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Question: The atomic weight of silicon is 28.086 and that of oxygen is 15.9994 (on the \[{{\text{C}}^{12}}\] s...

The atomic weight of silicon is 28.086 and that of oxygen is 15.9994 (on the C12{{\text{C}}^{12}} scale). Calculate the mass in grams of a single molecule of SiO2{\text{Si}}{{\text{O}}_{\text{2}}} .
A. 9.977 × 10−23gm{\text{9}}{\text{.977 }} \times {\text{ 1}}{{\text{0}}^{ - {\text{23}}}}{\text{gm}}
B. 9.8 × 10−22gm{\text{9}}{\text{.8 }} \times {\text{ 1}}{{\text{0}}^{ - {\text{22}}}}{\text{gm}}
C. 1 × 10−22gm{\text{1 }} \times {\text{ 1}}{{\text{0}}^{ - {\text{22}}}}{\text{gm}}
D. 6.6 × 10−23gm{\text{6}}{\text{.6 }} \times {\text{ 1}}{{\text{0}}^{ - {\text{23}}}}{\text{gm}}

Explanation

Solution

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 C12{{\text{C}}^{12}} scale). Calculate the molecular weight of silicon dioxide SiO2{\text{Si}}{{\text{O}}_{\text{2}}} .
Molecular weight of silicon dioxide =28.086+2(15.9994)=60.08 g\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 g60.08{\text{ g}}
One mole of silicon dioxide contains Avogadro’s number of molecules. The Avogadro’s number is 6.023×1023 molecules/mole6.023 \times {10^{23}}{\text{ molecules/mole}}
Thus, the weight of 6.023×10236.023 \times {10^{23}} molecules of silicon is 60.08 g60.08{\text{ g}}

Divide 60.08 g60.08{\text{ g}} with 6.023×10236.023 \times {10^{23}} to obtain the mass of single molecule of silicon dioxide
Mass of single molecule of silicon dioxide=60.08 g/mole6.023×1023 molecules/mole=9.977 × 10−23g\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 SiO2{\text{Si}}{{\text{O}}_{\text{2}}} is 9.977 × 10−23gm{\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
Mass of single molecule = MN{\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.