Question

a) Determine the number of sodium ions in the chemical formula of albite, ${\mathrm{Na}}_x{\mathrm{AlSi}}_3{\mathrm{O}}_g$. (b) Determine the number of hydroxide ions in the chemical formula of tremolite, ${\mathrm{Ca}}_2{\mathrm{Mg}}_5{\left({\mathrm{Si}}_4{\mathrm{O}}_{11}\right)}_2(\mathrm{OH}{)}_{\mathrm{x}}$ -

Short answer

(a) There is one sodium ion in the chemical formula of albite, ${\mathrm{Na}}_1{\mathrm{AlSi}}_3{\mathrm{O}}_8$. (b) There are two hydroxide ions in the chemical formula of tremolite, ${\mathrm{Ca}}_2{\mathrm{Mg}}_5{\left({\mathrm{Si}}_4{\mathrm{O}}_{11}\right)}_2(\mathrm{OH}{)}_2$.

Step-by-step solution

Write the charge of the ions

Write the charge of the albite ions: - Sodium ion (Na): $+1$ - Aluminum ion (Al): $+3$ - Silicon ion (Si): $+4$ - Oxygen ion (O): $-2$

Determine the charge of the compound

A stable compound has a total charge of zero. So, we can write the equation representing the total charge of the compound as: $$x(+1)+1(+3)+3(+4)+g(-2)=0$$

Solve for x and g

Solving the equation from Step 2: $$\begin{array}{rl}& x+3+12-2g=0\\ & x-2g=-15\end{array}$$ This equation has multiple solutions. However, only one solution provides integer values for x and g, which are x=1 and g=8.

Rewrite the chemical formula

Replacing x and g with their respective values, we have the chemical formula for albite as: $${\mathrm{Na}}_1{\mathrm{AlSi}}_3{\mathrm{O}}_8$$ Therefore, there is one sodium ion in the chemical formula of albite. #b) Determine the number of hydroxide ions in the chemical formula of tremolite.#

Write the charge of the ions

Write the charge of the tremolite ions: - Calcium ion (Ca): $+2$ - Magnesium ion (Mg): $+2$ - Silicon ion (Si): $+4$ - Oxygen ion (O): $-2$ - Hydroxide ion (OH): $-1$

Determine the charge of the compound

A stable compound has a total charge of zero. So, we can write the equation representing the total charge of the compound as: $$2(+2)+5(+2)+2\times (4\cdot (+4)+11\times (-2))+x(-1)=0$$

Solve for x

Solving the equation from Step 2: $$\begin{array}{rl}& 4+10+2(16-22)-x=0\\ & 14-12-x=0\\ & x=2\end{array}$$

Rewrite the chemical formula

Replacing x with its value, we have the chemical formula for tremolite as: $${\mathrm{Ca}}_2{\mathrm{Mg}}_5{\left({\mathrm{Si}}_4{\mathrm{O}}_{11}\right)}_2(\mathrm{OH}{)}_2$$ Therefore, there are two hydroxide ions in the chemical formula of tremolite.

Key concepts

Sodium Ions

Sodium ions are ubiquitous in chemistry and crucial in forming a myriad of compounds. They carry a positive charge, precisely a charge of +1. In the context of the given exercise, the sodium ion, denoted as Na⁺, contributes to the overall charge balance of the mineral albite. A fundamental principle when dealing with ionic compounds such as albite is that the total charge must be zero for the compound to be stable.

To determine the exact number of sodium ions in albite, one must understand the charges of all other components in the formula and balance them accordingly. The exercise provides a glimpse into this process, and as found through solving a simple algebraic equation, albite contains one sodium ion, helping balance the charges contributed by aluminum, silicon, and oxygen.

Hydroxide Ions

Hydroxide ions, with the chemical symbol OH^-, are negatively charged ions consisting of one oxygen atom bonded to one hydrogen atom. They play a vital role in the chemistry of bases and are often found in various minerals, including tremolite. The charge of a hydroxide ion is -1, which is crucial for maintaining the charge balance in ionic compounds.

In the tremolite formula provided in the exercise, determining the number of hydroxide ions is a matter of ensuring the overall neutrality of the compound. By applying charge balance principles, it's revealed that there are two hydroxide ions in the chemical composition of tremolite. The calculation involved brings to light the importance of hydroxide ions' charges in chemical equation solving.

Compound Charge Balance

The concept of compound charge balance is fundamental in chemistry and is especially relevant when working with ionic compounds. The core principle states that the total charge in a stable ionic compound must be zero. This means that the sum of positive charges from the cations must equal the sum of negative charges from the anions.

This balance can be visualized as a mathematical equation where the products of the number of ions and their respective charges are summed to equal zero. In the exercises provided, charge balance is used to determine the required number of sodium and hydroxide ions in the minerals albite and tremolite, respectively. Mastery of this concept not only aids in solving chemical formulas but also deepens the understanding of how ionic compounds form and remain stable.

Chemical Equation Solving

Solving chemical equations is an essential skill in chemistry that involves finding the proportions of reactants and products to satisfy the balanced equation principle. It echoes the law of conservation of mass, where the number of atoms for each element must be the same on both sides of the equation.

In the context of the exercises, the process of chemical equation solving is applied to determine the formula of ionic compounds. This involves setting up an equation based on the compound charge balance and solving for the unknowns, which in these cases were the number of sodium and hydroxide ions. Steps to find these values include writing the charge of each ion, establishing an equation that assumes total charge neutrality, and finally, solving for the unknowns, ensuring that whole numbers are used to represent the count of each ion within the compound's chemical formula.