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 -g sample of the compound was converted to \(1.27 \mathrm{~g}\) of AgCl. Determine the empirical formula of the compound.

Short answer

The empirical formula of the compound is \(C_{2}H_{3}Cl\).

Step-by-step solution

Finding moles of carbon

Determine the amount of carbon in the sample by using information about the combustion of the compound, which forms CO₂. Given CO₂ mass: 3.52 g. Obtain the CO₂ molar mass: \[44.01 \frac{g}{mol}\ (12.01 \,g \,of \,C + 2 \times 16.0 \,g \,of \,O).\] To find the moles of \(C\), divide the mass of CO₂ produced by the molar mass of CO₂: \[moles\,of\,C = \frac{mass\,of\,CO_2}{molar\,mass\,of\,CO_2} = \frac{3.52 \,g}{44.01 \frac{g}{mol}}.\]

Finding moles of chlorine

Determine the amount of chlorine in the sample by using information about the formation of AgCl. Given AgCl mass: 1.27 g. Obtain the AgCl molar mass: \[143.32 \frac{g}{mol}\ (35.45 \,g \,of \,Cl + 107.87 \,g \,of \,Ag).\] To find moles of \(Cl\), divide the mass of AgCl produced by the molar mass of AgCl: \[moles\,of\,Cl = \frac{mass\,of\,AgCl}{molar\,mass\,of\,AgCl} = \frac{1.27 \,g}{143.32 \frac{g}{mol}}.\]

Finding the mass of hydrogen

Presuming that the substance contains only C, H, and Cl, we can find the mass of hydrogen using the law of conservation of mass. \[mass\,of\,H = mass\,of\,sample - (mass\,of\,C + mass\,of\,Cl).\] Given the mass of sample: 1.50 g. Calculate the mass of C and Cl: - Mass of C: moles of C × molar mass of C - Mass of Cl: moles of Cl × molar mass of Cl

Finding moles of hydrogen

Find moles of H by dividing its mass by the molar mass of hydrogen. \[moles\,of\,H = \frac{mass\,of\,H}{molar\,mass\,of\,H} = \frac{mass\,of\,H}{1.01 \frac{g}{mol}}.\]

Finding the empirical formula

Determine the empirical formula by finding the lowest whole-number ratio between the moles of C, H, and Cl. Divide the moles of C, H, and Cl by the smallest mole value of the three. Round the resulting numbers to the nearest whole numbers, which will give the empirical formula of the compound.

Key concepts

Stoichiometry

The concept of stoichiometry is central to the field of chemistry and involves the calculation of the quantities of reactants and products involved in chemical reactions. It is based on the balanced chemical equation for the reaction and the mole concept, which allows chemists to relate the mass of a substance to the number of particles it contains.

Stoichiometry enables us to predict how much product will form from a given amount of reactants, or how much reactant is needed to produce a certain amount of product. In the case of the empirical formula determination exercise, stoichiometry allows us to calculate the moles of carbon, hydrogen, and chlorine from their masses and molar masses, giving us the vital ratios needed to deduce the empirical formula of the compound.

• Understanding the mole ratios in a balanced chemical equation.
• Using the mole concept to convert between mass and number of moles.
• Applying stoichiometry to infer the amounts of reactants and products.

Molar Mass

Molar mass is defined as the mass of one mole of a given substance and is expressed in grams per mole (g/mol). It is equivalent to the atomic or molecular weight of a substance, taken from the periodic table, and normalized to grams.

The molar mass serves as a conversion factor between the mass of a substance and the amount in moles. In the textbook exercise, the molar mass of CO₂ and AgCl is used to determine the number of moles of carbon and chlorine, respectively. The mass of CO₂ and AgCl formed during the experiments is divided by their respective molar masses to find the moles of each element present.

Key points:

• The molar mass is used as a conversion factor in stoichiometric calculations.
• Obtaining the molar mass from the sum of atomic weights of elements in a compound.
• The molar mass helps us establish the relationship between mass and mole in chemical equations.

Combustion Analysis

Combustion analysis is a laboratory method used to determine the elemental composition of a compound, especially those containing carbon and hydrogen. By igniting the compound in the presence of excess oxygen, it will combust fully to produce CO₂ and water. The masses of these combustion products can be measured to deduce the amounts of the constituent elements of the original compound.

In the empirical formula determination problem, combustion analysis allows us to find out how much carbon is in the sample as it is converted to CO₂. From the mass of the CO₂ produced, we can calculate the moles of carbon. This technique also plays a crucial role in ensuring the complete conversion of carbon, which aligns with the principle of the law of conservation of mass.

• Essential in identifying the proportion of carbon in organic compounds.
• Provides an accurate method to measure the content of combustible elements.
• Combustion products are analyzed to calculate the amount of the original elements.

Law of Conservation of Mass

The law of conservation of mass states that matter cannot be created or destroyed in an isolated system. In the context of a chemical reaction, this law implies that the total mass of reactants must equal the total mass of products.

When carrying out stoichiometric calculations, as shown in the empirical formula derivation, this law helps us determine masses of elements within a compound that were not directly measured. For example, in the problem at hand, once we know the mass of carbon and chlorine, we use the law of conservation of mass to infer the mass of hydrogen by subtracting the mass of carbon and chlorine from the total mass of the compound. Ensuring mass balance is integral to accurately calculating the empirical formula.

• Foundational principle in all chemical equations and reactions.
• Ensures accurate stoichiometric computations based on mass balance.
• Guides us in finding unmeasured masses within a compound.