Question

You take an aspirin tablet (a compound consisting solely of carbon, hydrogen, and oxygen) with a mass of 1.00 g, burn it in air, and collect 2.20 g of carbon dioxide and 0.400 g water. The molar mass of aspirin is between 170 and 190 g/mol. The molecular formula of aspirin is

Answer 1

Answer:

The formula of aspirin = $C_9H_8O_4$

Explanation:

Mass of water obtained = 0.400

Molar mass of water = 18 g/mol

Moles of $H_2O$ = 0.400 g /18 g/mol = 0.0222 moles

2 moles of hydrogen atoms are present in 1 mole of water. So,

Moles of H = 2 x 0.0222 = 0.0444 moles

Molar mass of H atom = 1.008 g/mol

Mass of H in molecule = 0.0444 x 1.008 = 0.0448 g  

Mass of carbon dioxide obtained = 2.20 g

Molar mass of carbon dioxide = 44.01 g/mol

Moles of $CO_2$ = 2.20 g  /44.01 g/mol = 0.05 moles

1 mole of carbon atoms are present in 1 mole of carbon dioxide. So,

Moles of C = 0.05 moles

Molar mass of C atom = 12.0107 g/mol

Mass of C in molecule = 0.05 x 12.0107 = 0.6005 g

Given that the aspirin acid only contains hydrogen, oxygen and carbon. So,

Mass of O in the sample = Total mass - Mass of C  - Mass of H

Mass of the sample = 1.00 g

Mass of O in sample = 1.00 - 0.6005 - 0.0448 = 0.3547 g  

Molar mass of O = 15.999 g/mol

Moles of O  = 0.3547  / 15.999  = 0.0222 moles

Taking the simplest ratio for H, O and C as:

0.0444 : 0.0222 : 0.05

= 8 : 4 : 9

The empirical formula is = $C_9H_8O_4$

Molecular formulas is the actual number of atoms of each element in the compound while empirical formulas is the simplest or reduced ratio of the elements in the compound.

Thus,  

Molecular mass = n × Empirical mass

Where, n is any positive number from 1, 2, 3...

Mass from the Empirical formula = 9×12 + 8×1 + 16×4= 180 g/mol

The molar mass of aspirin is between 170 and 190 g/mol

So,  

Molecular mass = n × Empirical mass

170 <  n × 180 < 190

⇒ n = 1

The formula of aspirin = $C_9H_8O_4$