Chapter 17, Problem 6PEB

Mica is a sheet silicate while quartz is a network silicate. On the basis of its silicate structure, which mineral has a higher percentage composition of silicon? (Silicon to oxygen ratio is 2:5 for a sheet and 1:2 for a network.)

To determine

The mineral that contains higher percentage silicon from mica and quartz.

Answer to Problem 6PEB

Solution:

Quartz

Explanation of Solution

Given data:

Silicon to oxygen ratio is 2:5 for a sheet and 1:2 for a network.

Formula used:

Write the mass percent of an element in a compound can be found from:

$\frac{\left(\begin{array}{l}\text{atomic weight of}\\ \text{ element}\end{array}\right)\left(\begin{array}{l}\text{number of atoms }\\ \text{of elements}\end{array}\right)}{\text{formula}\text{weight of compound}}\times 100\%\text{of compound}=\%\text{ of element}$

Explanation:

For mica:

The formula for a single tetrahedra based on ratio: ${\text{Si}}_2{\text{O}}_5$.

The formula weight of a single tetrahedra:

$\begin{array}{llll}Atoms\hfill & Atomicweight\hfill & \hfill & Total\hfill \\ 2\text{ of Si}\hfill & 2\times 28.09\text{ u}\hfill & =\hfill & 56.18\text{ u}\hfill \\ 5\text{ of O}\hfill & 5\times 16\text{ u}\hfill & =\hfill & 80.00\text{ u}\hfill \\ \hfill & \text{Formula weight}\hfill & =\hfill & 136.18\text{ u}\hfill \end{array}$

Recall the mass percent of an element in a compound:

$\frac{\left(\begin{array}{l}\text{atomic weight of}\\ \text{ Si}\end{array}\right)\left(\begin{array}{l}\text{number of atoms }\\ \text{of Si}\end{array}\right)}{\text{formula}{\text{weight of Si}}_2{\text{O}}_5}\times 100\%{\text{of Si}}_2{\text{O}}_5=\%\text{ of Si}$

Substitute $\left(28.09\text{ u Si}\right)$ for atomic weight of element, $\left(2\right)$ for number of atoms and $136.18{\text{ u Si}}_2{\text{O}}_5$ for formula weight of compound.

$\begin{array}{c}\frac{\left(28.09\text{ u Si}\right)\left(2\right)}{136.18{\text{ u Si}}_2{\text{O}}_5}\times 100\%{\text{ Si}}_2{\text{O}}_5=\%\text{ of Si}\\ \%\text{ of Si}=\frac{\left(28.09\text{ Si}\right)\left(2\right)}{136.18}\times 100\%\\ =41.25\text{\% Si}\end{array}$

For Quartz:

The formula for a double based on ratio: ${\text{Si}}_2{\text{O}}_5$.

The formula weight of a single tetrahedra:

$\begin{array}{llll}Atoms\hfill & Atomicweight\hfill & \hfill & Total\hfill \\ 1\text{ of Si}\hfill & 1\times 28.09\text{ u}\hfill & =\hfill & 28.09\text{ u}\hfill \\ 2\text{ of O}\hfill & 2\times 16\text{ u}\hfill & =\hfill & 32.00\text{ u}\hfill \\ \hfill & \text{Formula weight}\hfill & =\hfill & 60.09\text{ u}\hfill \end{array}$

Recall the mass percent of an element in a compound and it can be found from:

$\frac{\left(\begin{array}{l}\text{atomic weight of}\\ \text{ Si}\end{array}\right)\left(\begin{array}{l}\text{number of atoms }\\ \text{of Si}\end{array}\right)}{\text{formula}{\text{weight of Si}}_2{\text{O}}_5}\times 100\%{\text{of Si}}_2{\text{O}}_5=\%\text{ of Si}$

Substitute $\left(28.09\text{ u Si}\right)$ for atomic weight of element, $\left(1\right)$ for number of atoms and $69.09{\text{ u Si}}_2{\text{O}}_5$ for formula weight of compound.

$\begin{array}{c}\frac{\left(28.09\text{ u Si}\right)\left(1\right)}{69.09{\text{ u Si}}_2{\text{O}}_5}\times 100\%{\text{ Si}}_2{\text{O}}_5=\%\text{ of Si}\\ \%\text{ of Si}=\frac{\left(28.09\text{ si}\right)\left(1\right)}{60.09}\times 100\%\\ =46.74\text{\% Si}\end{array}$

Conclusion:

Quartz has the higher percent of silicon.