Question

Calculate the number of $\mathrm{P}$ atoms in one mole of ${\mathrm{P}}_4$?

Answer 1

Step 1: Understand Avogadro's law

According to Avogadro's law, similar volumes of various gases contain an equal number of molecules under the same circumstances of temperature and pressure (or, if remains constant).

This relationship is derived from the kinetic theory of gases under the assumption of ideal gas conditions.

One mole of a material or element is equal to $6.023\times {10}^{23}$ units of that substance, such as atoms, molecules, or ions, according to the law.

This value, $6.023\times {10}^{23}$ is known as Avogadro's number or Avogadro's constant.

Step 2: Find number of $\mathrm{P}$ atoms in one mole of ${\mathrm{P}}_4$

One mole of ${\mathrm{P}}_4$ $=6.023\times {10}^{23}$ molecules of ${\mathrm{P}}_4$.

One molecule of ${\mathrm{P}}_4$$=4\mathrm{atoms}\mathrm{of}\mathrm{P}$

Therefore, one mole of

${\mathrm{P}}_4$$$\begin{gathered} =4\mathrm{x}6.023\mathrm{x}{10}^{23}\mathrm{atoms}\mathrm{of}\mathrm{P} \\ =24.092\mathrm{x}{10}^{23}\mathrm{atoms}\mathrm{of}\mathrm{P} \end{gathered}$$

So, the number of $\mathrm{P}$ atoms in one mole of ${\mathrm{P}}_4$ is $24.092\mathrm{x}{10}^{23}$.