Recall that a sigma bond is a single bond where two orbitals have significant overlap. For alkanes (hydrocarbons with single bonds only) all carbon atoms have an sp^3 orbital hybridization. The sp^3 arrangement creates 4 hybridized orbitals that are 109.5^@ apart from one another with a tetrahedral geometry.
Consider Ethane (CH3CH3)
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Ethane has 4 sigma bonds for each carbon (one to the other carbon, three to each hydrogen). With the sp^3 hybridization, there is no way to a double bond between the carbons without causing significant strain and interference.
Consider the orbitals for ethene (CH_2CH_2), an alkene with a double bond between the two carbons.
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The carbon atoms in ethene have an sp^2 hybridization meaning that there are 3 hybridized orbitals in a trigonal planar geometric arrangement with 120^@ angles between them and one unybridized p orbital (the p_y orbital). The sp^2 hybridization facilitates a double bond between the carbons because it allows an sp^2 orbital to overlap through a sigma bond and the unhybridized p_y orbitals for each carbon to also overlap. This p orbital overlap is a pi bond.
Although a pi bond is higher energy than a sigma bond, the combination of a single sigma bond and a single pi bond in a double bond is much lower energy overall than trying to force two sigma bonds between two atoms.
