Question

Dieldrin, an insecticide, contains \(\mathrm{C}, \mathrm{H}, \mathrm{Cl}\) and \(\mathrm{O}\). Combustion of \(29.72 \mathrm{mg}\) of Dieldrin gave \(41.21 \mathrm{mg} \mathrm{CO}_{2}\) and \(5.63 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O}\). In a separate analysis \(25.31 \mathrm{mg}\) of Dieldrin was converted into \(57.13 \mathrm{mg} \mathrm{AgCl}\). What is the empirical formula of Dieldrin ? (a) \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{3} \mathrm{O}\) (b) \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{ClO}\) (c) \(\mathrm{C}_{12} \mathrm{H}_{\mathrm{g}} \mathrm{Cl}_{6} \mathrm{O}\) (d) \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{3} \mathrm{O}_{2}\)

Short answer

The empirical formula of Dieldrin is (a) \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{3} \mathrm{O}\).

Step-by-step solution

Calculate moles of carbon in CO2

Calculate the moles of carbon from the CO2 produced by using the molar mass of CO2 (44.01 g/mol). The mass of CO2 is given as 41.21 mg, which is 0.04121 g. The moles of carbon is the same as the moles of CO2 since each molecule of CO2 contains one carbon atom, calculated as moles of C = 0.04121 g / 44.01 g/mol.

Calculate moles of hydrogen in H2O

Calculate the moles of hydrogen from the mass of H2O produced using the molar mass of H2O (18.02 g/mol). The mass of H2O is given as 5.63 mg, which is 0.00563 g. Since each molecule of H2O contains two atoms of hydrogen, the moles of hydrogen is twice the moles of H2O, calculated as moles of H = 2 * (0.00563 g / 18.02 g/mol).

Calculate moles of chlorine in AgCl

Calculate the moles of chlorine from the mass of AgCl produced using the molar mass of AgCl (143.32 g/mol). The mass of AgCl is given as 57.13 mg, which is 0.05713 g. Since each molecule of AgCl contains one atom of chlorine, the moles of chlorine is the same as the moles of AgCl, calculated as moles of Cl = 0.05713 g / 143.32 g/mol.

Calculate the moles of oxygen in Dieldrin

Since the Dieldrin was completely combusted, the only oxygen in the products comes from the Dieldrin. To find the moles of O in the Dieldrin, calculate the total mass of C and H from the moles obtained in Steps 1 and 2 and subtract from the initial mass of Dieldrin. The remaining mass is due to oxygen. Convert this mass of oxygen to moles using the molar mass of O (16.00 g/mol).

Calculate the empirical formula

To find the empirical formula, divide the moles of each element by the smallest number of moles obtained among C, H, Cl, and O. This will give the mole ratio of the elements, which is used to determine the empirical formula.

Verify the correct empirical formula

Match the calculated empirical formula with the given options and verify the correct empirical option that fits the mole ratio obtained.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. In the context of empirical formula calculation, it entails measuring the proportions of elements in compounds and determining the simplest ratio of atoms in a molecule.

For instance, by conducting experiments, such as combustion analysis, one can determine the mass of carbon, hydrogen, and oxygen in an organic compound. Stoichiometry uses these masses to calculate the moles of each element, which can then be converted into mole ratios to find the empirical formula. By dividing the number of moles of each element by the smallest number of moles in the set, you get the ratio of atoms of each element in the simplest form, which is the empirical formula.

Mole Concept

The mole concept is an integral part of chemistry and a bridge between the macroscopic scale of substances and their atomic-scale properties. One mole is defined as the amount of any substance that contains the same number of entities as there are atoms in 12 grams of carbon-12, which is approximately \(6.022 \times 10^{23}\) entities, known as Avogadro's number.

In empirical formula calculations, the mole concept is used to convert the mass of an element to moles by dividing by its molar mass. Understanding how to apply the mole concept is essential in stoichiometry, as it allows chemists to count atoms by weighing, which is fundamental when determining the molecular or empirical formulas of compounds.

Combustion Analysis

Combustion analysis is a technique widely used in chemistry to determine the empirical formula of a hydrocarbon, which is a compound made of carbon, hydrogen, and sometimes oxygen. The process involves burning a known mass of the compound and measuring the mass of carbon dioxide (\(CO_2\)) and water (\(H_2O\)) produced. From these data, one can back-calculate to find the amount of carbon and hydrogen in the original compound.

The mass of carbon in the compound is found from the mass of \(CO_2\) produced, and the mass of hydrogen from the mass of \(H_2O\) produced. If the compound also contains oxygen, the mass of oxygen can be determined by subtracting the mass of carbon and hydrogen from the total mass of the compound. Each measured mass is then converted to moles, allowing for the determination of empirical formula using stoichiometry.

Chemical Formula Determination

Determining the chemical formula of a compound, whether it's the empirical or molecular formula, is a critical step in understanding the substance's chemical properties and behavior. The empirical formula represents the simplest whole-number ratio of elements in a compound, whereas the molecular formula is the actual number of atoms of each element in a molecule of the compound.

To find these formulas, chemists use strategies such as combustion analysis for organic compounds or other analytical methods for different types of compounds. Conversion of masses to moles allows for the comparison of each element's presence in the compound. As demonstrated in the Dieldrin example, the process involves a methodical approach where each element's moles are calculated separately, and then divided by the smallest mole number to obtain the simplest whole number ratios, concluding with empirical or molecular formula determination.