What is the value of `x` in colemanite, `Ca_(2)B_(x)O_(11).6H_(2)O` ?

Explanation

To find the value of \( x \) in colemanite, represented by the formula \( Ca_{2}B_{x}O_{11} \cdot 6H_{2}O \), we can follow these steps:

### Step 1: Identify the charges of the elements
- Calcium (Ca) has a charge of \( +2 \).
- Oxygen (O) has a charge of \( -2 \).
- Boron (B) can have a charge of either \( +3 \) or \( -3 \). However, in this case, we will assume it has a charge of \( +3 \) to balance the overall charge.

### Step 2: Write the charge balance equation
We need to ensure that the total charge of the compound is neutral (0). The formula can be expressed as:
\[ \text{Total charge} = \text{Charge from Calcium} + \text{Charge from Boron} + \text{Charge from Oxygen} = 0 \]

### Step 3: Substitute the values into the equation
From the formula \( Ca_{2}B_{x}O_{11} \):
- The contribution from Calcium is \( 2 \times (+2) = +4 \).
- The contribution from Boron is \( x \times (+3) = +3x \).
- The contribution from Oxygen is \( 11 \times (-2) = -22 \).

Putting this into the equation gives:
\[ 4 + 3x - 22 = 0 \]

### Step 4: Simplify the equation
Rearranging the equation:
\[ 3x - 18 = 0 \]

### Step 5: Solve for \( x \)
Adding 18 to both sides:
\[ 3x = 18 \]
Now, divide both sides by 3:
\[ x = \frac{18}{3} = 6 \]

### Conclusion
The value of \( x \) in colemanite \( Ca_{2}B_{x}O_{11} \cdot 6H_{2}O \) is \( 6 \).

### Final Answer
Thus, \( x = 6 \).

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