Question

In a mineral with formula $KAl_3Si_3O_{10}(F_{0.5}OH_x)$, the value of ‘x’ is ________ . (Round off to one decimal place)

Answer 1

Correct Answer: 1.5

Solution: Charge Balance Calculation for a Mineral Formula 

Step 1: Understand the Formula

The given formula is:

\[ \text{KAl}_3\text{Si}_3\text{O}_{10}(\text{F}_{0.5}\text{OH}_x) \]

This represents a mineral where the sum of **fluorine (F⁻)** and **hydroxyl (OH⁻)** groups should balance the structural requirement.

Step 2: Charge Balance Calculation

The total content of **fluorine (F⁻)** and **hydroxyl (OH⁻)** ions must equal 2. Therefore, we have the equation:

\[ \text{F}^{0.5} + \text{OH}^x = 2 \]

Substituting **F⁻ = 0.5**, we get:

\[ 0.5 + \text{OH}^x = 2 \]

Step 3: Solve for x

Solving for **x**:

\[ \text{OH}^x = 2 - 0.5 = 1.5 \]

Thus, the value of **x** is: 1.5.