How to Calculate the Number of Carbon Atoms in Acetone?

Understanding the Problem

Acetone (CH3COCH3) is a common organic compound used as a solvent. To calculate the number of carbon atoms in 15.6 kg of acetone, we need to use the given information about the density of acetone and its chemical formula.

Given Data

Mass of acetone = 15.6 kg
Density of acetone = 1.30 g/ml
Chemical formula of acetone = CH3COCH3

Conversion of Units

Since the density is given in grams per milliliter, we need to convert the mass of acetone from kilograms to grams.

1 kg = 1000 g

Therefore, 15.6 kg = 15,600 g

Calculating the Molar Mass of Acetone

The molar mass of acetone (CH3COCH3) can be calculated by adding the atomic masses of carbon, hydrogen, and oxygen present in the chemical formula.

Carbon (C) atomic mass = 12.01 g/mol
Hydrogen (H) atomic mass = 1.01 g/mol
Oxygen (O) atomic mass = 16.00 g/mol

Molar mass of acetone = (3 x 12.01) + (6 x 1.01) + (1 x 16.00) = 58.08 g/mol

Calculating the Number of Moles

Number of moles of acetone = Mass / Molar Mass

Number of moles of acetone = 15,600 g / 58.08 g/mol = 268.91 mol

Finding the Number of Carbon Atoms

Since there are 2 carbon atoms in a molecule of acetone, we can calculate the number of carbon atoms as follows:

Number of carbon atoms = 2 x Number of moles

Number of carbon atoms = 2 x 268.91 = 537.82

Final Answer

There are approximately 537.82 carbon atoms in 15.6 kg of acetone.