Question

$76 grams$ of fluorine gas contains:
A. $4 gram$ atoms of fluorine atoms
B. $2 moles$ of fluorine molecules
C. $12 \times {10^{23}}$ fluorine molecules
D. All of the above

Answer 1

Hint: The number of moles of a substance is the ratio of given weight of the substance to that of the atomic/ molecular weight of that substance. In terms of particles, the number of moles of that substance is the ratio of the given number of particles to that of the Avogadro number of particles (atoms or ions or molecules).

Complete step by step answer:
Let us solve each sub-question one by one.
(i) One mole of any substance contains one gram atom of that substance. This means that the number of moles of fluorine gas is equal to the number of gram atoms of fluorine.
The mathematical representation of number of moles in terms of given weight of substance is given by:
$n = \dfrac{w}{{G.A.W}}$
Where, $w = $ Given weight of fluorine$ = 76g$
$G.A.W = $ gram atomic weight of fluorine$ = 19g$
$n = $ number of moles
Now, substituting the values in the above equation, we get the number of moles of fluorine atoms as:
$n = \dfrac{{76g}}{{19g}} = 4 moles$
Hence, the number of gram atoms = number of moles of fluorine = 4
(ii) As we know that the fluorine is a diatomic molecule. Hence, the relation between the number of moles of fluorine molecules and its given weight is:
$n = \dfrac{w}{{G.M.W}}$
Where, $w = $ Given weight of fluorine$ = 76g$
$G.M.W = $ gram molecular weight of fluorine$ = 38g$
$n = $ number of moles
Now, substituting the values in the above equation, we get the number of moles of fluorine molecules as:
$n = \dfrac{{76g}}{{38g}} = 2 moles$
Hence, the number of gram molecules = number of moles of fluorine = 2
(iii) The relation between the numbers of moles of fluorine molecule with the number of molecules is given by:
$n = \dfrac{N}{{{N_A}}}$
Where, $N = $ number of fluorine molecules
${N_A}$ = Avogadro number =$6 \times {10^{23}}$ molecules
$n = $ number of moles$ = 2$
Now, substituting the values in the above equation, we have:
$2 = \dfrac{N}{{{N_A}}} \Rightarrow N = 2 \times 6 \times {10^{23}} = 12 \times {10^{23}}molecules$ .

So, the correct answer is Option D .

Note:
The relation between the number of moles of a substance, its given weight, Its given volume in the solution and the number of particles that it is composed of is given by the following relation:
$n = \dfrac{w}{{{M_w}}} = \dfrac{N}{{{N_A}}} = \dfrac{V}{{22.4(l)}}$
Where, $w = $ given weight
${M_w} = $ gram atomic weight/ gram molecular weight
$N = $ Number of particles
${N_A} = $ Avogadro number
$V = $ Given volume of the substance