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Chapter 5: Problem 134

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

Expert verified
The empirical formula for adipic acid is C₃O₂H₅, and the molecular formula is C₆O₄H₁₀.

Step by step solution

01

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.
02

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
03

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.
04

Determine the empirical formula

Based on the whole number ratios we calculated, the empirical formula for adipic acid is: C₃O₂H₅
05

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.

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