The energies of liquid/vapor interfaces can be measured directly, whereas the energies of the solid/vapor and solid/liquid interfaces are experimentally not directly accessible. Usually, they are derived indirectly via contact angle measurements and the Young equation in combination with some type of model predicting certain links between the various interfacial energies. Currently, two competing models are under discussion, and neither one has been proven experimentally to be correct or false. The surface tension components theory (STC theory) assumes that the interfacial energy consists of combinations of different components that are unique for each interface. The equation of state approach (EQS theory) proposes that there are strong links between the various interfacial energies. The so-called Langmuir wetting configuration allows one to measure sufficient independent data on the interfacial energies and the contact angle to directly test the EQS theory. In the following, we will prove the invalidity of the EQS theory for this configuration and thus the invalidity of a general equation of state approach for interfacial energies.