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).
2. 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.
3. 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 \( M \).
4. 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.
5. 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.