Question

Number of grams –atoms in $8$ gram of He are:
A. $2$
B. $1.204 \times {10^{24}}$
C. $3.10 \times {10^{23}}$
D. None of these

Answer 1

Hint:We will use the Avogadro number to determine the number of atoms in the given gram. For this first, we have to calculate the moles of He in the given gram. For this, we will use the mole formula. Then by using the Avogadro number we will determine the numbers of atoms.


Complete solution:
According to the Avogadro, one mole of any substance has $\,6.02 \times {10^{23}}$ atoms, ions or molecules. This number $\,6.02 \times {10^{23}}$ is known as the Avogadro number.
The mole formula is as follows:
${\text{mole}}\,\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,\,{\text{mass}}}}$
The molar mass of the He is $4.0$g/mol.
On substituting $8$ gram for the mass of He and $4.0$g/mol for molar mass of He,
${\text{mole}}\,\,{\text{ = }}\,\dfrac{{{\text{8}}\,{\text{g}}}}{{{\text{4}}\,{\text{g/mol}}}}$
${\text{mole}}\,\,{\text{ = }}\,{\text{2}}\,{\text{mol}}$
So, the mole of He in eight gram is ${\text{2}}$.
According to the Avogadro number,
Helium is a monatomic, so, the number of atoms in the He element is one.
One mole =$\,6.02 \times {10^{23}}$ atoms
Two moles = $\,1.204 \times {10^{24}}$atoms.
So, two moles or we can say eight gram of He contains $1.204 \times {10^{24}}$atoms.
So, the number of grams –atoms in $8$ gram of He are$1.204 \times {10^{24}}$.

Therefore, option (B) $1.204 \times {10^{24}}$, is correct.


Note:The number of atoms present in $12\,{\text{g}}$ of carbon-12 is known as one mole. The total number of atoms is the sum of all the atoms of a compound. Helium is monoatomic. If the given element is diatomic such as oxygen then we have to multiply the number of atoms with two also because one mole of an element contains two moles. In case of an ionic compound, we determine the total number of ions by multiplying the total number of moles with the Avogadro number.