Rank these systems in order of decreasing entropy: ? 1 mol methane gas at 273k and 40l 1 mol helium gas at 273k and 40l 1 mol hydrogen gas at 273k and 40l 1 mol helium gas at 273k and 20l 1/2 mol helium gas at 273k and 20l 1/2 mol helium gas at 100k and 20l 1/2 mol of liquid helium at 100k

Entropy is a measure of disorder in a system. The higher the disorder of a system results to higher value of entropy. Ranking the given systems in decreasing order means ranking them from the most disorder system to the least disorder system. The rank is as follows:

 1 mol methane gas at 273 K and 40 L
 1mol hydrogen gas at 273 K and 40 L
 1 mol helium gas at 273 K and 40 L
 1 mol helium gas at 273 K and 20 L
 1/2 mol helium gas at 273 K and 20 L
 1/2 mol helium gas at 100 K and 20 L
 1/2 mol of liquid helium at 100 K

At same conditions, 1 mol of methane is more disordered than 1 mol of hydrogen because methane has more atoms than hydrogen. Helium is less disordered than hydrogen since helium is monoatomic. It only goes by only 1 atom as compared to the diatomic atom like hydrogen. On the other hand, a smaller volume of the same amount of substance is less disordered because molecules has less space to wander around and be more disordered. Also, when the temperature goes down the kinetic energy of the molecules as well decreases thus the less energetic the molecules are. Lastly, the liquid state of a substance is in a more ordered state than when the substance is in a gaseous state thus less entropy.