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

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:
$n = \dfrac{w}{{{M_w}}}$ ….(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:
$n = \dfrac{2}{{16}}moles$
The number of moles of a substance in terms of number of atoms present in it can also be represented by the following relation:
$n = \dfrac{N}{{{N_A}}}$….(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:
$\Rightarrow \dfrac{2}{{16}} = \dfrac{N}{{6.022 \times {{10}^{23}}}}$
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:
$\Rightarrow \dfrac{4}{{32}} = \dfrac{{{N_S}}}{{6.022 \times {{10}^{23}}}}$
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:
$n = \dfrac{{{w_{(given)}}}}{{{M_w}}} = \dfrac{N}{{{N_A}}} = \dfrac{{{V_{(given)}}}}{{22.4(l)}}$
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