Towards a greater understanding of the effects of organic molecules in biomembranes, the effects of a flexible alkyl chain on the morphologies of phospholipid vesicles are investigated. Vesicles composed of 1,2-dipalmitoyl-sn-glycerol-3-phosphocholine and tetradecane (TD) rupture during cooling from the liquid-crystalline phase to the gel phase. A model calculation based on the size-dependent rupture probability indicates that the bending rigidity of the bilayer in the gel phase is more than 10 times higher than that without TD, resulting in the rupture arising from elastic stress. The rigidification is caused by the denser molecular packing in the hydrophobic region by TD. There is little change of the rigidity in the liquid-crystalline phase. Additionally, the rigidification produces a characteristic morphology of the ternary giant vesicles including TD. Reported thermal behaviors imply that molecules with a linear and long alkyl chain, such as trans fatty acids, universally exhibit a similar effect, in contrast to rigid and bulky molecules, such as cholesterol.