Calculating the number of carbon atoms depends on what information you have available. Here are several methods, each suited to different scenarios:
Determining the Mass of a Single Carbon Atom
The Core Principle
The fundamental way to calculate the mass of a single carbon atom relies on the known molar mass of carbon and Avogadro's number.
Calculation Steps
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Molar Mass: The molar mass of carbon is approximately 12.0 grams per mole (or 0.012 kg per mole).
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Avogadro's Number: Avogadro's number is approximately 6.022 × 10²³ atoms/mole, representing the number of particles in one mole.
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Divide: To get the mass of a single carbon atom, divide the molar mass by Avogadro’s number:
- Mass of a carbon atom = (12.0 g/mol) / (6.022 × 10²³ atoms/mol) = 1.99 x 10⁻²³ g/atom
- Converting to kilograms : (0.012 kg/mol) / (6.022 × 10²³ atoms/mol) = 1.99 x 10⁻²⁶ kg/atom
As referenced, Doing so yields 1.99 ´ 10–26 kg as the mass of a carbon atom.
This yields 1.99 × 10⁻²⁶ kg, or 1.99 x 10⁻²³ g, as the mass of a single carbon atom.
Calculating the Number of Carbon Atoms in a Given Mass
The Method
When you know the total mass of carbon, you can calculate the number of carbon atoms.
Steps
- Convert Mass to Moles: Divide the total mass of carbon (in grams) by the molar mass of carbon (12.0 g/mol) to get the number of moles.
- Convert Moles to Atoms: Multiply the number of moles by Avogadro's number (6.022 × 10²³ atoms/mol) to get the number of atoms.
Example
Let's say you have 24 grams of carbon:
- Moles: 24 g / 12.0 g/mol = 2 moles of carbon
- Atoms: 2 moles × 6.022 × 10²³ atoms/mol = 1.2044 × 10²⁴ carbon atoms
Carbon Atoms in Molecules
Molecular Formula
If you have a molecule with a known formula, counting carbon atoms is simple.
Example
- In methane (CH₄), there is 1 carbon atom per molecule.
- In ethane (C₂H₆), there are 2 carbon atoms per molecule.
- In glucose (C₆H₁₂O₆), there are 6 carbon atoms per molecule.
If you know the number of moles of the molecule, you can calculate the total number of carbon atoms:
- Total atoms: (Number of molecules) * (Number of carbon atoms per molecule)
Summary Table
| Calculation | Method | Units |
|---|---|---|
| Mass of a single carbon atom | Molar mass of carbon / Avogadro’s Number (12.0 g/mol / 6.022 x 10^23 atoms/mol or 0.012 kg/mol / 6.022 x 10^23 atoms/mol) | g/atom or kg/atom |
| Number of carbon atoms in a known mass | Mass of carbon / Molar mass of Carbon (12.0 g/mol) to get moles, then multiply by Avogadro's number | atoms |
| Number of carbon atoms in a molecule | Molecular formula (count the carbon atoms within a molecule), or number of molecules multiplied by the number of carbon atoms in the molecule | atoms |
