To determine which organic compound requires the maximum amount of [tex]\( O_2 \)[/tex] gas for complete oxidation, we will look at each compound and calculate the moles of [tex]\( O_2 \)[/tex] required. Here are the four compounds:
1. [tex]\( CH_3CHO \)[/tex] (Acetaldehyde):
- Number of Carbon atoms (C): 2
- Number of Hydrogen atoms (H): 4
- Number of Oxygen atoms (O): 1
2. [tex]\( CH_3CH_3 \)[/tex] (Ethane):
- Number of Carbon atoms (C): 2
- Number of Hydrogen atoms (H): 6
- Number of Oxygen atoms (O): 0
3. [tex]\( CH_3CH_2OH \)[/tex] (Ethanol):
- Number of Carbon atoms (C): 2
- Number of Hydrogen atoms (H): 6
- Number of Oxygen atoms (O): 1
4. [tex]\( CH_3CO_2H \)[/tex] (Acetic Acid):
- Number of Carbon atoms (C): 2
- Number of Hydrogen atoms (H): 4
- Number of Oxygen atoms (O): 2
The general formula for calculating the amount of [tex]\( O_2 \)[/tex] needed for complete oxidation of a compound [tex]\( C_xH_yO_z \)[/tex] is:
[tex]\[ \text{O}_2 \text{ needed} = x + \frac{y}{4} - \frac{z}{2} \][/tex]
Let's calculate the moles of [tex]\( O_2 \)[/tex] needed for each compound:
1. [tex]\( CH_3CHO \)[/tex]:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = 4 \][/tex]
[tex]\[ z = 1 \][/tex]
[tex]\[ \text{O}_2 \text{ needed} = 2 + \frac{4}{4} - \frac{1}{2} = 2 + 1 - 0.5 = 2.5 \][/tex]
2. [tex]\( CH_3CH_3 \)[/tex]:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = 6 \][/tex]
[tex]\[ z = 0 \][/tex]
[tex]\[ \text{O}_2 \text{ needed} = 2 + \frac{6}{4} - \frac{0}{2} = 2 + \frac{3}{2} = 3.5 \][/tex]
3. [tex]\( CH_3CH_2OH \)[/tex]:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = 6 \][/tex]
[tex]\[ z = 1 \][/tex]
[tex]\[ \text{O}_2 \text{ needed} = 2 + \frac{6}{4} - \frac{1}{2} = 2 + 1.5 - 0.5 = 3.0 \][/tex]
4. [tex]\( CH_3CO_2H \)[/tex]:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = 4 \][/tex]
[tex]\[ z = 2 \][/tex]
[tex]\[ \text{O}_2 \text{ needed} = 2 + \frac{4}{4} - \frac{2}{2} = 2 + 1 - 1 = 2 \][/tex]
After performing the calculations, we find the amount of [tex]\( O_2 \)[/tex] required for each compound:
- [tex]\( CH_3CHO \)[/tex]: 2.5 moles
- [tex]\( CH_3CH_3 \)[/tex]: 3.5 moles
- [tex]\( CH_3CH_2OH \)[/tex]: 3.0 moles
- [tex]\( CH_3CO_2H \)[/tex]: 2.0 moles
The compound that requires the maximum amount of [tex]\( O_2 \)[/tex] for complete oxidation is [tex]\( CH_3CH_3 \)[/tex] (Ethane), which requires 3.5 moles of [tex]\( O_2 \)[/tex].
Thus, the answer is:
e. [tex]\( CH_3CH_3 \)[/tex]
