Question

What amount of Dioxygen (in grams) contains $1.8 \times {10^{22}}$ molecules?
A) 0.0960
B) 0.960
C) 9.60
D) 96.0

Answer 1

The given question will make the use of the Avogadro’s Number. The Avogadro’s number is the number of molecules or units present in one mole of a substance. The number is $6.022 \times {10^{23}}$ molecules/units.

Complete answer:
Avogadro’s number is defined as the number of molecules/atoms/units in one mole of a substance. This consideration of the value is same for both Heavier (Bromine, Chlorine) and Lighter gases (like Hydrogen, Helium). The number is $6.022 \times {10^{23}}$ . The molar mass of a substance is defined as the mass of one mole of the substance. The number of moles can be found out by using the molar mass of the substance (provided the mass of substance in grams is given). If the molar mass is known the number of moles can be found out by using the formula: $\dfrac{{Mass(g)}}{{Molar{\text{ Mass (}}g/mol)}}$
It was found that one mole of a substance contains $6.022 \times {10^{23}}$ atoms of the element. Using the molar mass we can find the number of moles of the substance, and then the number of atoms/molecules present in it. Take the example of Carbon (Molar Mass $= 12g/mol$ ). Hence we can say that $12g$ of carbon will be one mole and will contain $6.022 \times {10^{23}}$ carbon atoms.
Similarly, the molar mass of Dioxygen is $32g/mol$ , and one mole of Dioxygen will have $6.022 \times {10^{23}}$ molecules. Hence, number of moles of Dioxygen containing $1.8 \times {10^{22}}$ molecules will be:
$1mol = 6.022 \times {10^{23}}$molecules
$'x'moles = 1.8 \times {10^{22}}$molecules
$\therefore x = \dfrac{{1.8 \times {{10}^{22}}}}{{6.022 \times {{10}^{22}}}}mol = 0.03mol$ of Dioxygen.
To find the grams of Dioxygen, we’ll use the formula given above (Molar Mass is $32g/mol$ ).
$Mass = 0.03 \times 32 = 0.96g$ of Dioxygen.
Therefore, the correct answer is Option (B).

Note:
It is necessary to remember the Molar Masses of generally occurring elements. Given a compound being dioxygen, it contains two oxygen molecules. The molar mass of one oxygen molecule is $16g/mol$. Hence the mass of Dioxygen will be $2 \times 16 = 32g/mol$ .