Question

The atomic weight of silicon is 28.086 and that of oxygen is 15.9994 (on the \[{{\text{C}}^{12}}\] scale). Calculate the mass in grams of a single molecule of \[{\text{Si}}{{\text{O}}_{\text{2}}}\] .
A. \[{\text{9}}{\text{.977 }} \times {\text{ 1}}{{\text{0}}^{ - {\text{23}}}}{\text{gm}}\]
B. \[{\text{9}}{\text{.8 }} \times {\text{ 1}}{{\text{0}}^{ - {\text{22}}}}{\text{gm}}\]
C. \[{\text{1 }} \times {\text{ 1}}{{\text{0}}^{ - {\text{22}}}}{\text{gm}}\]
D. \[{\text{6}}{\text{.6 }} \times {\text{ 1}}{{\text{0}}^{ - {\text{23}}}}{\text{gm}}\]

Answer 1

Hint:To obtain the molecular weight, add the individual atomic weights. The molecular weight represents the weight of one mole of compound and contains Avogadro’s number of molecules.

Complete answer:
The atomic weight of silicon is 28.086 and that of oxygen is 15.9994 (on the \[{{\text{C}}^{12}}\] scale). Calculate the molecular weight of silicon dioxide \[{\text{Si}}{{\text{O}}_{\text{2}}}\] .
\[\text{Molecular weight of silicon dioxide } = 28.086 + 2\left( {15.9994} \right) = 60.08{\text{ g}}\]
The weight of one mole of silicon dioxide is \[60.08{\text{ g}}\]
One mole of silicon dioxide contains Avogadro’s number of molecules. The Avogadro’s number is \[6.023 \times {10^{23}}{\text{ molecules/mole}}\]
Thus, the weight of \[6.023 \times {10^{23}}\] molecules of silicon is \[60.08{\text{ g}}\]

Divide \[60.08{\text{ g}}\] with \[6.023 \times {10^{23}}\] to obtain the mass of single molecule of silicon dioxide
\[\text{Mass of single molecule of silicon dioxide} =\dfrac{{60.08{\text{ g/mole}}}}{{6.023 \times {{10}^{23}}{\text{ molecules/mole}}}} = {\text{9}}{\text{.977 }} \times {\text{ 1}}{{\text{0}}^{ - {\text{23}}}}{\text{g}}\]
The mass in grams of a single molecules of \[{\text{Si}}{{\text{O}}_{\text{2}}}\] is \[{\text{9}}{\text{.977 }} \times {\text{ 1}}{{\text{0}}^{ - {\text{23}}}}{\text{gm}}\].

Hence, the option A is the correct option.

Note:
In general, if N is the Avogadro’s number and M is the molecular weight of a compound, then you can use the following formula to calculate the mass of single molecule of that compound
\[{\text{Mass of single molecule = }}\dfrac{{\text{M}}}{{\text{N}}}\]
This formula is applicable to all the substances irrespective of the identity of the substance.