Problem 104 - Chemistry: An Atoms-Focused Approach

Question

The calcium silicate mineral grossular is also formed under pressure in a reaction between anorthite \(\left(\mathrm{CaAl}_{2} \mathrm{Si}_{2} \mathrm{O}_{8}\right)\) gehlenite \(\left(\mathrm{Ca}_{2} \mathrm{Al}_{2} \mathrm{SiO}_{7}\right),\) and wollastonite \(\left(\mathrm{CaSiO}_{3}\right)\) (EQUATION CANNOT COPY) a. Balance this chemical equation. b. Express the composition of gehlenite the way mineralogists often do: as the percentage of the metal and metalloid oxides in it- that is, $$96 \mathrm{CaO}, \% \mathrm{Al}_{2} \mathrm{O}_{3}$$ $$\text { and } \% \mathrm{SiO}_{2}$$

Step-by-Step Solution

Answer

Answer: The balanced chemical equation for the reaction is: $$\mathrm{CaAl}_{2}\mathrm{Si}_{2}\mathrm{O}_{8} + 2\mathrm{Ca}_{2}\mathrm{Al}_{2} \mathrm{SiO}_{7} \rightarrow 7 \mathrm{CaSiO}_{3}$$. The composition of gehlenite in terms of metal and metalloid oxides is 40.87% CaO, 37.23% Al2O3, and 21.90% SiO2.

Step 1: Write the Unbalanced Chemical Equation

Write the unbalanced equation using the given formulas for anorthite, gehlenite, and wollastonite: $$\mathrm{CaAl}_{2}\mathrm{Si}_{2}\mathrm{O}_{8} + \mathrm{Ca}_{2}\mathrm{Al}_{2} \mathrm{SiO}_{7} \rightarrow \mathrm{CaSiO}_{3}$$

Step 2: Balance the Chemical Equation

Balance the equation using the law of conservation of mass which states that the number of atoms should be equal on both sides of the equation: $$\mathrm{CaAl}_{2}\mathrm{Si}_{2}\mathrm{O}_{8} + 2\mathrm{Ca}_{2}\mathrm{Al}_{2} \mathrm{SiO}_{7} \rightarrow 7 \mathrm{CaSiO}_{3}$$ Now, the chemical equation is balanced.

Step 3: Calculate the Molar Mass of the Components

Determine the molar mass of each component of gehlenite: Using the periodic table, find the molar masses of each element and sum them according to their presence in the molecule formula: Ca = 40 Al = 27 Si = 28 O = 16 Molar mass of CaO: 40 + 16 = 56 g/mol Molar mass of Al2O3: 54 + (3 * 16) = 102 g/mol Molar mass of SiO2: 28 + 32 = 60 g/mol

Step 4: Calculate the Composition of Gehlenite

Determine the composition of gehlenite in terms of percentages. First, calculate the molar mass of gehlenite: $$\mathrm{Ca}_{2}\mathrm{Al}_{2} \mathrm{SiO}_{7} = 2 (56)+102+60=274$$ g/mol Now, divide the molar mass of each component by the total molar mass of gehlenite, and multiply by 100 to get the percentage of each component: $$ \% \mathrm{CaO} = \frac{2(56)}{274} \times 100 = 40.87 \% $$ $$ \% \mathrm{Al}_{2}\mathrm{O}_{3} = \frac{102}{274} \times 100 = 37.23 \% $$ $$ \% \mathrm{SiO}_{2} = \frac{60}{274} \times 100 = 21.90 \% $$

Key Concepts

Calcium Silicate Mineral

Calcium silicate minerals are important compounds found naturally in the Earth's crust.
They play a key role in reactant and product formation under specific conditions, like high pressure. One example is grossular, a type of garnet mineral.
These minerals can form through chemical reactions involving other silicate compounds, such as anorthite and gehlenite.Anorthite is comprised of calcium, aluminum, silicon, and oxygen with the formula \(\text{CaAl}_2\text{Si}_2\text{O}_8\).
Gehlenite contains \(\text{Ca}_2\text{Al}_2\text{SiO}_7\), combining calcium, aluminum, silicon, and oxygen in a distinct form.
Wollastonite, on the other hand, has the chemical formula \(\text{CaSiO}_3\).
All share the common peer element: calcium, varying in silicon, aluminum, and oxygen components.Understanding these bases helps in relating mineral properties to their formations and transformations in geological processes.
Their intricate compositions and interactions highlight the structural complexities and natural beauty of minerals.

Law of Conservation of Mass

The Law of Conservation of Mass is a fundamental principle of chemistry.
It states that matter cannot be created or destroyed in a chemical reaction.
Thus, the number of each type of atom must be the same on both sides of a chemical equation.When balancing a chemical equation, like the reaction between anorthite, gehlenite, and wollastonite, it's crucial to account correctly for each element's atoms.
For example:

• Anorthite starts with the formula \(\text{CaAl}_2\text{Si}_2\text{O}_8\).
• The gehlenite adds more elements with \(2\text{Ca}_2\text{Al}_2\text{SiO}_7\).
• Finally, it reacts to form \(7\text{CaSiO}_3\).

Balancing ensures the equation follows the conservation law, so that before and after the reaction, the total mass remains constant. This concept is essential not only in chemistry but also in understanding natural processes where different materials transform. It helps in identifying the correctness of reactions and predicting reaction outcomes.

Molar Mass Calculation

Calculating molar mass is a necessary step for determining the composition of various substances.
It is computed by summing the atomic masses of each element within a compound.
Molar mass, typically in units of grams per mole, assists in translating molecular formulas into measurable quantities.When seeking to determine the percentage composition of a compound like gehlenite \(\text{Ca}_2\text{Al}_2\text{SiO}_7\), we follow several steps:

• Calculate the molar mass of each component: \(\text{CaO}, \text{Al}_2\text{O}_3, \text{SiO}_2\).
• Use the periodic table to find individual atomic masses (e.g., Ca = 40, Al = 27).
• Then, find the total molar mass of the compound \(= 274 \, \text{g/mol}\).

To express a component's composition percentage, divide its molar mass by the total molar mass and multiply by 100.
This method reveals the proportions of minerals, providing insight into their chemical makeup and behaviors.
Understanding molar mass and percentage compositions enhances the study of mineralogy and chemistry, aiding in analyses and practical applications.