Question

An organic compound was found to contain only \(C, H\), and Cl. When a \(1.50\)-g sample of the compound was completely combusted in air, \(3.52 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) was formed. In a separate experiment the chlorine in a \(1.00-\mathrm{g}\) sample of the compound was converted to \(1.27 \mathrm{~g}\) of \(\mathrm{AgCl}\). Determine the empirical formula of the compound.

Short answer

The empirical formula of the compound is \(C_{2}H_{5}Cl\).

Step-by-step solution

Calculate the number of moles of Carbon

First, we need to find the number of moles of carbon in the compound by using the mass of CO₂ produced from the given experiment. Given: Mass of CO₂ = 3.52 g Molecular weight of CO₂ = 44.01 g/mol (12.01 g/mol for Carbon + 16 g/mol for each Oxygen) Number of moles of CO₂ formed = Mass of CO₂ / Molecular weight of CO₂ \[\frac{3.52 \mathrm{~g~} CO₂}{44.01 \mathrm{~g/mol}} \approx 0.0800 \mathrm{~mol}\] Since there's one carbon atom in each CO₂ molecule, the number of moles of carbon in the organic compound is also 0.0800 moles.

Calculate the number of moles of Chlorine

Now, we will use the mass of AgCl produced from the experiment to determine the number of moles of chlorine in the compound. Given: Mass of AgCl = 1.27 g Molecular weight of AgCl = 143.32 g/mol (35.45 g/mol for Chlorine + 107.87 g/mol for Silver) Number of moles of AgCl formed = Mass of AgCl / Molecular weight of AgCl \[\frac{1.27 \mathrm{~g~} AgCl}{143.32 \mathrm{~g/mol}} \approx 0.00885 \mathrm{~mol}\] Since there's one chlorine atom in each AgCl molecule, the number of moles of chlorine in the organic compound is also 0.00885 moles.

Calculate the mass of Hydrogen

We know the total mass of the compound and the masses of carbon and chlorine in it. We can now find the mass of hydrogen. Mass of compound = 1.50 g Mass of Carbon = 0.0800 moles * 12.01 g/mol (molecular weight of carbon) Mass of Chlorine = 0.00885 moles * 35.45 g/mol (molecular weight of chlorine) Mass of Hydrogen = Mass of compound - Mass of Carbon - Mass of Chlorine

Calculate the number of moles of Hydrogen

We will now find the number of moles of hydrogen by dividing the mass of hydrogen by the molecular weight of hydrogen. Molecular weight of Hydrogen = 1.008 g/mol Number of moles of Hydrogen = Mass of Hydrogen / Molecular weight of Hydrogen

Determine the empirical formula

To find the empirical formula, divide the number of moles of each element by the lowest number of moles. Find the ratio: C:H:Cl Divide the moles of each element by the lowest number of moles of the three elements. The empirical formula is the whole number ratio obtained as the result, rounded. Please note: If any of the ratios are not whole numbers (e.g., x.5 or x.33), multiply them by the smallest integer to obtain a whole number ratio. Write the empirical formula based on the whole number ratio obtained.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that involves the calculation of the quantities of reactants and products in chemical reactions. It is fundamentally based on the law of conservation of mass, which states that in a chemical reaction, the total mass of the reactants equals the total mass of the products. The stoichiometric calculations often use the mole concept and molar ratios derived from the balanced chemical equations to predict the amount of product that will form from a given amount of reactants, or to identify the amount of reactants needed to create a certain amount of product.

For instance, in the provided example, you start by determining the amount of carbon from the carbon dioxide produced in a combustion reaction. This requires converting the given mass of carbon dioxide into moles, which illustrates the direct application of stoichiometry. The balanced chemical equation would dictate that one mole of carbon reacts with oxygen to produce one mole of carbon dioxide, reflecting a 1:1 mole ratio for carbon to carbon dioxide. Understanding this stoichiometric relationship allows us to accurately determine the composition of the unknown compound.

Combustion Analysis

Combustion analysis is an effective technique commonly used in chemistry to determine the empirical formula of unknown organic compounds. During this process, a known mass of the compound is burned in excess oxygen, and the masses of the combustion products, usually carbon dioxide and water, are measured. These measurements can then be used to calculate the number of moles of carbon and hydrogen in the original compound.

In the given problem, the mass of carbon dioxide generated from the combustion of the organic compound is used to calculate the moles of carbon. The key here is to remember that carbon dioxide is always produced when carbon-containing substances combust in the presence of oxygen. By using stoichiometry, you calculate the amount of carbon in the compound from the carbon dioxide produced. Similarly, if water were produced, its mass would be used to calculate the moles of hydrogen. These calculations are crucial for finding the empirical formula and require careful measurement and conversion to ensure accuracy.

Mole Concept

The mole concept is a fundamental principle in chemistry that allows chemists to work with the submicroscopic world of atoms and molecules on a macroscopic scale. A mole is defined as the amount of substance that contains as many elementary entities (e.g., atoms, molecules, ions) as there are atoms in 12 grams of pure carbon-12. This number, known as Avogadro's number, is approximately 6.022 x 10²³ entities per mole.

Utilizing the mole concept allows us to convert between the mass of a substance and the number of moles. For example, with respect to the problem at hand, the mass of carbon dioxide and silver chloride produced is first converted into moles, which then allows us to infer the number of moles of carbon and chlorine in the original compound. The mole concept is essential when manipulating chemical quantities and relating them to the empirical formula.