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Ch.23 - Organic and Biological Chemistry
All textbooksMcMurry 8th EditionCh.23 - Organic and Biological ChemistryProblem 135
Chapter 23, Problem 135

Fumaric acid is an organic substance widely used as a food additive. Its elemental composition is 41.4% C, 3.5% H, and 55.1% O. A solution made by dissolving 0.1500 g of fumaric acid in water and diluting to a volume of 100.0 mL gave rise to an osmotic pressure of 240.3 mm Hg at 298 K. On titration of a sample weighing 0.573 g, 94.1 mL of 0.105 M NaOH was required to reach an equivalence point. Fumaric acid reacts with 1 mol of H2 to give a hydrogenation product. (a) What is the empirical formula of fumaric acid? (b) What is the molecular weight of fumaric acid? (c) Draw three possible structures for fumaric acid. (d) If fumaric acid contains a trans double bond, which of your structures is correct?

Verified step by step guidance
1
Step 1: Determine the empirical formula of fumaric acid by converting the percentage composition to moles. Assume 100 g of fumaric acid, which gives 41.4 g of C, 3.5 g of H, and 55.1 g of O. Convert these masses to moles using their respective molar masses: C (12.01 g/mol), H (1.008 g/mol), and O (16.00 g/mol).
Step 2: Calculate the mole ratio of the elements by dividing each element's mole value by the smallest number of moles calculated in Step 1. This will give you the simplest whole number ratio of atoms in the compound, which is the empirical formula.
Step 3: Use the osmotic pressure data to find the molar mass of fumaric acid. Use the formula for osmotic pressure: \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor (assume 1 for non-electrolytes), \( M \) is the molarity, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin. Rearrange to solve for \( M \).
Step 4: Calculate the molar mass of fumaric acid using the titration data. Use the formula \( n = MV \) to find the moles of NaOH, where \( M \) is the molarity and \( V \) is the volume in liters. Since fumaric acid is a diprotic acid, it reacts with 2 moles of NaOH per mole of acid. Use this to find the moles of fumaric acid and then its molar mass.
Step 5: Draw possible structures for fumaric acid considering it is an unsaturated dicarboxylic acid. Use the information that it contains a trans double bond to identify the correct structure.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Empirical Formula

The empirical formula represents the simplest whole-number ratio of the elements in a compound. To determine it, one must convert the percentage composition of each element into moles, then simplify the ratio of these moles. For fumaric acid, this involves calculating the moles of carbon, hydrogen, and oxygen based on the given percentages and finding the smallest whole-number ratio.
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Empirical vs Molecular Formula

Molecular Weight

The molecular weight (or molar mass) of a compound is the sum of the atomic weights of all atoms in its molecular formula. It can be determined by first finding the empirical formula and then using the molar mass of each element to calculate the total mass. In the case of fumaric acid, the molecular weight can also be inferred from the osmotic pressure data using the ideal gas law and the relationship between osmotic pressure and molarity.
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Weight Conversion Example

Structural Isomers

Structural isomers are compounds that have the same molecular formula but different arrangements of atoms. For fumaric acid, drawing possible structures involves considering the placement of double bonds and functional groups. The presence of a trans double bond indicates specific geometric configurations, which can help identify the correct structure among the isomers based on the spatial arrangement of atoms.
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Related Practice
Textbook Question
Cyclohexane, C6H12, is an important starting material used in the industrial synthesis of nylon. Each carbon has four covalent bonds, two to hydrogen and two to other carbons. Draw the structural formula of cyclohexane.
Textbook Question

Isooctane, the substance in gasoline from which the term octane rating derives, has the formula C8H18. Each carbon has four covalent bonds, and the atoms are connected in the sequence shown. Draw the complete structural formula of isooctane.