Question

Volume of a mixture of $6.02 \times {10^{23}}$ oxygen atoms and $3.01 \times {10^{23}}$ hydrogen molecules at NTP is:
A. $28.0litre$
B. $33.6litre$
C. $11.2litre$
D. $22.4litre$

Answer 1

Hint:Avogadro is a proportionality factor which determines the number of constituents in one mole of substance. It states that in one mole of a substance there are $6.02 \times {10^{23}}$ numbers of constituents are present. That constituents are the number of ions, number of atoms. It is represented by ${N_A}$ . The avogadro constant has SI units as reciprocal of mole.

Complete step by step answer:
As according to the question,
Number of oxygen atoms = $6.02 \times {10^{23}}$
Number of hydrogen molecules = $3.01 \times {10^{23}}$
As there is one mole of oxygen atom that means it is $0.5mol$ of ${O_2}$
If we talk about number of moles of hydrogen molecules,
$1mol = 6.02 \times {10^{23}}atoms$
So, $3.01 \times {10^{23}}atoms = 0.5mol$
Let, ${n_1}$ = number of moles of oxygen molecules
And ${n_2}$ = number of moles of hydrogen molecules
${n_1} = 0.5$ and ${n_2} = 0.5$
Let $n$ be the total number of moles.
So, $n = {n_1} + {n_2}$
$\
   \Rightarrow n = 0.5 + 0.5 \\
   \Rightarrow n = 1 \\
\ $
As, the volume at NTP is given by:
Volume = number of moles multiply by $22.4litre$
So, volume at NTP of a mixture of $6.02 \times {10^{23}}$ oxygen atoms and $3.01 \times {10^{23}}$ hydrogen molecules will be:
Volume = $n \times 22.4litre$
$\
   \Rightarrow 1 \times 22.4litre \\
   \Rightarrow 22.4litre \\
\ $
So, the volume of a mixture of $6.02 \times {10^{23}}$ oxygen atoms and $3.01 \times {10^{23}}$ hydrogen molecules at NTP is $22.4litre$ .

Hence, option D is correct.
Note:
The Avogadro constant also relates the molar volume of a substance to the average volume nominally occupied by one of its particles, when both are expressed in the same units of volume. For example, since the molar volume of water in ordinary conditions is about $18ml/mol$ the volume occupied by one molecule of water is about $\dfrac{{18}}{{6.02 \times {{10}^{23}}}}ml$ , or about $30\mathop {{A^3}}\limits^o $ . For a crystalline substance, it similarly relates its molar volume (in $ml/mol$ ), the volume of the repeating unit cell of the crystals (in $ml$ ), and the number of molecules in that cell.