Final answer:
The pattern with the equation dG = dH - TdS is the Gibbs-Helmholtz equation, not Boyle's Law, Charles's Law or the Van der Waals equation.
Step-by-step explanation:
The pattern seen with the equation dG = dH - TdS is represented by the Gibbs-Helmholtz equation, which is a thermodynamic equation used to predict the spontaneity of a process at constant pressure and temperature. In this equation, dG represents the change in Gibbs free energy, dH is the change in enthalpy, and TdS is the product of temperature and the change in entropy. Unlike Boyle's Law Charles's Law, and the Van der Waals equation, which are associated with the behavior of gases the Gibbs-Helmholtz equation is associated with the free energy changes of a system, which can help determine whether a reaction is spontaneous.
The accuracy of different methods such as graphs and equations like Boyle’s Law or the Van der Waals equation depends on the particular conditions being modeled and the assumptions they are based on.