What causes an increase in entropy?

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This section is a short primer on what kind of chemical processes **increase** entropy, and what kind of process **decreases** it.

We can calculate exact entropy changes by looking up standard molar entropies and working out the change from there. Or, we can do experiments to work it out. However, it’s perfectly possible to guess what increases and decreases entropy.

Degrees of freedom

A a degree of freedom is something that is allowed to vary. It pops up in statistical contexts a lot. In a chemical context, however, we can think of it as being how free molecules are to move. This can be related to their structure, or the molecules’ ability to move around.

Processes that increase entropy

• Melting from solid (fixed positions) to liquids (freer positions)
• Vaporising from liquid to gas (fast moving, easily fills a container)
• Reactions that dissolve solids
• Reactions that increase the number of gas molecules
• Breaking molecules into two (increasing the number of molecules in gas or solution)
• Ring-opening – going from more fixed, rigid, ring-like structures to long, flexible chains

Processes that decrease entropy

• Freezing, and condensation
• Reactions that combine two molecules into one (addition)
• Reactions that reduce the number of gas molecules
• Reactions that make a molecule more rigid (going from long chains to inflexible rings)

Processes where we need to know more details

• Reactions that reduce the number of molecules or make them more rigid… but may free up solvent molecules in the process
• Reactions where the number of gas molecules don’t change

So we can see that where the freedom for molecules to move and rearrange themselves naturally lead to more possible combinations and arrangements of them. This results in higher entropy.

This comes from the statistical approach to entropy, where the energy associated with entropy is a function of the number of possible arrangements of the system. There are more ways of arranging chaotic, and loosely connected water molecules than there are in rigid and crystalline ice. Therefore liquid water has a higher entropy.

AN INTRODUCTION TO ENTROPY

This page provides a simple, non-mathematical introduction to entropy suitable for students meeting the topic for the first time.

At this level, in the past, we have usually just described entropy as a measure of the amount of disorder in a system. A very regular, highly ordered system (diamond, for example) will have a very low entropy. A very disordered system (a mixture of gases at a high temperature, for example) will have a high entropy.

We now expand on this a bit, but luckily not too much! Let's look at this with a couple of thought experiments . . .

Suppose you held a stack of ten coins between your finger and thumb. That's a fairly ordered state for them to be in. And then you dropped them on the floor. Every time you did this, you would get a different random pattern of coins on the floor - arranged just by chance. That is now a disordered system.

Now, it is just imaginable that when you dropped them, by chance they would fall into a neat stack of coins like the one you started with, but the probability of that happening, compared to all the other ways that the coins might fall, is so very, very tiny that you would be totally amazed if it happened.

Technically, entropy applies to disorder in energy terms - not just to disordered arrangements in space. But we often just quickly look at how disordered a system is in space in order to make a judgement about its entropy. A system which is more disordered in space will tend to have more disorder in the way the energy is arranged as well.

Suppose you managed to arrange some gaseous molecules in a container so that they were all exactly evenly spaced and so that they all had exactly the same energy - a fairly ordered state. And then you let them go and do what molecules do - move around, and bump into each other and the walls of the container.

Each collision between two molecules will cause them to change direction, and it will probably speed up one of them, and slow down the other. After a very short time, their arrangement in space will be chaotic, and so will the way energy is shared between them. The faster moving particles have more energy; the slower ones less. The entropy has increased in terms of the more random distribution of the energy.

In essence . . . "a system becomes more stable when its energy is spread out in a more disordered state".

That is really all you need to know. If you look in textbooks or on the web, you will find explanations of increasing difficulty - some very scary indeed! Don't waste time on these at this level.

Entropy changes during physical changes

Changes of state

This includes solid to liquid, liquid to gas and solid to aqueous solution.

Entropy is given the symbol S, and standard entropy (measured at 298 K and a pressure of 1 bar) is given the symbol S°. You might find the pressure quoted as 1 atmosphere rather than 1 bar in older sources. Don't worry about it - they are nearly the same. 1 bar is 100 kPa; 1 atmosphere is 101.325 kPa. Use whatever units the examiners give you.

Here are some standard entropies for a few solids, all with the units J K-1mol-1:

These all have low entropies because they are highly ordered solids, but notice that the entropy usually increases as the solid gets more complicated.

What happens during change of state? The following figures are for the standard entropy of water in different states.

The entropy increases as the molecules become more disordered as you go from solid to liquid to gas.

Notice that there isn't very big jump in entropy when ice turns to water. That's because the hydrogen bonding between the liquid molecules imposes a fair amount of order on them even in the liquid.

