What is the value of `x` in the silicate mineral, `Be_(3)Al_(2)Si_(x) O_(18)` ?

Explanation

To find the value of `x` in the silicate mineral `Be_(3)Al_(2)Si_(x)O_(18)`, we need to analyze the charges of the elements involved and ensure that the overall charge of the compound is neutral (0). Here’s a step-by-step solution:

### Step 1: Identify the charges of each element
- Beryllium (Be) has a charge of +2.
- Aluminium (Al) has a charge of +3.
- Silicon (Si) has a charge of +4.
- Oxygen (O) has a charge of -2.

### Step 2: Write the total charge contributions
Now, we will calculate the total charge contributed by each element in the formula `Be_(3)Al_(2)Si_(x)O_(18)`:
- For Beryllium: There are 3 Be atoms, so the total charge is:
\[ 3 \times (+2) = +6 \]

- For Aluminium: There are 2 Al atoms, so the total charge is:
\[ 2 \times (+3) = +6 \]

- For Silicon: There are `x` Si atoms, so the total charge is:
\[ x \times (+4) = +4x \]

- For Oxygen: There are 18 O atoms, so the total charge is:
\[ 18 \times (-2) = -36 \]

### Step 3: Set up the equation for overall charge
The overall charge of the compound must equal 0. Therefore, we can set up the equation:
\[ (+6) + (+6) + (+4x) + (-36) = 0 \]

### Step 4: Simplify the equation
Combining the constants gives:
\[ 12 + 4x - 36 = 0 \]
This simplifies to:
\[ 4x - 24 = 0 \]

### Step 5: Solve for `x`
Now, we can solve for `x`:
\[ 4x = 24 \]
\[ x = \frac{24}{4} = 6 \]

### Conclusion
Thus, the value of `x` in the silicate mineral `Be_(3)Al_(2)Si_(x)O_(18)` is **6**. The final formula is `Be_(3)Al_(2)Si_(6)O_(18)`.

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