Problem 75 - Chemistry The Central Science

Question

(a) Determine the number of calcium ions in the chemical formula of the mineral hardystonite, \(\mathrm{Ca}_{x} \mathrm{Zn}\left(\mathrm{Si}_{2} \mathrm{O}_{7}\right) .(\mathbf{b})\) Determine the number of hydroxide ions in the chemical formula of the mineral pyrophylite, \(\mathrm{Al}_{2}\left(\mathrm{Si}_{2} \mathrm{O}_{5}\right)_{2}(\mathrm{OH})_{x}\)

Step-by-Step Solution

Answer

\(a)\) There are 2 calcium ions in the chemical formula of hardystonite: \(\mathrm{Ca}_{2} \mathrm{Zn}\left(\mathrm{Si}_{2}\mathrm{O}_{7}\right)\). \(b)\) There are 2 hydroxide ions in the chemical formula of pyrophylite: \(\mathrm{Al}_{2}\left(\mathrm{Si}_{2} \mathrm{O}_{5}\right)_{2}(\mathrm{OH})_{2}\).

Step 1: Determine the charges of ions in hardystonite

In the chemical formula of hardystonite, we have three types of ions: calcium ions \(\mathrm{Ca}^{2+}\), zinc ions \(\mathrm{Zn}^{2+}\), and the silicate anions \(\left(\mathrm{Si}_{2}\mathrm{O}_{7}\right)^{6-}\). The charges of calcium and zinc ions are +2, while the charge of the silicate anion is -6.

Step 2: Balance charges in hardystonite

In order to balance the charges in the chemical formula, we represent the total positive charge with x calcium ions and one zinc ion and balance it with one silicate anion. Therefore, we have the following equation: \(x\cdot 2 + 2 = 6\).

Step 3: Solve for x in hardystonite

Solve the equation from Step 2 for x: \(x\cdot 2 = 4\). Thus, \(x = 2\). So, there are two calcium ions in hardystonite's chemical formula: \(\mathrm{Ca}_{2} \mathrm{Zn}\left(\mathrm{Si}_{2}\mathrm{O}_{7}\right)\).

Step 4: Determine the charges of ions in pyrophylite

In the chemical formula of pyrophylite, we have three types of ions: aluminum ions \(\mathrm{Al}^{3+}\), silicate anions \(\left(\mathrm{Si}_{2}\mathrm{O}_{5}\right)^{4-}\), and hydroxide ions \(\mathrm{OH}^{-}\). The charges of aluminum ions are +3, the charge of the silicate anion is -4, and the charge of the hydroxide ion is -1.

Step 5: Balance charges in pyrophylite

In order to balance the charges in the chemical formula, we represent the total positive charge with two aluminum ions and balance it with the net negative charge contributed by two silicate anions and x hydroxide ions. Therefore, we have the following equation: \(2\cdot 3 = 2\cdot 4 + x \cdot (-1)\).

Step 6: Solve for x in pyrophylite

Solve the equation from Step 5 for x: \(6 = 8 - x\). Thus, \(x = 2\). So, there are two hydroxide ions in pyrophylite's chemical formula: \(\mathrm{Al}_{2}\left(\mathrm{Si}_{2} \mathrm{O}_{5}\right)_{2}(\mathrm{OH})_{2}\). To sum up the results: - There are 2 calcium ions in the chemical formula of hardystonite. - There are 2 hydroxide ions in the chemical formula of pyrophylite.

Key Concepts

Understanding Calcium Ions

Calcium ions, represented as \( \mathrm{Ca}^{2+} \), play a crucial role in chemical compounds. These ions are formed when calcium atoms lose two electrons, resulting in a positive charge. Calcium ions are essential in various biological and chemical processes. In mineral chemistry, they contribute to the structure and stability of compounds. For instance, in hardystonite, calcium ions balance the negative charge of the silicate anion. Balancing charges is vital for creating stable and neutral compounds in mineral formulas.

Examining Hydroxide Ions

Hydroxide ions, depicted as \( \mathrm{OH}^{-} \), are fundamental in chemistry, especially in forming bases. These ions consist of an oxygen and hydrogen atom, carrying a single negative charge due to an extra electron. Hydroxide ions play a significant role in mineral chemistry by contributing to the overall charge balance of compounds. In minerals like pyrophylite, hydroxide ions ensure the compound remains electrically neutral by compensating for the positive charges of other ions present.

The Art of Charge Balancing

Charge balancing is a critical concept in chemistry and involves ensuring that the total positive and negative charges in a compound equal zero. This balance is necessary to achieve a stable and neutral compound. The charges of individual ions must be considered. For example, in hardystonite, the charges of the calcium \( \mathrm{Ca}^{2+} \) and zinc \( \mathrm{Zn}^{2+} \) ions need to balance with the silicate anion \( \left(\mathrm{Si}_{2}\mathrm{O}_{7}\right)^{6-} \). Formulating this balance involves finding the correct number of ions, ensuring that the sum of positive charges matches the sum of negative charges for a stable compound.

Exploring Mineral Chemistry

Mineral chemistry involves studying the composition and properties of minerals, which are naturally occurring substances. The chemical formulas of minerals reveal their constituent ions and molecules, indicating the balance of charges within the structure. Minerals such as hardystonite and pyrophylite exemplify how different ions come together to form stable compounds. Each mineral has a unique formula representing its intricate structure and charge balance, illustrating the relationship between compositional elements and mineral properties.