Question

Question: Certain kinds of zeolite have the general formula ${\mathrm{M}}_2\mathrm{O}.{\mathrm{Al}}_2{\mathrm{O}}_3.{\mathrm{ySiO}}_2.{\mathrm{wH}}_2\mathrm{O}$, where M is an alkali metal such as sodium or potassium, yis 2 or more, and wis any integer. Compute the mass percentage of aluminum in a zeolite that has$\mathrm{M}=\mathrm{K},\mathrm{y}=4,\mathrm{and}\mathrm{w}=6$.

Short answer

The mass percentage of aluminum in a zeolite is 10.50%

Step-by-step solution

Step 1:

Zeolites are the compound having hydrated form of aluminosilicate.

The formula of mass % is,

$\mathrm{Mass}\%=\frac{\mathrm{Massofgivensubstance}}{\mathrm{TotalMass}}\times 100$

Step 2:

According to the question the formula of the Zeolite is,

${\mathrm{K}}_2\mathrm{O}.{\mathrm{Al}}_2{\mathrm{O}}_3.4{\mathrm{SiO}}_2.6{\mathrm{H}}_2\mathrm{O}$

Molar mass of$\mathrm{Al}\mathrm{is}27\mathrm{g}/\mathrm{mol}$

The molar mass of ${\mathrm{K}}_2\mathrm{O}$is$2\times 39+16=64\mathrm{g}/\mathrm{mol}$

The molar mass of ${\mathrm{Al}}_2{\mathrm{O}}_3$is$2\times 27+3\times 16=102\mathrm{g}/\mathrm{mol}$

The molar mass of $4{\mathrm{SiO}}_2$is$\left(28+2\times 16\right)4=240\mathrm{g}/\mathrm{mol}$

The molar mass of $6{\mathrm{H}}_2\mathrm{O}$is$\left(2\times 1+16\right)6=108\mathrm{g}/\mathrm{mol}$

So the total mass of zeolite is,$64+102+240+108=514\mathrm{g}/\mathrm{mol}$

$$\begin{gathered} \mathrm{Mass}\%=\frac{\mathrm{Massofgivensubstance}}{\mathrm{TotalMass}}\times 100 \\ \mathrm{Mass}\%\mathrm{of}\mathrm{Al}=\frac{54}{514}\times 100 \\ =10.50\% \end{gathered}$$