. . . and for benzene:

Notice that the benzene values are bigger than those of water-steam. This is because benzene is a more complicated molecule. There are more ways of arranging the energy of the molecule in a disordered way over bigger molecules than smaller ones.

What happens when an ionic solid dissolves in water?

The ionic solid is highly ordered, and so has a relatively low entropy. Pure liquid water also has a certain amount of order as explained above. But when the solid dissolves in water, the whole system becomes highly disordered as the crystal breaks up and the ions find their way between the water molecules. Entropy increases.

Entropy, S, is defined as the measure of the disorder or randomness in a system.

The more “mixed up” or “disorderly” or “messy” a system becomes, we say the entropy of the system increases.

4 Factors that affects the Entropy of a chemical system:

1) Change in Phase (Physical State)

Sgas >> Sliquid > Ssolid

A solid has the lowest entropy because their particles are closely packed together and held in regular pattern. Thus, it’s structure is highly ordered.

A liquid has higher entropy than solid because its particles are arranged in an irregular pattern, although the particles are still quite close together.

The entropy of a gas is much greater than that of a liquid because gaseous particles are very far apart from each other and can move freely at great speeds. They are not constrained to be close to each other.

2) Change in Temperature

As temperature increases, the entropy of a system also increases.

As temperature increases, the particles undergo greater vibration (in solids) and more rapid movement (in liquids and gases). This causes more disorderliness. As such, entropy increases.

3) Change in Number of Particles (especially for Gases)

As the number of moles of particles in a system increases, it causes more disorderliness and thus entropy increases.

4) Mixing of Particles

Mixing always leads to increase in disorderliness i.e. entropy increases.

Example 1:

When you dissolve a solute into a solvent to form a solution (a mixture), the entropy increases since the solute particles are now randomly arranged in between the solvent particles.

Example 2:

When you mixed 2 gases together, diffusion will occur randomly between the gases and their orderliness is reduced i.e. entropy increases.

I am sure you learned something useful today regarding how changes in temperature, phase, number of moles of particles and mixing can cause changes in the entropy of a system.

Applications of Entropy:

Next, we are going to look at the application side of how entropy is commonly discussed in everyday Chemistry.

To predict whether the entropy is increasing or decreasing in a particular system, let’s look into a few examples below:

A) Ice at 0 oC –> Liquid Water at 0 oC

Entropy (i.e. randomness) of the system increases because as ice melts to form liquid water, the regular crystalline structure of ice is broken and water molecules move freely in the liquid state i.e. system becomes more random, less orderly.

B) Liquid Water at 25 oC –> Liquid Water at 30 oC

Entropy (i.e. randomness) of the system increases because when temperature is increased, water molecules can now move more freely in the liquid and orderliness is reduced.

C) Na+(g) + Cl–(g) –> NaCl(s)

Entropy (i.e. randomness) of the system decreases because the crystalline structure of NaCl(s) formed is highly ordered and very regular i.e. system becomes more ordered, less random.

D) H2(g) at 3 atm –> H2(g) at 1 atm

Entropy (i.e. randomness) of the system increases when the pressure decreases from 3 atm to 1 atm. This is because H2 molecules are free to move in a larger volume [remember that Volume is inversely proportional to Pressure] and the system becomes less orderly.

GCE A-Level H2 Chemistry Exam-Based Questions on Entropy:

Question 1:
Which of the following substance has a greater entropy in each pair and explain your choice.

i) Diamond or Graphite

Answer: Graphite

Reason: Although both diamond and graphite are solids and have a giant molecular structure, graphite has a less ordered structure.

ii) 1 mole of NaCl(s) or 1 mole of HCl(g) at 25 oC

Answer: 1 mole of HCl(g)

Reason: Gases are more disordered than solids.

iii) 2 moles of HCl(g) or 1 mole of HCl(g) at 25 oC

Answer: 2 moles of HCl(g)

Reason: 2 moles of HCl(g) has twice the entropy (randomness) to that of a sample containing 1 mole of HCl(g).

iv) 1 mole of HCl(g) or 1 mole of Ar(g) at 25 oC

Answer: 1 mole of HCl(g)

Reason: HCl molecules have more ways of displaying itself by rotating in different directions. Argon is a monoatomic gas and exists as a spherical particle.

I hope you find the content easy for your understanding and if you have any questions, leave me a comment below. Feel free to share this blog post with your friends.

Do stay tuned to the upcoming posts as i will be discussing on the applications of Gibbs Free Energy, and how Enthalpy Changes and Entropy are all inter-related when it comes to Thermodynamics.

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