To determine the correct molecular formula for a three-carbon alkene with two double bonds, let's follow the steps:
1. Identify the General Formula for Alkenes:
Alkenes are hydrocarbons with at least one double bond. The general formula for an alkene with one double bond is [tex]\(C_nH_{2n}\)[/tex].
2. Apply the General Formula for a Three-Carbon Alkene (One Double Bond):
If we have three carbons ([tex]\(n = 3\)[/tex]), the formula for a three-carbon alkene with one double bond is:
[tex]\[
C_3H_{2(3)} = C_3H_6
\][/tex]
3. Consider the Impact of Additional Double Bonds:
Each additional double bond in the alkene will reduce the number of hydrogen atoms by 2.
4. Calculate the Number of Hydrogens for a Three-Carbon Alkene with Two Double Bonds:
Starting with [tex]\(C_3H_6\)[/tex], one additional double bond will reduce the number of hydrogen atoms by 2. Therefore:
[tex]\[
C_3H_6 - 2H = C_3H_4
\][/tex]
So, the molecular formula for a three-carbon alkene with two double bonds is [tex]\(C_3H_4\)[/tex].
Therefore, the correct answer is:
A. [tex]\(\mathbf{C_3H_4}\)[/tex]
