Question

For $XXg$ of sulphur has as many atoms as in $33g$ of carbon. The value of $XX$ is:
$\left( A \right)$ $4$
 $\left( B \right)$ $8$
$\left( C \right)$ $16$
$\left( D \right)$ 32

Answer 1

Hint:The given question can be solved by using Avogadro's number which states that in an element one mole of substance contains $6.022 \times {10^{23}}$ unit of substance such as atoms, molecules or ions. The number $6.022 \times {10^{23}}$ is known as Avogadro’s number.

Complete step by step answer:
In the question it is given that $XXg$ of sulphur $\left( S \right)$ which has same number of atom as that in $33g$ of carbon $\left( C \right)$
Therefore, $Xg$ of sulphur $\left( S \right)$ will have the same atom as that in $3g$ of carbon.
Now, Atomic mass of carbon$ = 12g/mol$ .
I.e mass of ${N_A}$ atom of carbon$ = 12g$
Therefore number of atom in $12g$ of carbon$ = {N_A}$
$ \Rightarrow $ Number of atom in $1g$ of carbon$ = \dfrac{{{N_A}}}{{12}}$
And, number of atom in $3g$ of carbon $ = \dfrac{{{N_A}}}{{12}} \times 3 = \dfrac{{{N_A}}}{4}$
Now, atomic mass of sulphur $ = 32g/mol$
I.e mass of ${N_A}$ atom of sulphur $ = 32g$
Therefore, number of atom in $32g$ of sulphur $ = {N_A}$
$ \Rightarrow $ Number of atom in \[1g\] of sulphur $ = \dfrac{{{N_A}}}{{32}}$
And, number of atom in $XXg$ of sulphur $ = \dfrac{{{N_A}}}{{32}} \times XX$
As per the question it is given that $XXg$ sulphur has as many atoms as $33g$ of carbon
So, $\dfrac{{{N_A}}}{{32}} \times XX = \dfrac{{{N_A}}}{4}$
$ \Rightarrow $ $XX = 8g$
Hence, we get the value of $XX$ is $8g$ , so the correct answer is $B.$

ADDITIONAL INFORMATION:
Atomic mass is a weighted average of all of the isotopes of that element, in which mass of each isotope is multiplied by the abundance of that particular isotope. It is also referred to as atomic weight, but the term ‘mass’ is more accurate.
Avogadro number: One mole of substance is equal to $6.022 \times {10^{23}}$ unit of that substance such as atoms, molecules, or ions. The number $6.022 \times {10^{23}}$is known as Avogadro’s number.

Note:
It is to be noted that the value of mole is equal to the number of atoms in exactly $12g$ of pure carbon-$12$ . The number of particles in one mole is called Avogadro’s number, the mass of one mol of atom of an element.