Question

Adipic acid is an organic compound composed of \(49.31 \%\) 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 for adipic acid is C₃O₂H₅, and the molecular formula is C₆O₄H₁₀.

Step-by-step solution

Convert the percentage composition to grams

Assuming we have a 100 g sample of adipic acid, we can convert the percentage composition directly to grams for easier calculation. - 49.31% C will be equal to 49.31 g of C - 43.79% O will be equal to 43.79 g of O - For the rest of the hydrogen, we subtract the percentage of C and O from 100% to find out the percentage of hydrogen present in adipic acid, which is 100 - 49.31 - 43.79 = 6.9%. In grams, it will be 6.9 g of H.

Convert grams to moles of each element

We need to convert the amounts of elements in grams to moles by using the molar masses of each element. For carbon (C): Molar mass = 12.01 g/mol For oxygen (O): Molar mass = 16 g/mol For hydrogen (H): Molar mass = 1 g/mol - Moles of C = 49.31 g / 12.01 g/mol = 4.104 moles - Moles of O = 43.79 g / 16 g/mol = 2.737 moles - Moles of H = 6.9 g / 1 g/mol = 6.9 moles

Find the simplest whole-number ratio of moles

To find the simplest whole-number ratio of moles, we should divide the moles of all elements by the smallest mole value among them. In this case, the smallest value is the moles of O at 2.737 moles. - Ratio for C = 4.104 moles / 2.737 moles = 1.5 - Ratio for O = 2.737 moles / 2.737 moles = 1 - Ratio for H = 6.9 moles / 2.737 moles = 2.52 We should have whole numbers in the ratio. Almost all the values are close to whole numbers, so we can multiply all the ratios by 2 to get the whole number ratios: - Ratio for C = 1.5 * 2 = 3 - Ratio for O = 1 * 2 = 2 - Ratio for H = 2.52 * 2 = 5.04 ≈ 5 (rounded) Now we have the whole number ratios: C = 3, O = 2, and H = 5.

Determine the empirical formula

Based on the whole number ratios we calculated, the empirical formula for adipic acid is: C₃O₂H₅

Determine the molecular formula

Now, we need to compare the empirical formula's mass with the given molar mass of adipic acid (146.1 g/mol). Empirical formula mass = (3 * 12.01) + (2 * 16) + (5 * 1) = 36.03 + 32 + 5 = 73.03 g/mol To find the relationship between the empirical formula and the molecular formula, we can divide the molar mass of the molecule by the empirical formula mass: 146.1 g/mol / 73.03 g/mol ≈ 2 This means that the molecular formula has twice the empirical formula composition. Molecular formula = (C₃O₂H₅) * 2 = C₆O₄H₁₀ The molecular formula for adipic acid is C₆O₄H₁₀.

Key concepts

Percentage Composition

Percentage composition is an important aspect of chemistry as it helps us to determine the proportion of elements within a compound. When given the percentage composition of an element in a compound, you can easily convert these percentages into actual mass values. Assuming a 100 g sample simplifies this process.

For example, adipic acid is composed of 49.31% carbon and 43.79% oxygen. In the case of a 100 g sample, this corresponds to 49.31 g of carbon and 43.79 g of oxygen. The remainder, in this situation, would be hydrogen, completing the 100% as 6.9 g.

Understanding percentage composition is crucial when attempting to determine both empirical and molecular formulas of a substance.

Mole Ratio

The mole ratio is a key concept when translating mass into a formula representation. Once you have determined the amount of each element in moles, using their respective molar masses, you will need to find the simplest whole-number ratio between them.

In the adipic acid example, the moles of carbon, oxygen, and hydrogen are calculated. Carbon is 4.104 moles, oxygen is 2.737 moles, and hydrogen is 6.9 moles. The next step is identifying the smallest number among these, which is the moles of oxygen.

• Convert each mole value into a ratio by dividing by the smallest mole value (2.737 for oxygen).
• Round these ratios to the nearest whole number if necessary.

This process reveals the empirical formula by expressing the relative number of atoms in their simplest form.

Molar Mass

Molar mass is essential in determining the molecular formula. It is the mass of one mole of a substance, expressed in grams per mole (g/mol), enabling chemists to relate the empirical formula mass to the molar mass. By dividing the compound's given molar mass by the empirical formula mass, you gain the multiplier needed to determine the molecular formula.

In adipic acid's case, the empirical formula mass (C₃O₂H₅) calculates to be 73.03 g/mol. With a given molar mass of 146.1 g/mol, you divide these to get approximately 2. This result implies that the molecular formula consists of two units of the empirical formula, leading to C₆O₄H₁₀.

This procedure helps verify and express the accurate composition in the form of the molecular formula, which is crucial for further chemical applications and analyses.