To determine which of the given molecular formulas represents an alkene, we need to understand the general characteristics and formula of alkenes. Alkenes are hydrocarbons that contain at least one carbon-carbon double bond and follow the general molecular formula [tex]\( C_nH_{2n} \)[/tex].
Let's evaluate each molecular formula provided:
1. Decane [tex]\(\left( C_{10}H_{22} \right) \)[/tex]:
- The molecular formula is [tex]\( C_{10}H_{22} \)[/tex].
- If we apply the general formula for an alkene [tex]\( C_nH_{2n} \)[/tex], we get:
[tex]\[
C_{10}H_{2 \cdot 10} = C_{10}H_{20}
\][/tex]
- Since [tex]\( C_{10}H_{22} \)[/tex] does not match [tex]\( C_{10}H_{20} \)[/tex], Decane is not an alkene.
2. Propene [tex]\(\left( C_3H_6 \right) \)[/tex]:
- The molecular formula is [tex]\( C_3H_6 \)[/tex].
- For an alkene with [tex]\( n = 3 \)[/tex], the formula would be:
[tex]\[
C_3H_{2 \cdot 3} = C_3H_6
\][/tex]
- Since [tex]\( C_3H_6 \)[/tex] matches [tex]\( C_3H_6 \)[/tex], Propene is an alkene.
3. Butane [tex]\(\left( C_4H_{10} \right) \)[/tex]:
- The molecular formula is [tex]\( C_4H_{10} \)[/tex].
- For an alkene with [tex]\( n = 4 \)[/tex], the expected formula would be:
[tex]\[
C_4H_{2 \cdot 4} = C_4H_8
\][/tex]
- Since [tex]\( C_4H_{10} \)[/tex] does not match [tex]\( C_4H_8 \)[/tex], Butane is not an alkene.
4. Ethane [tex]\(\left( C_2H_6 \right) \)[/tex]:
- The molecular formula is [tex]\( C_2H_6 \)[/tex].
- For an alkene with [tex]\( n = 2 \)[/tex], the general formula is:
[tex]\[
C_2H_{2 \cdot 2} = C_2H_4
\][/tex]
- Since [tex]\( C_2H_6 \)[/tex] does not match [tex]\( C_2H_4 \)[/tex], Ethane is not an alkene.
Reviewing all the options, only Propene [tex]\(\left( C_3H_6 \right)\)[/tex] fits the general formula [tex]\( C_nH_{2n} \)[/tex] for alkenes.
Thus, the molecular formula that represents an alkene is:
Propene [tex]\(\left( C_3H_6 \right)\)[/tex]
