Answer :
To find the empirical formula of the compound with the given subscripts [tex]\( \text{Al}_6 \text{O}_9 \)[/tex], we need to follow these steps:
1. Identify the subscripts for each element:
- The subscript for aluminum (Al) is 6.
- The subscript for oxygen (O) is 9.
2. Find the greatest common divisor (GCD) of the subscripts:
- The greatest common divisor of 6 and 9 is 3.
3. Divide each subscript by the GCD to simplify the formula:
- For aluminum (Al): [tex]\( \frac{6}{3} = 2 \)[/tex]
- For oxygen (O): [tex]\( \frac{9}{3} = 3 \)[/tex]
4. Write the empirical formula using the simplified subscripts:
- The empirical formula is [tex]\( \text{Al}_2 \text{O}_3 \)[/tex].
So, the empirical formula of [tex]\( \text{Al}_6 \text{O}_9 \)[/tex] is:
[tex]\[ \boxed{\text{Al}_2 \text{O}_3} \][/tex]
Therefore, the correct answer from the given options is [tex]\( \text{Al}_2 \text{O}_3 \)[/tex].
1. Identify the subscripts for each element:
- The subscript for aluminum (Al) is 6.
- The subscript for oxygen (O) is 9.
2. Find the greatest common divisor (GCD) of the subscripts:
- The greatest common divisor of 6 and 9 is 3.
3. Divide each subscript by the GCD to simplify the formula:
- For aluminum (Al): [tex]\( \frac{6}{3} = 2 \)[/tex]
- For oxygen (O): [tex]\( \frac{9}{3} = 3 \)[/tex]
4. Write the empirical formula using the simplified subscripts:
- The empirical formula is [tex]\( \text{Al}_2 \text{O}_3 \)[/tex].
So, the empirical formula of [tex]\( \text{Al}_6 \text{O}_9 \)[/tex] is:
[tex]\[ \boxed{\text{Al}_2 \text{O}_3} \][/tex]
Therefore, the correct answer from the given options is [tex]\( \text{Al}_2 \text{O}_3 \)[/tex].
