To determine the empirical formula for the compound given the ratios of 5 parts Carbon (C), 8 parts Hydrogen (H), and 2 parts Oxygen (O), we need to convert these ratios to the smallest whole numbers.
The initial step involves identifying the smallest ratio among C, H, and O. Here, the ratios are:
- Carbon (C): 5
- Hydrogen (H): 8
- Oxygen (O): 2
Out of these, the smallest ratio is 2 (for Oxygen).
Next, we divide each ratio by the smallest ratio (which is 2) to obtain:
- [tex]\( \frac{5}{2} = 2.5 \)[/tex] parts Carbon
- [tex]\( \frac{8}{2} = 4 \)[/tex] parts Hydrogen
- [tex]\( \frac{2}{2} = 1 \)[/tex] part Oxygen
The ratio then becomes:
- Carbon (C): 2.5
- Hydrogen (H): 4
- Oxygen (O): 1
Since our goal is to have whole number ratios, we observe that 2.5 is not a whole number. To convert these into whole numbers, we need to multiply all the ratios by a common factor that will eliminate the decimal.
In this case, multiplying each of the ratios by 2 gives us:
- Carbon (C): [tex]\( 2.5 \times 2 = 5 \)[/tex]
- Hydrogen (H): [tex]\( 4 \times 2 = 8 \)[/tex]
- Oxygen (O): [tex]\( 1 \times 2 = 2 \)[/tex]
So the resulting whole number ratios are:
- Carbon (C): 5
- Hydrogen (H): 8
- Oxygen (O): 2
Therefore, the empirical formula for the compound, based on these whole-number ratios, is [tex]\( \boxed{\text{C}_5 \text{H}_8 \text{O}_2} \)[/tex].
Thus, the correct answer is:
2) [tex]\( \text{C}_5 \text{H}_8 \text{O}_2 \)[/tex]
