Calculate The Number of Atoms in 54.0 G of Aluminum
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Reviewed by Calculator Editorial Team
Calculating the number of atoms in a given mass of a substance is a fundamental chemistry calculation. This guide explains how to determine the number of atoms in 54.0 grams of aluminum using Avogadro's number and the molar mass of aluminum.
How to Calculate the Number of Atoms
To find the number of atoms in a sample of aluminum, you'll need to know the mass of the sample and the molar mass of aluminum. The calculation involves these steps:
- Determine the molar mass of aluminum (26.98 g/mol)
- Calculate the number of moles of aluminum in the sample
- Multiply by Avogadro's number (6.022 × 10²³ atoms/mol) to get the number of atoms
The result will give you the number of aluminum atoms in the specified mass.
The Formula
Number of Atoms Formula
Number of atoms = (Mass of sample / Molar mass of element) × Avogadro's number
Where:
- Mass of sample = mass of aluminum in grams
- Molar mass of element = molar mass of aluminum (26.98 g/mol)
- Avogadro's number = 6.022 × 10²³ atoms/mol
This formula converts the mass of aluminum to moles, then scales up to the number of individual atoms using Avogadro's number.
Worked Example
Let's calculate the number of atoms in 54.0 g of aluminum using the formula:
- Mass of aluminum = 54.0 g
- Molar mass of aluminum = 26.98 g/mol
- Avogadro's number = 6.022 × 10²³ atoms/mol
Calculation:
Calculation Steps
Number of moles = Mass / Molar mass = 54.0 g / 26.98 g/mol ≈ 2.000 moles
Number of atoms = Number of moles × Avogadro's number = 2.000 × 6.022 × 10²³ ≈ 1.205 × 10²⁴ atoms
Therefore, there are approximately 1.205 × 10²⁴ atoms in 54.0 g of aluminum.
FAQ
- What is Avogadro's number?
- Avogadro's number (6.022 × 10²³) is the number of constituent particles (atoms or molecules) that are contained in one mole of a substance.
- Why is the molar mass of aluminum 26.98 g/mol?
- The molar mass of aluminum is 26.98 g/mol because it's the average mass of one mole of aluminum atoms, calculated from the atomic masses of its isotopes.
- Can I use this calculation for other elements?
- Yes, this same method can be used for any element by substituting the appropriate molar mass.
- What if I have a different mass of aluminum?
- Just plug your specific mass into the formula to get the number of atoms for your sample.