Question

Methyl salicylate is a common "active ingredient" in liniments such as Ben-Gay \(^{\pi \prime}\). It is also known as oil of wintergreen. It is made up of carbon, hydrogen, and oxygen atoms. When a sample of methyl salicylate weighing \(5.287 \mathrm{~g}\) is burned in excess oxygen, \(12.24 \mathrm{~g}\) of carbon dioxide and \(2.505 \mathrm{~g}\) of water are formed. What is the simplest formula for oil of wintergreen?

Short answer

Question: Determine the simplest formula for oil of wintergreen (methyl salicylate) given the weights of the products formed when it is burned in excess oxygen (carbon dioxide and water). Answer: The simplest formula for oil of wintergreen (methyl salicylate) is C3H3O.

Step-by-step solution

Moles of carbon dioxide and water

First, let's find the moles of carbon dioxide and water produced from the combustion reaction by using their respective molar masses: Moles of CO2 = (12.24 g) / (44.01 g/mol) = 0.278 moles CO2 Moles of H2O = (2.505 g) / (18.02 g/mol) = 0.139 moles H2O

Moles of carbon and hydrogen in the compound

Next, we will determine the moles of carbon and hydrogen present in the compound since we know that one mole of carbon and two moles of hydrogen are present in one mole of CO2 (carbon dioxide) and one mole of H2O (water): Moles of C = 0.278 moles Moles of H = 0.139 moles * 2 = 0.278 moles

Moles of oxygen in the compound

Now we can find the moles of oxygen present in the compound. To do this, we will calculate the mass of carbon and hydrogen present in the compound and subtract it from the mass of the compound. Then we will divide the mass of oxygen by its molar mass to obtain the moles of oxygen: Mass of C = 0.278 moles * 12.01 g/mol = 3.335 g Mass of H = 0.278 moles * 1.01 g/mol = 0.281 g Mass of O = 5.287 g - (3.335 g + 0.281 g) = 1.671 g Moles of O = (1.671 g) / (16.00 g/mol) = 0.104 moles

Find the simplest whole-number ratio

Lastly, find the simplest whole-number ratio by dividing each number of moles by the smallest one (0.104 moles): Moles ratio of C : H : O = (0.278/0.104) : (0.278/0.104) : (0.104/0.104) = 2.67 : 2.67 : 1 Since the numbers are close to whole numbers, we can round them to get the whole-number ratio: Moles ratio of C : H : O = 3 : 3 : 1

Determine the simplest formula

Based on the whole-number ratio obtained, we can conclude that the simplest formula for oil of wintergreen (methyl salicylate) is: C3H3O

Key concepts

Combustion Analysis

Combustion analysis is a method used in chemistry to determine the composition of an unknown compound by burning it in excess oxygen and analyzing the amounts of the products, usually carbon dioxide (CO2) and water (H2O). During this process, all carbon atoms in the compound are converted to CO2, and all hydrogen atoms are converted to H2O.
To calculate the empirical formula, we start by measuring the masses of CO2 and H2O produced from the combustion. We then use these measurements to determine the moles of carbon and hydrogen atoms, since we know the fixed number of these atoms present in one mole of CO2 and H2O. However, because oxygen is part of both the reactant (the unknown compound) and the products (CO2 and H2O), we often need to find the oxygen content by difference — that is, subtracting the mass of carbon and hydrogen from the total mass of the unknown compound.

Molar Mass

Molar mass is a fundamental concept in chemistry, defined as the mass of one mole of a substance (the mass per unit amount of substance). It is expressed in units of grams per mole (g/mol), and it provides a bridge between the mass of a compound and the amount of substance (moles) present. This concept is crucial when translating the mass of substances produced in a reaction, such as CO2 and H2O from combustion analysis, into moles, which are used in stoichiometric calculations.
Understanding molar mass allows chemists to use the mass data obtained from experiments to calculate moles, which can then be used to deduce empirical formulas of unknown compounds. Different elements have different molar masses — for example, carbon has a molar mass of 12.01 g/mol, and oxygen is 16.00 g/mol — which must be taken into account when finding the moles of each element in a compound.

Stoichiometry

Stoichiometry is the area of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It involves using balanced chemical equations to calculate the moles of reactants needed or products formed. A stoichiometric calculation hinges on the concept of the mole and employs the mole ratios between reactants and products
Using stoichiometry in combustion analysis allows us to connect the mass of reactants to the mass of products through the mole-to-mole ratios dictated by the chemical reaction. This information can then be used to infer the amounts of carbon, hydrogen, and oxygen in the original compound and ultimately determine its empirical formula.

Mole-to-Mole Ratio

The mole-to-mole ratio is the ratio of moles of one substance to the moles of another substance in a balanced chemical reaction. It is derived from the coefficients of each substance in a balanced chemical equation and is essential when solving stoichiometric problems. For instance, in the combustion of a hydrocarbon, the mole-to-mole ratio between the hydrocarbon and produced CO2 or H2O is crucial to establish.
To determine this ratio, we examine the molecular formulas of the reactants and products. For the complete combustion of a compound containing carbon and hydrogen, we know that one mole of the compound will yield one mole of CO2 for each atom of carbon, and one mole of H2O for every two atoms of hydrogen. Once we have the empirical formula of a compound, we can also use the mole-to-mole ratio to predict the amounts of products that a given amount of the compound will produce under complete combustion.