Question

One mole of ${P_4}$ molecule contains:
A) $1$ molecule of $P$
B) $4$ molecules of $P$
C) $\dfrac{1}{4} \times 6.023 \times {10^{23}}$ atoms of $P$
D) $24.088 \times {10^{23}}$ atoms of $P$

Answer 1

According to Avogadro’s law, $1$ mole of ${P_4}$ has $6.023 \times {10^{23}}$ number of atoms. Also, $1$ molecules of ${P_4}$ have $4$ atoms of $P$.

Complete answer:
The Avogadro's law states that under the same conditions of temperature and pressure (or, if remains constant), equal volumes of different gases contain an equal number of molecules. This relation is produced from the kinetic theory of gases under the assumption of the conditions of an ideal gas.
According to the law, one mole of a substance, or element is equal to $6.023 \times {10^{23}}$ number of units of that substance, such as atoms, molecules, or ions. This particular number $6.023 \times {10^{23}}$is known as Avogadro's number or Avogadro's constant.
So, According to the question, $1$ molecule of ${P_4}$ has $4$ atoms of $P$.
Now, according to Avogadro’s law, $1$ mole of ${P_4}$ has $6.023 \times {10^{23}}$ number of atoms.
Therefore, $1$ mole of ${P_4}$ has $\left( {6.023 \times {{10}^{23}} \times 4} \right) = 24.088 \times {10^{23}}$ number of atoms of $P$ molecule.
Hence the correct answer is option D.

Additional information:
Avogadro’s constant is the proportionality factor. It links up two data- the number of constituent particles in a substance and the amount of substance in that substance. This is a dimensionless number, which is contained in one mole. To be precise, the number is actually $6.02214076 \times {10^{23}}$. The unit of this number varies differently. It may be electrons, ions, atoms, or molecules. The unit totally depends on the nature of the substance and also on the character of the reaction (if there are any).

Note:
Always remember, the mole is used as the unit for the number of atoms or molecules which are contained in an element or substance. For example, one mole is always equal to $6.023 \times {10^{23}}$ number of atoms (Avogadro's number). Also, the different elements have different molar masses, which depends on the weight of $6.023 \times {10^{23}}$ number of atoms (for one mole).