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Chapter 3: Problem 190

You take 1.00 g of an aspirin tablet (a compound consisting solely of carbon, hydrogen, and oxygen), burn it in air, and collect 2.20 $\mathrm{g} \mathrm{CO}_{2}\( and 0.400 \)\mathrm{g} \mathrm{H}_{2} \mathrm{O} .$ You know that the molar mass of aspirin is between 170 and 190 $\mathrm{g} / \mathrm{mol}\( . Reacting 1 \)\mathrm{mole}$ of salicylic acid with 1 mole of acetic anhydride \(\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) gives you 1 mole of aspirin and 1 mole of acetic acid $\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\right)$ Use this information to determine the molecular formula of salicylic acid.

Short Answer

Expert verified
The molecular formula of salicylic acid is C10H10O5.

Step by step solution

01

Calculate the moles of carbon and hydrogen from the combustion products

We are given the amounts of CO2 and H2O produced from the combustion of the aspirin tablet. We can use this information to determine the moles of carbon and hydrogen present in the tablet. Moles of carbon (from CO2) = mass of CO2 produced / molar mass of CO2 Moles of carbon = \( \frac{2.20 \mathrm{g}}{44.01 \mathrm{g/mol}} \) = 0.0500 mol C Moles of hydrogen (from H2O) = mass of H2O produced / molar mass of H2O Moles of hydrogen = \( \frac{0.400 \mathrm{g}}{18.02 \mathrm{g/mol}} \) = 0.0222 mol H
02

Calculate the moles of oxygen in the tablet

Since the aspirin tablet consists only of carbon, hydrogen, and oxygen, we can calculate the moles of oxygen in the tablet by subtracting the masses of carbon and hydrogen from the total mass of the tablet. Mass of oxygen = Total mass of tablet - Mass of carbon - Mass of hydrogen Mass of oxygen = 1.00 g - (0.0500 mol C * 12.01 g/mol C) - (0.0222 mol H * 1.01 g/mol H) Mass of oxygen = 0.351 g Moles of oxygen = mass of oxygen / molar mass of oxygen Moles of oxygen = \( \frac{0.351 \mathrm{g}}{16.00 \mathrm{g/mol}} \) = 0.0219 mol O
03

Determine the empirical formula of the aspirin tablet

Now that we have the moles of carbon, hydrogen, and oxygen present in the aspirin tablet, we can determine the empirical formula. First, we need to find the mole ratio of the elements. Mole ratio of C:H:O = 0.0500 : 0.0222 : 0.0219 Divide each ratio by the smallest value (0.0219) to get: Mole ratio of C:H:O = 2.28 : 1.01 : 1 Round the ratio to the nearest whole number to get the empirical formula: Empirical formula = C2H1O1 (or simply CH2O)
04

Determine the molecular formula of aspirin

Now that we have the empirical formula, we can determine the molecular formula using the provided molar mass range for aspirin (170-190 g/mol). Empirical formula mass of CH2O = 12.01 g/mol C + 1.01 g/mol H + 16.00 g/mol O = 29.02 g/mol We'll use the middle value of the given molar mass range (180 g/mol) and divide it by the empirical formula mass: \( \frac{180 \mathrm{g/mol}}{29.02\mathrm{ g/mol}} \) ≈ 6 Since the empirical formula mass multiplied by 6 gives a value within the given molar mass range, the molecular formula for aspirin is: Aspirin molecular formula = C12H12O6
05

Determine the molecular formula of salicylic acid

Lastly, we will determine the molecular formula of salicylic acid using the provided reaction information. The reaction is given as: 1 mole of salicylic acid + 1 mole of acetic anhydride (C4H6O3) → 1 mole of aspirin (C12H12O6) + 1 mole of acetic acid (C2H4O2) Comparing the products, we have: salicylic acid + C4H6O3 = C14H16O8 Now, we can determine the molecular formula for salicylic acid by subtracting the acetic anhydride from the aspirin molecular formula: Salicylic acid = C14H16O8 - C4H6O3 Salicylic acid = C10H10O5 Therefore, the molecular formula of salicylic acid is C10H10O5.

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