What happens to the solidity of a fat as the fatty acid chain length increases?

As the fatty acid chain length increases, the solidity or melting point of the fat tends to increase as well. This is primarily due to the fact that longer fatty acid chains have more carbon atoms, which leads to a greater number of van der Waals forces (dispersion forces) between the chains. These forces are responsible for holding the molecules together in a solid state.

In fats with longer fatty acid chains, the increased surface area allows for more interactions between the fatty acid molecules, contributing to a firmer structure at room temperature. Conversely, shorter chain fatty acids are often more liquid at room temperature because they are less able to pack closely together, resulting in weaker intermolecular forces.

While unsaturation affects the solidity of fats, as the chain becomes more saturated (more single bonds), that typically results in higher solidity at given lengths. Lengthening the chain while maintaining the degree of saturation solidifies the fat further due to the reasons stated above.