Chapter 12, Problem 12.96QP

(a)

Interpretation Introduction

To determine: The balanced chemical equation for a given reaction.

Interpretation: The balanced chemical equation for a given reaction is to be stated.

Concept introduction: The balanced chemical reactions consist of the same number of atoms or elements and equal charges on the both sides of reactants and products.

Answer to Problem 12.96QP

The balanced reaction is,

${\text{CaAl}}_2{\text{Si}}_2{\text{O}}_8+{\text{Ca}}_2{\text{Al}}_2{\text{SiO}}_7+3{\text{CaSiO}}_3\to 2{\text{Ca}}_3{\text{Al}}_2{\left({\text{SiO}}_4\right)}_3$.

Explanation of Solution

The given reaction is,

${\text{CaAl}}_2{\text{Si}}_2{\text{O}}_8+{\text{Ca}}_2{\text{Al}}_2{\text{SiO}}_7+{\text{CaSiO}}_3\to {\text{Ca}}_3{\text{Al}}_2{\left({\text{SiO}}_4\right)}_3$

The above equation of reaction is unbalanced. The balanced reaction consists of three moles of wollastonite on the reactant side and two moles of Grossular on the product side. The balanced reaction is given as,

${\text{CaAl}}_2{\text{Si}}_2{\text{O}}_8+{\text{Ca}}_2{\text{Al}}_2{\text{SiO}}_7+3{\text{CaSiO}}_3\to 2{\text{Ca}}_3{\text{Al}}_2{\left({\text{SiO}}_4\right)}_3$

(b)

Interpretation Introduction

To determine: The chemical composition gehlenite.

Interpretation: The chemical composition of gehlenite is to be calculated.

Concept introduction: The balanced chemical reactions consist of the same number of atoms or elements and equal charges on the both sides of reactants and products. The mass percentage of constituent compound is calculated by the formula,

$\text{Mass}\%\text{of}\text{constituent}=\frac{n\times M_{\text{m}}}{M_{\text{T}}}\times 100$

Answer to Problem 12.96QP

The composition of gehlenite consists of $\underset{\_}{40.9\%}\text{CaO}$, $\underset{\_}{21.9\%}{\text{SiO}}_2$ and $\underset{\_}{37.2\%}{\text{Al}}_2{\text{O}}_3$.

Explanation of Solution

The equation of decomposition reaction of gehlenite is,

${\text{Ca}}_2{\text{Al}}_2{\text{SiO}}_7\to 2\text{CaO}+{\text{SiO}}_2+{\text{Al}}_2{\text{O}}_3$.

The molar mass of the $\text{CaO}$ is $56.078\text{g}/\text{mol}$.

The molar mass of the ${\text{SiO}}_2$ is $60.08\text{g}/\text{mol}$.

The molar mass of the ${\text{Al}}_2{\text{O}}_3$ is $101.96\text{g}/\text{mol}$.

The total mass of the gehlenite is $274.20\text{g}/\text{mol}$.

The mass percentage of constituent compound is calculated by the formula,

$\text{Mass}\%\text{of}\text{constituent}=\frac{n\times M_{\text{m}}}{M_{\text{T}}}\times 100$ (1)

Where,

• $M_{\text{m}}$ is the molar mass of the constituent.
• $M_{\text{T}}$ is the molar mass of the compound.

Substitute the values of $M_{\text{m}}$ of $\text{CaO}$ and $M_{\text{T}}$ in equation (1).

$\begin{array}{c}\text{Mass}\%\text{of}\text{CaO}=\frac{2\times 56.078\text{g}/\text{mol}}{274.20\text{g}/\text{mol}}\times 100\\ =\underset{\_}{40.9\%}\end{array}$

Similarly,

Substitute the values of $M_{\text{m}}$ of ${\text{SiO}}_2$ and $M_{\text{T}}$ in equation (1).

$\begin{array}{c}\text{Mass}\%\text{of}{\text{SiO}}_2=\frac{1\times 60.08\text{g}/\text{mol}}{274.20\text{g}/\text{mol}}\times 100\\ =\underset{\_}{21.9\%}\end{array}$

Substitute the values of $M_{\text{m}}$ of ${\text{Al}}_2{\text{O}}_3$ and $M_{\text{T}}$ in equation (1).

$\begin{array}{c}\text{Mass}\%\text{of}{\text{Al}}_2{\text{O}}_3=\frac{1\times 101.96\text{g}/\text{mol}}{274.20\text{g}/\text{mol}}\times 100\\ =\underset{\_}{37.2\%}\end{array}$

Therefore, the composition of gehlenite consists of $\underset{\_}{40.9\%}\text{CaO}$, $\underset{\_}{21.9\%}{\text{SiO}}_2$ and $\underset{\_}{37.2\%}{\text{Al}}_2{\text{O}}_3$.

Conclusion

1. a. The balanced reaction is,

   ${\text{CaAl}}_2{\text{Si}}_2{\text{O}}_8+{\text{Ca}}_2{\text{Al}}_2{\text{SiO}}_7+3{\text{CaSiO}}_3\to 2{\text{Ca}}_3{\text{Al}}_2{\left({\text{SiO}}_4\right)}_3$.

2. b. The composition of gehlenite consists of $\underset{\_}{40.9\%}\text{CaO}$, $\underset{\_}{21.9\%}{\text{SiO}}_2$ and $\underset{\_}{37.2\%}{\text{Al}}_2{\text{O}}_3$.