GRAS List for Food Additives The alcohol geraniol is on the...

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?

Key Concepts

Empirical Formula Determination

The empirical formula of a compound is derived by determining the simplest whole-number ratio of the elements present. After calculating the moles of carbon, hydrogen, and deducing oxygen by the conservation of mass, these values are scaled by dividing by the smallest number of moles to obtain the simplest ratio, resulting in the empirical formula.

Combustion Analysis

Combustion analysis is a method used to determine the elemental composition of a compound by burning it in oxygen and measuring the masses of the products, typically CO2 and H2O. This technique exploits the fact that all the carbon in a compound is converted to CO2 and all the hydrogen to H2O, allowing the determination of the amounts of carbon and hydrogen present by back-calculating from the masses of these products.

Stoichiometry and Mole Conversions

Stoichiometry involves converting between mass and moles using molar masses, enabling the calculation of how much of each element is present in a sample. In the context of combustion analysis, the masses of CO2 and H2O are converted to moles to determine the number of moles of carbon and hydrogen, which forms the basis for finding the ratios in the empirical formula.

Transcript

00:01 Let's go through how to find the empirical formula in a combustion reaction.

00:07 So we're given 0 .175 grams of geraniel, and it combusts into 0 .49 grams of carbon dioxide, and 0 .184 grams of water vapor.

00:25 So this compound geraniel is going to have a formula of c something, h something o something and that's going to be our basic formula for combustion of this alcohol alright so let's look at this we're going to have 0 .49 grams of carbon dioxide and 0 .184 grams of water vapor so the carbon is going to be turned into carbon dioxide and the hydrogen is going to be turned into water vapor so we need to find out how much carbon and how much hydrogen we have in this gerennial.

01:11 So to do that, we're going to take the mass, which colors.

01:21 We're going to take the mass of the carbon dioxide that we have.

01:27 And we're going to divide that by the molar mass of this carbon dioxide.

01:34 So that's going to be 44.

01:38 And then we're going to multiply it by how much carbon we have.

01:44 So we divided this number, this 0 .49, by the atomic mass of carbon dioxide.

01:53 And if we just want carbon, we need to multiply it by the atomic mass of carbon.

01:58 So we'll do that.

02:00 And if we do 0 .499 divided by 44, and then we multiply that by 12, we'll get 0 .136.

02:11 We'll get 0 .136.

02:14 And that's going to be our amount of carbon.

02:20 0 .136 grams.