Problem 68 - Chemistry: An Atoms-Focused Approach

Question

GRAS List for Food Additives The alcohol geraniol is on the U.S. Food and Drug Administration's GRAS (generally recognized as safe) list and can be used in foods and personal care products. By itself, geraniol has a roselike odor, but it is frequently blended with other scents to produce the fruity fragrances of some personal care products. Complete combustion of 175 mg of geraniol produces \(499 \mathrm{mg} \mathrm{CO}_{2}\) and \(184 \mathrm{mg} \mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of geraniol?

Step-by-Step Solution

Answer

Answer: The empirical formula of geraniol is CH₂.

Step 1: Calculate moles of CO₂ and H₂O produced

Given the mass of CO₂ and H₂O produced, we need to convert these masses into moles using the molar mass of CO₂ and H₂O. Molar mass of CO₂ = 12 g (C) + 2(16 g) (O) = 44 g/mol Molar mass of H₂O = 2 g (H) + 16 g (O) = 18 g/mol Moles of CO₂ = 499 mg × (1 g/1000 mg) × (1 mol/44 g) ≈ 0.0113 mol Moles of H₂O = 184 mg × (1 g/1000 mg) × (1 mol/18 g) ≈ 0.01022 mol

Step 2: Determine moles of carbon and hydrogen in geraniol

Since the combustion reaction produces CO₂ and H₂O, all the carbon in geraniol comes from the CO₂ produced and all the hydrogen in geraniol comes from the H₂O produced. Thus, the moles of carbon and hydrogen in geraniol are same as the moles of CO₂ and H₂O produced. Moles of C in geraniol = moles of CO₂ = 0.0113 mol Moles of H in geraniol = 2 × moles of H₂O = 2 × 0.01022 mol ≈ 0.02044 mol

Step 3: Ratio of moles of carbon and hydrogen

To find the empirical formula, we need to determine the ratio of moles of carbon to moles of hydrogen. To do this, divide the moles of each element by the smallest number of moles. Ratio of C to H = (0.0113 mol / 0.0113 mol) : (0.02044 mol / 0.0113 mol) ≈ 1 : 1.809 However, this ratio is approximately equal to 1:2. Hence, the empirical formula of geraniol is CH₂.

Key Concepts

Complete Combustion

In chemistry, when we talk about complete combustion, we refer to a chemical process where a substance reacts with oxygen to produce a limited number of distinct products. For hydrocarbons, like geraniol, this typically means carbon dioxide (CO₂) and water (H₂O) are the two main byproducts. Complete combustion is characterized by the fact that it uses up all of the reactant fuel with oxygen without leaving any residue or incomplete byproducts like carbon monoxide or soot.
The complete combustion of organic compounds is essential in environmental science because it ensures the utmost conversion of fuel into energy and products that are less harmful to the environment. In geraniol's case, when it undergoes complete combustion, the carbon atoms in geraniol combine with oxygen to form carbon dioxide, and the hydrogen atoms form water.
Understanding complete combustion helps in calculating the empirical formula of substances through stoichiometric methods by measuring the amounts of CO₂ and H₂O generated during the reaction.

Moles of CO2

The calculation of moles of CO₂ is foundational for determining the original composition of a combusted substance. By measuring the amount of CO₂ produced, we gain insight into how much carbon was initially present in the substance.
To calculate the moles from the mass of CO₂, we use the molar mass of CO₂, which is derived from its atomic composition: one carbon atom (12 g/mol) and two oxygen atoms (16 g/mol each). Hence, the molar mass is 44 g/mol. This allows us to convert the mass of CO₂ in milligrams to moles, which is a practical step in stoichiometry.
In the original exercise, we are given 499 mg of CO₂, which can be converted as follows: \[\text{Moles of CO}_2 = 499 \text{ mg} \times \left(\frac{1 \text{ g}}{1000 \text{ mg}}\right) \times \left(\frac{1 \text{ mol}}{44 \text{ g}}\right) \approx 0.0113 \text{ mol} \]Understanding this conversion is crucial because it allows us to move from a measurement of mass to a count of molecules, which are expressed in moles.

Moles of H2O

The production of water in a combustion reaction is indicative of the presence of hydrogen in the original compound. To find the number of moles of H₂O, we follow a similar process to what we did for CO₂.
Water's molar mass is calculated from two hydrogen atoms (each 1 g/mol) and one oxygen atom (16 g/mol), yielding a total molar mass of 18 g/mol. By converting the mass of H₂O into moles, we determine how much hydrogen was in geraniol before combustion.
For 184 mg of water produced, the conversion is as follows:\[\text{Moles of H}_2\text{O} = 184 \text{ mg} \times \left( \frac{1 \text{ g}}{1000 \text{ mg}} \right) \times \left( \frac{1 \text{ mol}}{18 \text{ g}} \right) \approx 0.01022 \text{ mol} \]The moles of water formed further aid in confirming the hydrogen-content of geraniol by doubling since each molecule of water contains two hydrogen atoms. This gives us a calculated hydrogen mole that forms the basis of comparison in determining the empirical formula.

GRAS List

The GRAS list, an acronym for "Generally Recognized As Safe," is a classification by the U.S. Food and Drug Administration (FDA) for substances added to food. If a chemical or ingredient is on this list, it means that experts deem it safe based on a long history of common use in food or solid scientific research.
Being on the GRAS list does not mean a substance is without regulation, but it signals that the FDA does not require it to undergo extensive pre-market approval process, unlike other food additives. This status simplifies its usage in food and personal care products.
Geraniol, for instance, benefits from being on the GRAS list, making it widely acceptable in various applications, such as food flavoring or cosmetic fragrances, due to its pleasant rose-like scent. Knowing the GRAS status of a component can help scientists and manufacturers ensure they use ingredients that are safe for consumers and comply with federal regulations.