How Do You Find the Number of Atoms in a Sample?

To find the number of atoms in a sample, multiply the number of moles of the substance by Avogadro's number.

Understanding Atoms and Moles

What is an Atom?

An atom is the smallest unit of an element that retains the properties of that element.

What is a Mole?

A mole is a unit used to measure the amount of a substance. One mole of any substance contains approximately 6.022 x 10²³ entities (atoms, molecules, ions, etc.). This number is known as Avogadro's number.

Calculating the Number of Atoms

To calculate the number of atoms in a sample, you can use the following formula:

the number of atoms = the number of moles × Avogadro's number

Example Calculation

Let's say you have 2 grams of Tin (Sn). To find the number of atoms in this sample:

1. Convert the mass to moles: First, determine the number of moles of Tin (Sn).
2. Apply Avogadro's Number: Multiply the number of moles by Avogadro's number to find the number of atoms.

Steps:

1. Calculate moles of Tin (Sn):

   • Given that 2g of Tin corresponds to 1.685 × 10^-2 moles.

2. Use Avogadro's Number:

   • Multiply the number of moles by Avogadro's number (6.022 × 10²³ atoms/mole).

   Substance	Mass (g)	Moles	Avogadro's Number	Number of Atoms
   Tin (Sn)	2	1.685 × 10-2	6.022 × 1023	1.015 × 1022

Calculation:

1 mole Sn = 1.685 × 10^-2 moles Sn × 6.022 × 10²³ atoms / 1 mole Sn = 1.015 × 10²² atoms

Therefore, there are 1.015 × 10²² atoms in 2g of Tin (Sn).

Practical Insights

• Precision in Measurement: Accurate measurement of mass and proper calculation of moles are crucial for determining the correct number of atoms.
• Understanding Units: Ensure you are using the correct units throughout the calculation. Moles and grams are different units, so it's important to convert between them accurately.

Summary

To find the number of atoms in a sample:

1. Determine the number of moles of the substance.
2. Multiply the number of moles by Avogadro's number (6.022 × 10²³).

This method provides a straightforward way to calculate the number of atoms in a given sample, bridging the microscopic world of atoms with the macroscopic world of measurable quantities.