Question

Given,$2g$ of oxygen contain number of atoms equal to that contained by:
A. $0.5g$ of hydrogen
B. $4g$ of sulfur
C. $7g$ of nitrogen
D. $2.3g$ of sodium

Answer 1

Hint:The mole (symbol: mol) is the unit of measurement for amount of substance in the International System of Units (SI). A mole of a substance or a mole of particles is defined as exactly the $6.022\times {10}^{23}$ particles, which may be atoms, molecules, ions, or electrons. In short, for particles, $1mol=6.022\times {10}^{23}$.

Complete step by step answer:
Oxygen is a p-block element which has an atomic number of 8 and atomic weight equal to 16. Mathematically, the atomic weight for oxygen atom can be written as:
$M_w=16$
The number of moles for a substance can be represented as:
$n={\displaystyle \frac{w}{M_w}}$ ….(i)
Where, $n=$ number of moles of the substance
$w=$ given weight of oxygen = $2g$
$M_w=$ atomic weight of oxygen
Substituting these values in the above equation, we have:
$n={\displaystyle \frac{2}{16}}moles$
The number of moles of a substance in terms of number of atoms present in it can also be represented by the following relation:
$n={\displaystyle \frac{N}{N_A}}$….(ii)
Where, $n=$ number of moles of the substance
$N=$ number of atoms of oxygen = $?$
$N_A=6.022\times {10}^{23}$ atoms = Avogadro number
Substituting these values in the above equation, we have:
$\Rightarrow {\displaystyle \frac{2}{16}}={\displaystyle \frac{N}{6.022\times {10}^{23}}}$
On solving, we have:
$\Rightarrow N=7.52\times {10}^{22}$ atoms
The given weight of sulfur in the question is = $4g$
The atomic weight of the sulfur atom = $32g$
Substituting these values for sulfur in equation (ii), we have:
 $\Rightarrow {\displaystyle \frac{4}{32}}={\displaystyle \frac{N_S}{6.022\times {10}^{23}}}$
On solving, we have:
$\Rightarrow N_S=7.52\times {10}^{22}$ atoms
Thus, we can say that the number of atoms in $2g$ of oxygen contains the number of atoms equal to that contained by $4g$ of sulfur.
The correct option is B.$4g$ of sulfur.

Note:
There are various methods in various conditions for writing the mathematical equation for the number of moles of a substance. They can be depicted as following:
$n={\displaystyle \frac{w_{(given)}}{M_w}}={\displaystyle \frac{N}{N_A}}={\displaystyle \frac{V_{(given)}}{22.4(l)}}$
Where, $w_{(given)}=$ given weight of the substance
$M_w=$ atomic or molecular weight of the substance
$N=$ number of particles of the substance
$N_A=6.022\times {10}^{23}$ atoms = Avogadro number
$$V_{(given)}=$$ given volume of the substance
$22.4l$ = volume of the substance at standard conditions of STP