To determine the molecular formula of a three-carbon alkene with two double bonds, let's follow through the logical steps to arrive at the correct answer.
1. Identify the Basic Formula for a Simple Alkene:
- Alkenes are hydrocarbons that contain at least one carbon-carbon double bond. The simplest formula for an alkene with one double bond follows the formula [tex]\( C_nH_{2n} \)[/tex]. Here, [tex]\( n \)[/tex] represents the number of carbon atoms.
2. Starting with Three Carbons:
- Given that [tex]\( n = 3 \)[/tex], if we consider a simple alkene with one double bond, the formula would be [tex]\( C_3H_{2*3} \)[/tex], which simplifies to [tex]\( C_3H_6 \)[/tex].
3. Adjusting for Multiple Double Bonds:
- Each additional double bond in the molecule reduces the number of hydrogen atoms by 2. This is because each double bond subtracts two hydrogen atoms from the total number of hydrogens that would be present in a single bond situation.
4. Calculating the Number of Hydrogens for Two Double Bonds:
- Since our molecule has two double bonds, we start with the hydrogen count from the formula of a simple alkene [tex]\( C_3H_6 \)[/tex].
- For the first double bond, the base formula gives us [tex]\( C_3H_6 \)[/tex].
- The second double bond reduces the hydrogen count by 2. Therefore:
[tex]\[
\text{Initial number of hydrogens} = 6
\][/tex]
[tex]\[
\text{Hydrogens reduced by second double bond} = 2
\][/tex]
[tex]\[
\text{Total number of hydrogens} = 6 - 2 = 4
\][/tex]
5. Final Molecular Formula:
- With the three carbons and the adjusted hydrogen count for two double bonds, the molecular formula for the alkene is [tex]\( C_3H_4 \)[/tex].
Therefore, the correct answer is:
A. [tex]\( C_3H_4 \)[/tex]
