Question

Find the percentage by mass of silicon in a sample of silicon dioxide?
A.21%
B.33%
C.47%
D.54%
E.78%

Answer 1

Hint: Silicon dioxide has the chemical formula $\text{Si}{\text{O}}_{\text{2}}$ which means it is made up of one silicon atom and two oxygen atoms.
The percentage by weight or by mass of an element in a compound can be calculated if the relative masses of the constituent elements of the compound are known.

Complete step by step answer:
We are given a sample of silicon dioxide and we need to find out the percentage by mass of silicon in silicon dioxide.
To determine the percent by mass of silicon in silicon dioxide, first we need to know the atomic masses of the constituent elements silicon and oxygen.
Step 1: Find the atomic masses of silicon and oxygen.
Silicon has the atomic symbol Si and oxygen has the atomic symbol O. From the periodic table of the elements, we can see that the element silicon occurs near the top of the table on the right half in row 3. Oxygen occurs in row 2 above silicon. In other words, silicon appears in group 14 and oxygen appears in group 16.
Thus, from the periodic table, we can see that the atomic mass of silicon is $$28.1$$ g/ mol and the atomic mass of oxygen is 16 g/ mol.
Step 2: Determine the molecular mass of silicon dioxide.
The molecular mass of a substance can be obtained by adding the atomic masses of all the atoms present in a molecule of the substance.
So, the molecular mass of silicon dioxide will be obtained by adding the atomic masses of one silicon and two oxygen atoms.
So, the molecular mass of silicon dioxide
$$\begin{gathered} =28.1\times 1+16\times 2 \\ =28.1+32 \\ =60.1\text{g/mol} \end{gathered}$$
Step 3: Calculate the weight percentage of silicon in silicon dioxide:
Fraction of silicon in silicon dioxide is equal to the atomic mass of silicon divided by the molecular mass of silicon dioxide. Thus, weight fraction of silicon:
$$\begin{gathered} {\displaystyle \frac{28.1}{60.1}} \\ =0.47 \end{gathered}$$
Then, multiply this by 100 to convert it into weight percent.
So, the percent by mass of silicon in silicon dioxide is
$$\begin{gathered} =0.47\times 100 \\ =47\mathrm{\%} \end{gathered}$$

Thus, option C is correct.

Note:
Majority of the earth’s crust is composed of silicate minerals, which are compounds of silicon and oxygen. Silicates are mainly used in Portland cement and when combined with silica sand and gravel, they are used in making concrete.
Silicate minerals are also used in making ceramics like porcelain which contains the silicate mineral kaolinite.