Question

A hypothetical mineral has the formula \( X_7Si_8O_{22}(OH)_2 \), where X is a cation. The valence state of \( X \) is .............. (In integer)

Hint:

To find the valence state of a cation, balance the charges of the anions and cations in the mineral formula.

Answer 1

Correct Answer: 3

The formula of the mineral is \( X_7Si_8O_{22}(OH)_2 \), where \( X \) is the cation. To find the valence state of \( X \), let's balance the charges on both sides.
Step 1. The oxide ions \( O^{2-} \) contribute a total charge of:
\[ 8 \, O^{2-} \Rightarrow 8 \times (-2) = -16 \]

Step 2. The hydroxide ions \( OH^- \) contribute a total charge of:
\[ 2 \, OH^- \Rightarrow 2 \times (-1) = -2 \]

Step 3. The silicon atoms \( Si \) each have a charge of \( +4 \) (since Si is a group 4 element), so:
\[ 8 \, Si^{4+} \Rightarrow 8 \times (+4) = +32 \]
Now, the total charge from the cation \( X \) must balance the charges from \( O^{2-} \), \( OH^- \), and \( Si^{4+} \). Let the charge on \( X \) be \( q_X \). The total charge balance equation is:
\[ 7 \times q_X + 32 + (-16) + (-2) = 0 \]
Simplifying this:
\[ 7 \times q_X + 32 - 18 = 0 \]
\[ 7 \times q_X + 14 = 0 \] \[ 7 \times q_X = -14 \]
\[ q_X = -14 / 7 = -2 \]
Thus, the valence state of \( X \) is +3.
\[ \boxed{+3} \]