Question

Adipic acid is an organic compound composed of \(49.31 \% \mathrm{C}\). \(43.79 \% \mathrm{O}\), and the rest hydrogen. If the molar mass of adipic acid is \(146.1 \mathrm{~g} / \mathrm{mol}\), what are the empirical and molecular formulas for adipic acid?

Short answer

The empirical formula of adipic acid is C3H5O2 and the molecular formula is C6H10O4.

Step-by-step solution

Moles of Carbon

Given: Carbon percentage: 49.31% Assume: mass of sample = 100g Moles of Carbon = (mass of carbon / molar mass of carbon) Moles of Carbon = (49.31g / 12.01g/mol) = 4.108 mol

Moles of Oxygen

Given: Oxygen percentage: 43.79% Moles of Oxygen = (mass of oxygen / molar mass of oxygen) Moles of Oxygen = (43.79g / 16.00g/mol) = 2.737 mol

Moles of Hydrogen

Given: Carbon, Oxygen, and Hydrogen percentages add up to 100%: Hydrogen percentage: 100 - 49.31 - 43.79 = 6.9% Moles of Hydrogen = (mass of hydrogen / molar mass of hydrogen) Moles of Hydrogen = (6.9g / 1.008g/mol) = 6.846 mol #Step 2: Determine the mole ratios of each element.# Now we will find the mole ratios by dividing the moles of each element by the smallest number of moles (2.737 in this case).

Mole Ratios

Carbon : (4.108 / 2.737) ≈ 1.5 Oxygen : (2.737 / 2.737) = 1 Hydrogen : (6.846 / 2.737) ≈ 2.5 Since we cannot have fractions in an empirical formula, we will multiply each ratio by 2 to remove the fractions. Carbon : 1.5 × 2 = 3 Oxygen : 1 × 2 = 2 Hydrogen : 2.5 × 2 = 5 #Step 3: Write the empirical formula.# The empirical formula will be written by utilizing the mole ratios that we have found.

Empirical Formula

Empirical Formula = C3H5O2 #Step 4: Calculate the molecular formula.# To calculate the molecular formula, we must first find the molar mass of the empirical formula. Then, we will compare it to the given molar mass of adipic acid and find the ratio between them.

Molar Mass of Empirical Formula

Molar Mass (C3H5O2) = (3 × 12.01) + (5 × 1.008) + (2 × 16.00) ≈ 73.05 g/mol Now, we will determine the ratio between the given molar mass and the empirical molar mass.

Ratio Between Molar Masses

Ratio = (146.1 g/mol) / (73.05 g/mol) ≈ 2 Since the ratio is 2, we just need to multiply each element in the empirical formula by 2 to obtain the molecular formula. #Step 5: Write the molecular formula.# Now we write the molecular formula for adipic acid, based on the ratio.

Molecular Formula

Molecular Formula = C6H10O4

Key concepts

Stoichiometry

Stoichiometry is the mathematical relationship between the relative quantities of reactants and products in chemical reactions. It allows chemists to predict the amounts of substances consumed and produced in a given reaction. The concept is founded on the principle of the conservation of mass, which states that in a chemical reaction, matter is neither created nor destroyed.

Understanding stoichiometry involves balancing chemical equations to reflect the conservation of atoms. The coefficients in a balanced equation tell us in what ratio the substances react and are formed. For example, in the complete combustion of propane, we have the chemical equation \( C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \). This equation indicates that one molecule of propane reacts with five molecules of oxygen to produce three molecules of carbon dioxide and four molecules of water. Stoichiometry is a tool that would allow us to calculate the masses of reactants needed to produce a desired amount of product or, as in the case of the adipic acid example, determine the empirical and molecular formulas of a compound.

Molar Mass Calculation

Molar mass calculation is a fundamental concept in stoichiometry, as it links the mass of a substance to the amount of substance in terms of moles. The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). One mole contains Avogadro's number \(6.022 \times 10^{23}\) of entities, whether they are atoms, molecules, ions, or electrons.

To calculate the molar mass, one must sum the atomic masses of all the atoms in the molecular formula. For example, the molar mass of water, \(H_2O\), is calculated by adding the mass of two hydrogen atoms and one oxygen atom, which results in approximately 18.02 g/mol. In our adipic acid exercise, the molar mass calculation is crucial for determining the molecular formula. By comparing the molar mass of the empirical formula with the given molar mass of adipic acid, we arrive at the molecular formula, further illustrating the practical application of molar mass in solving chemical problems.

Mole-to-Mole Conversion

Mole-to-mole conversion is a vital process in stoichiometry that involves using the balanced chemical equation to convert between the amounts of reactants and products in moles. This process relies on the mole ratios derived from the coefficients in a balanced chemical equation, ensuring that atoms are conserved in a reaction.

For example, if the equation for the reaction of nitrogen with hydrogen to form ammonia is given as \(N_2 + 3H_2 \rightarrow 2NH_3\), the mole ratio of \(N_2:H_2:NH_3\) is 1:3:2. This tells us that for every mole of nitrogen used, three moles of hydrogen are required, and two moles of ammonia are produced. In the exercise solution, mole-to-mole conversion is illustrated when the moles of each element are compared with the smallest number of moles to establish the simplest whole number ratio among the elements. This ratio is crucial for determining the empirical formula, which is then used to find the molecular formula through the use of molar mass calculations and mole-to-mole conversions.