Question

An organic compound was found to contain only \(\mathrm{C}, \mathrm{H}\), 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 organic compound containing C, H, and Cl is \(C_{2}H_{5}Cl\).

Step-by-step solution

Calculate moles of carbon from CO₂ mass.

To find the moles of carbon in the compound, we will use the mass of CO₂ formed upon combustion. The molar mass of CO₂ is (12.01 g/mol for C) + (2 × 16.00 g/mol for O) = 44.01 g/mol. Using the given mass of CO₂ (3.52 g), we can find the moles of carbon as: moles of carbon in CO₂ = (mass of CO₂) / (molar mass of CO₂) moles of carbon = \( \frac{3.52\,\mathrm{g}}{44.01\,\mathrm{g/mol}} \)

Calculate the moles of chlorine from AgCl mass.

To find the moles of chlorine in the compound, we will use the mass of AgCl formed when reacting with silver. The molar mass of AgCl is (107.87 g/mol for Ag) + (35.45 g/mol for Cl) = 143.32 g/mol. Using the given mass of AgCl (1.27 g), we can find the moles of chlorine as: moles of chlorine in AgCl = (mass of AgCl) / (molar mass of AgCl) moles of chlorine = \( \frac{1.27\,\mathrm{g}}{143.32\,\mathrm{g/mol}} \)

Calculate the mass of hydrogen in the compound.

We can calculate the mass of hydrogen in the 1.50-g sample of the compound using the mass of carbon and chlorine. From the moles of carbon obtained in step 1, we can find the mass of carbon in the sample as: mass of carbon = moles of carbon × molar mass of C From the moles of chlorine obtained in step 2, we can find the mass of chlorine in the sample as: mass of chlorine = moles of chlorine × molar mass of Cl Now, we can calculate the mass of hydrogen as: mass of hydrogen = mass of sample - (mass of carbon + mass of chlorine)

Calculate the moles of hydrogen.

Next, we need to find the moles of hydrogen in the compound. We can do this by dividing the mass of hydrogen calculated in step 3 by the molar mass of hydrogen (1.01 g/mol): moles of hydrogen = mass of hydrogen / molar mass of H

Determine the empirical formula.

Finally, we need to determine the ratio of C, H, and Cl in the compound. To do this, divide all the moles obtained in steps 1, 2, and 4 by the smallest mole value. This will give us a whole number ratio of the elements present in the compound. After finding the value of the ratio, we can write the empirical formula of the compound.

Key concepts

Stoichiometry

The field of stoichiometry is a fundamental aspect of chemistry that involves determining the amounts of substances consumed and produced in chemical reactions. It is essentially the study of the quantitative relationships between reactants and products in a chemical equation.

Stoichiometry is crucial when working to find the empirical formula of a compound, as it provides a clear guide to understand the ratios of different atoms within a molecule. This is done by comparing the number of moles of each element, which is a measure of quantity in chemistry. The process requires precise calculations to ensure accuracy and to reflect the true proportions of the elements.

Combustion Analysis

Combustion analysis is an experimental procedure used in chemistry to determine the composition of organic compounds. During this process, a known mass of a compound is burned in excess oxygen, and the masses of the resulting carbon dioxide and water are measured. These measurements then allow chemists to calculate the amount of carbon and hydrogen in the original compound.

When the compound also contains elements like chlorine, additional steps are necessary such as treating with silver to precipitate out silver chloride, AgCl, which can then be weighed to find the mass -- and therefore the moles -- of chlorine. This systematic approach enables the determination of the empirical formula by highlighting the proportional amounts of each element in the sample.

Mole Concept

The mole concept is an essential principle in chemistry that defines the amount of substance. One mole contains Avogadro's number of particles, which is approximately 6.022 x 1023. This concept is pivotal when dealing with the microscopic world of atoms and molecules, providing a bridge between the mass of a substance and the number of its constituent particles.

Moles allow comparisons of elements and compounds on a common scale and serve as a critical intermediary in stoichiometry. They offer a way to convert between the mass of a substance (in grams) and the number of its particles (atoms, molecules, ions, etc.), which is particularly handy when determining ratios of elements within compounds.

Molar Mass

The molar mass is defined as the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is directly related to the molecular weight of a compound, which is the sum of the atomic weights of all atoms present in the molecule. The atomic weights are found on the periodic table and represent the average mass of an element’s atoms.

In empirical formula determination, the molar mass enables the conversion of masses from experiments (like the mass of CO₂ produced in combustion or the mass of AgCl formed) to moles. This step is fundamental to proportionally compare elements within a compound, leading to the ratio of atoms in the empirical formula. For instance, the molar mass of carbon dioxide (CO₂) is central to finding the number of moles of carbon when a sample is combusted.