Which of the following transformations represent an increase in the entropy of the system.

Question

Which of the following transformations represent an increase in the entropy of the system.

Choose all that apply

43 g C₂H₅OH (liquid, 171K)  43 g C₂H₅OH (liquid, 340K)

47 g Co (liquid, 1.768×10³K)  47 g Co (solid, 1.768×10³K)

4 mol Xe (0.528 atm, 409K)  4 mol Xe (0.528 atm, 205K)

43 g C₂H₅OH (liquid, 352K)  43 g C₂H₅OH (gas, 352K)

3 mol O₂ (6.24 L, 249K)  3 mol O₂ (12.5 L, 249K)

Answer 1

Hi Ahmad!

As a general rule, Entropy (ΔS) will increase when any of the following occur:

1. liquids are formed from a solid
2. gases are formed from either a liquid or a solid
3. the total number of gas molecules increase from reactants to products
4. the temperature increases.

For the sake of this question, I am going to refer to each of the answer choices as #1, #2, #3, #4 and #5 respectively.

#1. The substance here is remaining in the liquid phase, and no more was added, however, we can see that the temperature increases from 171K to 340K so, the entropy in increasing.

#2. In this option, we can see that the substance underwent a physical change from the liquid phase to the solid phase so in this case the entropy of the system is actually decreasing.

#3. Here we can see that the temperature decreases from 409K to 205K, meaning that the entropy of the system is decreasing as well.

#4. For #4, the substance underwent a change from the liquid stage to the gaseous stage which indicates an increase in entropy.

#5. This one is definitely the trickiest to understand. Everything here remains constant except for the volume of the container which increases from 6.24L to 12.5 L. When the volume is small, the 3 moles of gas are confined and pressurized which makes the substance act more closely to a liquid. In a larger volume container, the 3 moles of gas are less pressurized and therefore, more disordered. So, for this one, the entropy of the system must be increasing.

I hope this helps!!

Answer 2

Entropy represents a change in the disorder of a system.

43 g C₂H₅OH (liquid, 171K)  43 g C₂H₅OH (liquid, 340K)

No phase change but there is an increase in temperature. An increase in temperature allows for more rearrangements so this does represent an increase in entropy.

47 g Co (liquid, 1.768×10³K)  47 g Co (solid, 1.768×10³K)

Phase change (liquid->solid). This represents a decrease in entropy since there are less rearrangements that can occur

4 mol Xe (0.528 atm, 409K)  4 mol Xe (0.528 atm, 205K)

No phase change, no change in number of elements, no change in molecular weight. But there is a decrease in temperature, therefore a decrease in entropy.

43 g C₂H₅OH (liquid, 352K)  43 g C₂H₅OH (gas, 352K)

Phase change (liquid->gas). This represents an increase in entropy (more rearrangements)

3 mol O₂ (6.24 L, 249K)  3 mol O₂ (12.5 L, 249K)

No phase change, no change in # of elements, no change in MW, no change in T. But there is an increase in volume. This represents an increase in entropy (more room = more opportunities for rearrangement of molecules)

Therefore, the first fourth and fifth transformations represent an increase in entropy.

Hope this helps!