vanilla): } C 63.15 \% \text { , }} \\ {\text { H } 5.30 \%, 031.55 \%}\end{array} $$

Short answer

The empirical formula for methyl butyrate is C5H10O2, and for vanillin is C8H8O3

Step-by-step solution

Calculate Moles of Each Element for Methyl Butyrate

Convert the percentage of each element to moles by assuming 100 g of the substance, which allows us to use the percent directly as grams. Then, divide by the atomic mass: Carbons, C: 58.80 g / 12.01 g/mol = 4.896 moles, Hydrogens, H: 9.87 g / 1.008 g/mol = 9.792 moles, Oxygens, O: 31.33 g / 16.00 g/mol = 1.958 moles.

Determine the Simplest Whole Number Ratio for Methyl Butyrate

Divide the moles of each element by the smallest number of moles obtained in the previous step to get the simplest whole number ratio: C: 4.896 / 1.958 = 2.5, H: 9.792 / 1.958 = 5, O: 1.958 / 1.958 = 1. Since we can't have a half atom, we multiply each number by 2 to get whole numbers: C: 2.5 * 2 = 5, H: 5 * 2 = 10, O: 1 * 2 = 2.

Calculate Moles of Each Element for Vanillin

Repeat steps 1 and 2 for vanillin. Convert the percentage of each element to moles, assuming 100 g of the substance: Carbons, C: 63.15 g / 12.01 g/mol = 5.258 moles, Hydrogens, H: 5.30 g / 1.008 g/mol = 5.258 moles, Oxygens, O: 31.55 g / 16.00 g/mol = 1.972 moles.

Determine the Simplest Whole Number Ratio for Vanillin

Divide the moles of each element by the smallest number of moles obtained to get the simplest whole number ratio: C: 5.258 / 1.972 = 2.667, H: 5.258 / 1.972 = 2.667, O: 1.972 / 1.972 = 1. The ratio of C:H is approximately 8:8 which simplifies to 1:1, so we attempt to get a whole number ratio closest to this simplification. Multiplying the ratios by 3 to approximate the simplest whole number ratio gives us: C: 2.667 * 3 ≈ 8, H: 2.667 * 3 ≈ 8, O: 1 * 3 = 3.

Key concepts

Stoichiometry

Stoichiometry is the aspect of chemistry that involves calculating the quantities of reactants and products involved in chemical reactions. In the context of empirical formula calculation, stoichiometry plays a crucial role because it helps determine the simplest whole number ratio of atoms in a compound. This ratio is derived from balancing the number of moles of each element present in the sample.

For example, when calculating the empirical formula of methyl butyrate, assuming 100 grams of the compound allows us to directly use the mass percentage as the mass. By converting this mass to moles (using the molar mass of each element), we identify the relative number of moles of carbon, hydrogen, and oxygen. The principle of stoichiometry then allows us to divide these mole values by the smallest mole value obtained, establishing a mole ratio that reflects the compound's chemical stoichiometry. If the ratio isn't a whole number, as seen with carbon (C) in methyl butyrate, we multiply all ratios by a factor (in this case, 2) to achieve whole numbers, ensuring the empirical formula represents actual atoms.

Molar Mass

Molar mass is a fundamental concept in stoichiometry, representing the mass of one mole of a substance (usually in grams per mole). This value is crucial since it allows chemists to convert between mass and moles, bridging the gap between the macroscopic samples we can weigh and the microscopic atoms and molecules we want to count.

When determining an empirical formula, the step of converting the given mass percentages to moles relies on the molar mass of the individual elements. For methyl butyrate, the molar mass of carbon is 12.01 g/mol, hydrogen is 1.008 g/mol, and oxygen is 16.00 g/mol. These conversions are the first step in stoichiometric calculations and are necessary to obtain the mole ratio for the empirical formula. Understanding and correctly using molar masses ensures accurate empirical formula determinations.

Chemical Composition

The chemical composition of a substance tells us which elements and how many of each element are present in a compound. In the case of empirical formula calculations, understanding the compound's chemical composition by analyzing mass percent composition is essential. It provides an initial quantitative assessment of the elements involved before any conversions to moles or adjustments for whole number ratios occur.

For natural flavors like methyl butyrate and vanillin, their flavor and aroma profiles connect directly to their unique chemical compositions. Determining the empirical formula requires the deconstruction of these compositions into their simplest form. It involves expressing the elemental composition as a ratio of moles and then translating this into a formula that represents the smallest whole number ratio of atoms in the compound. This empirical formula is an essential tool for chemists to characterize substances and understand their properties.