Final answer:
Under standard conditions, 1 dm₃ of methane has approximately 2.68 x 10²² particles based on Avogadro's Law, with the assumption that temperature and pressure are not factors since they are not specified.
Step-by-step explanation:
To determine in which state 1 dm³ of methane contains the most particles, we consider the conditions that increase the number of microstates of a gas, which, according to the Boltzmann distribution, correlates with higher entropy. In gases, more microstates typically occur with higher temperature and lower pressure, as increased temperature agitates particles and lowers their density, while lower pressure allows particles more volume to occupy. However, since a volume of methane (CH₄) is given and no mention of temperature or pressure is made, it's assumed that the question refers to standard conditions (0°C and 1 atm), at which the number of particles is determined by Avogadro's Law. Therefore, at standard conditions, 1 dm3 of methane or any ideal gas contains approximately 2.68 x 10²²particles, as 1 mole of any ideal gas occupies 22.414 dm³ at standard temperature and pressure (STP).