3.1 Entropy

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In addition to enthalpy (heat content), there is another important thermodynamic aspect of all chemical reactions - entropy.

All substances, be they individual atoms of a single element or a molecule of a compound, possess some degree of disorder because particles are always in constant motion. Thus, S is always a positive number.

Can you think of when S is theoretically equal to zero?

S = 0
only for pure crystals
at absolute zero
( 0 K or -273°C)

This is known as the
Third Law of Thermodynamics

E n t r o p y

A measure of the amount of randomness
or disorder in a system.

The symbol for entropy: S

The unit for entropy:

K·mole

Can S ever be a negative number?

Answer - no. A substance can not be less random than not random at all.

However, we are typically concerned with how entropy changes during a chemical reaction, or with ΔS rather than S:

ΔS = S_final – S_initial

Read this note about units.

What does the value of ΔS tell us about how entropy changes?

Let's make up some numbers and see.

Gas particles move about much more than do particles in the liquid phase, making them more random or disordered. Let's give a gas particle an entropy value of 10 and a liquid particle an entropy value of 5 (because it is less random, it should have a smaller number).

S_gas = 10

S_liquid = 5

If a system changes from a gas state to a liquid state, it becomes lessrandom, or more ordered, because liquid particles move about less randomly than do gas particles. Now calculate ΔS :

ΔS = S_liquid - S_gas

ΔS = 5 – 10 = –5

We see from the example that as a system becomes less random (more ordered) ΔS has a negative value.

How does entropy affect the direction of chemical change?

The Law of Disorder

also known as the

Second Law of Thermodynamics

states that spontaneous systems always
proceed in the direction of increasing entropy.

A negative value of ΔS indicates
a decrease in entropy—
the system becomes less random

A positive value of ΔS indicates
an increase in entropy—
the system becomes more random.

In other words (putting this very simply), systems tend to become more random over time, not more ordered.

Consider these examples:

Think of your bedroom at home. If you're like most people, over time the room becomes messier, or more random (less ordered) over time. It takes some effort (energy) to get things tidied up again.

How about a brand new deck of cards, nicely arranged in suits? As you play a game of cards the deck becomes much more random.

A sand castle on a beach? Decays into a pile of sand, a more random and disordered state.

Predicting Entropy Changes

You can predict entropy changes by looking at several factors in an equation.
The following changes suggest an increase in entropy:

Changes in state:
	solid → liquid liquid → gas solid → gas solid or liquid→ aqueous state (the dissolving process)
An increase in the number of moles. If the product side of the equation has more moles than the reactant side, the system has become more random; more particles moving about is a more random state than fewer particles moving about.
Increasing the temperature. An increase in temperature, caused by an increase in heat energy, increases molecular motion which in turn increases the degree of randomness

Calculating Entropy Changes

It is also possible to calculate a value for ΔS. You shouldn't find this difficult, as we use the same formula we used for Hess's Law, only now we are working with values for entropy instead of enthalpy:

ΔS = ΣS_products - ΣS_reactants

You'll find values for ΔS in the same Table of Thermochemical Data that you used for calculating ΔH.

Example:

Calculate ΔS for the following reaction, using a Table of Thermochemical Data, and state whether entropy increases (becomes more random) or decreases (becomes less random)? Based on entropy changes, do you predict a spontaneous reaction?

2 NO(g) + O₂(g) →N₂O₄(g)

Solution:

Look up ΔS values for all reaction participants. Multiply values by coefficients from the balanced equation.

	ΔS
NO	210.8	×	2	=	421.6
O₂	205.1	×	1	=	205.1
N₂O₄	304.3	×	1	=	304.3

Solve for ΔS

ΔS =	ΣS_products - ΣS_reactants	Since the value of ΔS is negative, we know that entropy decreases; the system becomes less random. On the basis of entropy changes alone, we predict that the reaction will not be spontaneous.
	[N₂0₄] - [2(NO) + O₂]
	304.3 - [421.6 + 205.1]
	304.3 - 626.7
ΔS =	-322.4 J/K