The value of n in molecular formula `Be_(n)Al_(2)Si_(6)O_(18)` (molecular mass = 537) is
Given : Atomic mass of Be = 9, Al = 27
Si = 28 and O = 16

Explanation

To find the value of \( n \) in the molecular formula \( Be_nAl_2Si_6O_{18} \) given the molecular mass of 537, we can follow these steps:

### Step 1: Write the expression for the molecular mass
The molecular mass can be expressed as the sum of the masses of all the atoms in the formula.

\[ \text{Molecular mass} = n \times \text{(atomic mass of Be)} + 2 \times \text{(atomic mass of Al)} + 6 \times \text{(atomic mass of Si)} + 18 \times \text{(atomic mass of O)} \]

### Step 2: Substitute the atomic masses
Substituting the given atomic masses:
- Atomic mass of Be = 9
- Atomic mass of Al = 27
- Atomic mass of Si = 28
- Atomic mass of O = 16

The equation becomes:

\[ 537 = n \times 9 + 2 \times 27 + 6 \times 28 + 18 \times 16 \]

### Step 3: Calculate the contributions from Al, Si, and O
Now, calculate the contributions from Al, Si, and O:

- Contribution from Al: \( 2 \times 27 = 54 \)
- Contribution from Si: \( 6 \times 28 = 168 \)
- Contribution from O: \( 18 \times 16 = 288 \)

### Step 4: Combine the contributions
Now, combine these contributions:

\[ 537 = n \times 9 + 54 + 168 + 288 \]

Calculating the total of the contributions:

\[ 54 + 168 + 288 = 510 \]

So the equation simplifies to:

\[ 537 = n \times 9 + 510 \]

### Step 5: Isolate \( n \)
Now, isolate \( n \):

\[ 537 - 510 = n \times 9 \]

This simplifies to:

\[ 27 = n \times 9 \]

### Step 6: Solve for \( n \)
Now, divide both sides by 9 to find \( n \):

\[ n = \frac{27}{9} = 3 \]

### Final Answer
Thus, the value of \( n \) is \( 3 \).

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