Question

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

Answer 1

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.

Answer 2

The decreasing order of entropy is as follows:

${\text{1 mol methane at 273 K and 40 L}}{\mathbf{ > }}{\text{1 mol hydrogen gas}}\;{\text{at 273 K and 40 L}}{\mathbf{ > }}\\{\text{1 mol helium gas at 273 K and 40 L}}{\mathbf{ > }}{\text{1 mol helium gas at 273 K and 20 L}}\\{\mathbf{ > }}\frac{{\text{1}}}{{\text{2}}}{\text{mol helium gas at 273 K and 20 L}}{\mathbf{ > }}\frac{{\text{1}}}{{\text{2}}}{\text{ mol helium gas at 100 K and 20 L}}{\mathbf{ > }}\\\frac{{\text{1}}}{{\text{2}}}{\text{mol of liquid helium at100 K}}$  

Further explanation:

In thermodynamics, criteria for spontaneity depend upon a thermodynamic parameter called entropy. This entropy is essentially the measure of randomness or disorder associated with the systems. Any chemical reaction is feasible or spontaneous only if the entropy change associated with the system is positive. Hence there is always a natural tendency for the system to become more chaotic or disordered with time.

Entropy is an extensive property hence the greater the number of particles greater is the entropy. Thus methane that contains the maximum number of atoms has greater entropy than hydrogen gas that contains only two hydrogen atoms at same temperature. Similarly ${\text{1 mol}}$hydrogen gas at${\text{273 K}}$and ${\text{20 L}}$has more entropy than${\text{1}}\;{\text{mol}}$of helium gas at the same temperature and pressure as helium is a monoatomic gas.

In general, the gaseous molecules are always in random motion hence the extent of disorder is maximum in gases followed by the liquids where the order is intermediate and the most ordered one are the solids whose molecules are rigid and have least intermolecular spaces between them. This explains why the liquid helium has the least disorder and hence the least entropy compared to all other gases. Thus methane that contains the maximum number of atoms has greater entropy than hydrogen gas that contains only two hydrogen atoms at the same temperature.

The entropy also varies with temperature and volume. An increase in temperature favors the chaotic movement of molecules by increasing their kinetic energies. Thus the randomness also increases with high temperature. Further greater the volume occupied by a molecule more is the intermolecular spaces available for the random motion. Hence the helium gas at higher volume ${\text{40 L}}$has greater entropy than same amount of helium that occupies lower volume ${\text{20 L}}$.  

Learn more:

1. Calculation of entropy of a reaction: https://brainly.com/question/12442928

2. Entropy changes in different states of matter: https://brainly.com/question/12632987

Answer details:

Grade: Senior School  

Subject: Chemistry

Chapter: Thermodynamics

Keywords: Thermodynamics,spontaneity, entropy,randomness,temperature,volume,kinetic energy,intermolecular spaces and disorder.