To determine the empirical formula for the compound with the molecular formula [tex]\( B_3H_6N_3 \)[/tex], we need to follow these steps:
### 1. Identify the Molecular Formula:
The given molecular formula is [tex]\( B_3H_6N_3 \)[/tex]. This formula indicates that the compound consists of 3 boron (B) atoms, 6 hydrogen (H) atoms, and 3 nitrogen (N) atoms.
### 2. List the Subscripts:
Extract the subscripts from the molecular formula:
- For Boron (B): 3
- For Hydrogen (H): 6
- For Nitrogen (N): 3
### 3. Calculate the Greatest Common Divisor (GCD):
To simplify the subscripts to their smallest whole number ratios, we need to find the greatest common divisor (GCD) of these numbers. The subscripts are 3, 6, and 3.
The GCD of 3, 6, and 3 is 3.
### 4. Divide Each Subscript by the GCD:
Divide each subscript in the molecular formula by the GCD (which is 3):
- For Boron (B): [tex]\( \frac{3}{3} = 1 \)[/tex]
- For Hydrogen (H): [tex]\( \frac{6}{3} = 2 \)[/tex]
- For Nitrogen (N): [tex]\( \frac{3}{3} = 1 \)[/tex]
### 5. Write the Empirical Formula:
After dividing, we obtain the subscripts that represent the simplest whole number ratio of the elements in the compound. Thus, the empirical formula is:
[tex]\( B_1H_2N_1 \)[/tex]
Typically, chemists omit the ‘1’ subscript from the formula, so the empirical formula is written as:
[tex]\[ BH_2N \][/tex]
In conclusion, the empirical formula for the compound with the molecular formula [tex]\( B_3H_6N_3 \)[/tex] is [tex]\( BH_2N \)[/tex].
