Trimellitic acid is an organic acid that has a composition of 51.44% C,2.88% H,and 45.68% O by mass.A 6.96-g sample of trimellitic acid dissolved in 30.00 g of acetone,CH₃COCH₃,has a boiling point of 58.09°C.What is the molecular formula of trimellitic acid? (K_b for acetone is 1.71°C/m,and pure acetone has a boiling point of 56.20°C.)

Question

Quizplus · Accepted Answer

1. Calculate the empirical formula:
- Convert the percentages to masses:
C: 6.96 g x 51.44% = 3.58 g
H: 6.96 g x 2.88% = 0.20 g
O: 6.96 g x 45.68% = 3.18 g
- Convert the masses to moles:
C: 3.58 g / 12.011 g/mol = 0.298 mol
H: 0.20 g / 1.008 g/mol = 0.198 mol
O: 3.18 g / 15.999 g/mol = 0.199 mol
- Divide each of the mole values by the smallest one to get the simplest ratio:
C: 0.298 mol / 0.198 mol = 1.50
H: 0.198 mol / 0.198 mol = 1
O: 0.199 mol / 0.198 mol = 1.01
- Round the ratios to the nearest whole number to obtain the empirical formula: C1.5H1O1.01 (multiply by 2 to get whole numbers)

2. Determine the molecular formula:
- Calculate the empirical formula mass: 1.5(12.011 g/mol) + 1(1.008 g/mol) + 1.01(15.999 g/mol) = 67.10 g/mol
- Divide the molar mass given in the problem (molar mass = 3 x empirical formula mass) by the empirical formula mass to get the molecular formula coefficient: 
Molecular formula coefficient = (3 x 67.10 g/mol) / 296.13 g/mol = 2
- Multiply the subscripts in the empirical formula by the coefficient to obtain the molecular formula: C3H2O3

3. Calculate the expected boiling point of the solution:
- Calculate the molality of the solution: 
molality = moles of solute / mass of solvent (in kg)
moles of solute = 6.96 g / 296.13 g/mol = 0.0235 mol
mass of solvent = 30.00 g / 1000 g/kg = 0.0300 kg
molality = 0.0235 mol / 0.0300 kg = 0.783 mol/kg
- Calculate the expected boiling point elevation of the solution using the equation: 
ΔTb = Kb x molality
Kb for acetone is 1.71°C/m, so 
ΔTb = 1.71°C/m x 0.783 mol/kg = 1.34°C
- Calculate the expected boiling point of the solution:
Boiling point of solution = boiling point of pure solvent + ΔTb
Boiling point of solution = 56.20°C + 1.34°C = 57.54°C

The experimental boiling point of the solution is 58.09°C, which is higher than the expected value. This indicates that the solution is non-ideal and that the solute is present as more than one molecule in the solution. The molecular formula coefficient calculated earlier (2) indicates that trimellitic acid has 2 units of the C3H2O3 formula. Therefore, the actual molecular formula is 2(C3H2O3) = C6H4O6, which is option B.

Trimellitic Acid Is an Organic Acid That Has a Composition