The adsorption of gases on charcoal is influenced by several factors, including the nature of the gas molecules and the properties of the charcoal surface. In this case, we are given four gases: CO2, SO2, CH4, and H2, and we need to determine which gas shows the least adsorption on a definite amount of charcoal.

To predict the gas with the least adsorption, we can consider the following factors:

1. Molecular Size: The size of the gas molecules can affect their adsorption on the charcoal surface. Smaller molecules can penetrate the pores of the charcoal more easily, leading to stronger adsorption. Larger molecules may have difficulty accessing the charcoal surface and thus show weaker adsorption.

2. Polarity: The polarity of the gas molecules can also affect their adsorption. Polar molecules have dipole moments, which can interact with polar sites on the charcoal surface through dipole-dipole interactions. Nonpolar molecules, on the other hand, do not have dipole moments and may have weaker interactions with the charcoal surface.

Based on these factors, we can analyze the given gases:

a) CO2: Carbon dioxide is a relatively small molecule (linear with a molecular weight of 44 g/mol). It is also a polar molecule due to its linear geometry and the presence of polar carbon-oxygen bonds. CO2 can undergo dipole-dipole interactions with the charcoal surface, leading to moderate adsorption.

b) SO2: Sulfur dioxide is a larger molecule compared to CO2 (bent shape with a molecular weight of 64 g/mol). It is also a polar molecule due to the presence of polar sulfur-oxygen bonds. SO2 can undergo dipole-dipole interactions with the charcoal surface, similar to CO2. However, the larger size of SO2 may limit its access to the charcoal surface, resulting in weaker adsorption compared to CO2.

c) CH4: Methane is the smallest molecule among the given gases (tetrahedral shape with a molecular weight of 16 g/mol). It is a nonpolar molecule as it consists of only carbon-hydrogen bonds. Methane does not have a dipole moment and lacks the ability to form strong dipole-dipole interactions with the charcoal surface. Therefore, methane is expected to show weaker adsorption compared to CO2 and SO2.

d) H2: Hydrogen gas is the smallest molecule among the given gases (diatomic with a molecular weight of 2 g/mol). It is also a nonpolar molecule as it consists of two hydrogen atoms bonded together. Similar to methane, hydrogen gas lacks a dipole moment and strong dipole-dipole interactions with the charcoal surface. Therefore, hydrogen gas is expected to show weaker adsorption compared to CO2 and SO2.

Based on the analysis above, we can conclude that SO2 shows the least adsorption on a definite amount of charcoal among the given gases (CO2, SO2, CH4, and H2).