Calculate The Number of Atoms in 30.0 G of Zn

Calculating the number of atoms in a given mass of zinc (Zn) involves using Avogadro's number and the molar mass of zinc. This calculation is fundamental in chemistry for understanding the amount of substance in a sample.

How to Calculate the Number of Atoms

To determine the number of atoms in a sample of zinc, you need to know the mass of the sample and the molar mass of zinc. The steps are as follows:

Determine the molar mass of zinc (Zn).
Convert the given mass of zinc from grams to moles using the molar mass.
Multiply the number of moles by Avogadro's number (6.022 × 10²³ atoms/mol) to find the number of atoms.

This process allows you to relate the macroscopic mass of a substance to the microscopic number of atoms.

The Formula

The number of atoms (N) in a given mass (m) of zinc can be calculated using the following formula:

N = (m / M) × N_A Where: N = Number of atoms m = Mass of zinc (in grams) M = Molar mass of zinc (65.38 g/mol) N_A = Avogadro's number (6.022 × 10²³ atoms/mol)

This formula converts the mass of zinc to moles and then scales it by Avogadro's number to get the number of atoms.

Worked Example

Let's calculate the number of atoms in 30.0 grams of zinc:

Given mass (m) = 30.0 g
Molar mass of Zn (M) = 65.38 g/mol
Avogadro's number (N_A) = 6.022 × 10²³ atoms/mol
Number of moles = m / M = 30.0 g / 65.38 g/mol ≈ 0.459 mol
Number of atoms = (0.459 mol) × (6.022 × 10²³ atoms/mol) ≈ 2.76 × 10²³ atoms

The calculation shows that there are approximately 2.76 × 10²³ atoms of zinc in 30.0 grams.

Frequently Asked Questions

What is Avogadro's number?: Avogadro's number is a fundamental constant in chemistry that defines the number of constituent particles (atoms or molecules) in one mole of a substance. It is approximately 6.022 × 10²³ particles per mole.
Why is the molar mass of zinc important?: The molar mass of zinc is crucial because it allows chemists to convert between grams of a substance and moles, which is necessary for calculating the number of atoms or molecules.
Can this calculation be used for other elements?: Yes, the same method can be applied to any element by using the appropriate molar mass. The formula remains the same, only the molar mass value changes.
What if the mass of zinc is very small?: For very small masses, the number of atoms will be proportionally smaller. The calculation still follows the same steps, but the result will be a much smaller number of atoms.