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Nicky has taught a variety of chemistry courses at college level. Nicky has a PhD in Physical Chemistry.

Ever wonder why your bedroom always ends up a mess within hours of you tidying up? That is the magic of entropy. In this lesson, you'll learn why disorder is the natural state of matter and how we can predict entropy change in a physical or chemical reaction.

Introducing Entropy

Simply put, entropy (given the symbol S) is a measurement of the randomness or disorder of a system. Let me give you an example of this. Say you threw 100 coins into the air. The chances of them all landing heads up or all landing tails up are very low indeed. However, the chances that they will land in a random manner is very high. If you threw them up into the air a second time, they are highly likely to all land in a different random way, some heads and some tails.

There is only one way you can possibly get all the coins the same side up; but for randomness there are an infinite number of ways. Try it for yourself as a quick demonstration of how systems will tend to become more random on their own, if allowed to. Scientists will often use the word spontaneous instead of 'on their own,' and this means a process that could occur by itself without any work from the outside.

Another example of randomness or entropy is my bedroom. Again, there is a very high chance that, on its own, my bedroom will be a random jumble in a few days, with clothes, magazines and books everywhere. For me to stop this chaos, I have to put in effort (or, in other words, I have to put work into the system) to tidy it back up and get it into order. In general, nature tends to move spontaneously from more ordered to more random states. So, now we have given you a scientific reason to explain a messy bedroom, let's see what else we can do with this new concept.

Factors Affecting the Value of Entropy

When predicting whether a system has a high or low entropy we have to think about how many different places the particles can be in. In other words, can they move around and get disorganized? Think about line dancing, which is very orderly and very organized, and compare this to break dancing, which is far more free flow and chaotic. In physical and chemical systems, the following generally applies:

Liquid has higher entropy than the solid.

Here, our ice cube is really constrained - the water molecules are held in place in the solid by intermolecular forces and so are very ordered; there is very limited movement. The molecules cannot move outside of the solid structure, and they have very limited chance of randomness. However, the liquid has some freedom to spread away and become disordered. The forces holding the molecules together are weaker than the ice. The entropy has increased.

Gas has a higher entropy than the liquid.

Gas molecules are no longer held together by any forces and are free to move wherever they like. Here, our water vapor molecules can spread out in the room and move around. Our liquid, though, has still got some order. A simple way to remember entropy increases with the order of phases is 'Silly Little Goats.' Solids have the lowest entropy, and gases have the highest entropy values.

Heating things up increases the entropy.

The more something gets heated up, the more it can move around, the more disorder it has. Imagine you are in a club and you are dancing with your friends. When it is cold, you huddle together and move pretty slowly. Your group is pretty ordered as you keep together. However, as the club heats up and you get warmer and warmer, you start to spread out and move away from your friends. Your disorder, or entropy, has increased.

The more moles of gas, the higher the entropy.

We have already learned that gas has the highest entropy. So, it follows that the more moles of gas you have, the more entropy there is.

Predicting Entropy Change

When predicting whether a physical or chemical reaction will have an increase or decrease in entropy, look at the phases of the species present. Remember 'Silly Little Goats' to help you tell. We say that 'if entropy has increased, Delta S is positive' and 'if the entropy has decreased, Delta S is negative.' Here are two quick examples:

'Do you predict whether entropy will increase or decrease in this reaction?'

Reaction for example

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Okay, here we are going from three moles of gas to two moles of liquid. We know that 'Silly Little Goats' tells us that entropy increases from solid to gas. Now, here we are going from gas to liquid. So, entropy has decreased; in this reaction Delta S is negative.

Here's another example: 'Solid carbon dioxide sublimes.'

This physical reaction is simply dry ice. Carbon dioxide goes directly from the solid to the gas; this is called sublimation. Here, 'Silly Little Goats' tells us that entropy has increased and Delta S is positive.

Calculating Entropy Change in a Chemical Reaction

As well as predicting whether the entropy change will be positive or negative, we can also calculate the entropy change using values that we are given in a data table. We can do this because entropy, just like enthalpy, is a state function. Because this means we do not need to worry how we got from one place to another, all we care about is where we start and where we finish. To measure entropy change of a reaction, we can use the simple equation:

Equation of entropy change

Here, you can see that we calculate the entropy change by simply deducting the entropy value of the reactants from the entropy value of the products. The larger the positive number, the greater the increase in entropy. So, let us do a quick example.

Reaction for example

Okay, looking at this reaction, you should immediately be predicting whether there will be an increase or decrease in entropy. Here we are forming a gas and so our prediction is that entropy will increase. Let us see if that is true. We have some values of standard entropies we can use:

Compound

Value J/mol.K

CaCO3(s)

92.9

CaO(s)

39.8

CO2(g)

213.6

We can substitute these values into our equation and calculate the entropy change. So, we have 39.8 + 213.6 J per mole per K for the products, and we can subtract 92.9 J mol per K for the reactants. Our overall entropy change is +160.5 J per K. So, just as we predicted, there is a positive value for the entropy change and entropy has increased.

Lesson Summary

In this lesson, we learned that entropy is a measure of disorder or randomness of a system and that nature spontaneously moves towards systems with higher entropy. Entropy increases as you go from solid to liquid to gas, and you can predict whether entropy change is positive or negative by looking at the phases of the reactants and products. Whenever there is an increase in gas moles, entropy will increase. You can calculate the entropy change of a reaction by using the simple equation.

Learning Outcomes

Once you've finished with this lesson, you should have the ability to:

Define entropy

Describe how nature spontaneously moves in terms of entropy and the entropy of solids, liquids, and gases

Explain how to predict entropy change by looking at reactant and product phases

Identify the equation for calculating the entropy change of a reaction

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