Question

The mystery of the unknown substance A prominent automotive businessman has been murdered in New York. The Crime Scene Investigation (CSI) team finds a bottle with some clear liquid at the scene of the crime. The label on the bottle has fallen off. The detectives believe that this bottle belongs to the killer, who dropped it there in a hurry to get away. Their suspects include the victim’s business rival, his lawyer, and a theatre actress. The detectives think that if the CSI team can identify the liquid, they might be able to narrow down the suspects. One of the CSI technicians has analyzed the liquid using a mass spectrometer and found that the compound has a molar mass of 58.0714 g. Further analysis has also revealed that the compound consists of 18 g of carbon, 3 g of hydrogen, and 8 g of oxygen. Now, help the CSI team nab the killer. Answer the following questions to find the identity of the unknown substance.
What is the percent composition of all the components in the liquid?

What is the empirical formula of the compound?

What is the molecular formula of the unknown liquid?

By using infrared spectroscopy and reagent tests, this compound has been identified as a ketone. Go online and figure out the name of this compound. Research its characteristics and common uses. Can you identify the killer from this information? How?

Answer 1

Data:

1) molar mass: 58.0714 g.

2) mass analysis

C: 18 g
H: 3 g
O: 8 g.

Solution

What is the percent composition of all the components in the liquid?

mass of C + mass of H + mass of O = 18g + 3g + 8g = 29 g

Percent composition:

C: (18g / 29g) * 100 = 62%

H: (3g / 29g) * 100 = 10%

O: (8g / 29g) * 100 = 28%
                               --------------
           Total               100%

What is the empirical formula of the compound?

Convert masses to number of moles by dividing each mass by the atomic mass of the correspondant element:

C: 18 g/ 12.0 g/mol = 1.5 mol

H: 3 g / 1.0 g/mol = 3 mol

O: 8 g / 16 g/mol = 0.5 mol

Divide each number of moles by the smaller, i.e. 0.5 mol

=> C: 1.5 mol / 0.5 mol = 3 mol
=> H: 3 mol / 0.5 mol = 6 mol
=> O: 0.5 mol / o.5 mol = 1 mol

=> Empirical formula: C3 H6 O

What is the molecular formula of the unknown liquid?

First,calculate the molar mass of the empirical formula:

C3 H6 O => 3 * 12 g/mol + 6*1 g/mol + 16 g/mol = 58 g/ mol

Secont, given that the molar mass is the same that the empirical mass, the molecular formula is the same empirical formula.

=> Molecular formula = C3 H6 O.

This compound has been identified as a ketone.

Go online and figure out the name of this compound.

It is easy to find that this compound is propanone or acetone (both names are valid).

Now you can go online and find its  characteristics and common uses.

Can you identify the killer from this information? How?

Likely they think you can presume that the killer is the actress, because women use acetone regularlty to remove the nail polish.