Question

Explain how to calculate the number of atoms of a certain element in a given mass of a compound.

Answer 1

The number of atoms:

• To calculate the number of atoms first step is to calculate the number of moles.
• If the mass of an element/compound is given then divide the given mass by the molar mass of the element/compound to find the number of moles.
• In 1 mole of a substance, the number of atoms is ${\mathrm{N}}_{\mathrm{A}}$or $6.023\times {10}^{23}$ atoms.
• Multiply the given moles with ${\mathrm{N}}_{\mathrm{A}}$ to find the total number of atoms.

Example 1: To calculate the number of atoms in 46g of $\mathrm{Na}$

Step-1: Calculate the number of moles

• Number of moles = $\frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molar}\mathrm{mass}}=\frac{46}{23}=2\mathrm{mol}$

Step 2: Calculate the number of atoms

• The number of atoms= number of moles$\times {\mathrm{N}}_{\mathrm{A}}$=$2\times 6.023\times {10}^{23}=12.046\times {10}^{23}=1.2046\times {10}^{23}$atoms.

Example 2: To calculate the number of atoms of $\mathrm{C}$ in $22\mathrm{g}\mathrm{of}{\mathrm{CO}}_2$

Step-1: Calculate the number of moles

• Number of moles = $\frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molar}\mathrm{mass}}=\frac{22}{44}=0.5\mathrm{mol}$

Step 2: Calculate the number of atoms

• The number of atoms= number of moles$\times {\mathrm{N}}_{\mathrm{A}}$
• Since ${\mathrm{CO}}_2$ is triatomic. i.e $1$ molecule of ${\mathrm{CO}}_2$ contain $1$ atom of $\mathrm{C}$ and $2$ atom of $\mathrm{O}$
• The total number of atoms =$0.5\times 3\times 6.023\times {10}^{23}=9.0345\times {10}^{23}$ atoms.
• The number of atoms of $\mathrm{C}=0.5\times 1\times 6.023\times {10}^{23}=3.0115\times {10}^{23}$ atoms.