The state of matter that has the most potential energy is typically the gas state. In gases, the particles are widely spaced and move freely, which allows them to store energy in the form of kinetic energy as well as potential energy due to their positional arrangement.
Potential energy in the context of states of matter can be understood through the interactions between particles. In solids, particles are tightly packed and have a fixed position, resulting in lower potential energy. In liquids, particles are still close together but can move past one another, which increases the potential energy slightly compared to solids. However, in gas, the particles are far apart and can have a lot of energy relative to each other, which means they can store more potential energy.
Furthermore, when considering the energy in a system, the state of matter with more degrees of freedom for particle movement (as in gases) allows for greater energy storage capabilities, especially under varying conditions such as temperature and pressure. Therefore, under standard conditions, gases represent a state of matter where potential energy is maximized.