Today we’ll be covering:
- What is Entropy?
- Standard entropy
- Entropy changes
- State & Temperature change
- Reaction with a change in the number of gaseous molecules
- Calculating the entropy change for a reaction
- What is a spontaneous/feasible reaction?
What is Entropy?
A measure of dispersal of energy at a specific temperature.
It is also a measure of disorder of a system.
The higher the disorder or the more spread out the energy of a substance, the higher the entropy.
It is denoted as a capital ‘S’.
It is measured as:
Energy transferred in a reaction per Kelvin of temperature per mole of substance
= Joules per Kelvin per Mole
Why does entropy tend to increase?
This is all due to probability.
|Consider the different possible arrangements for particles in a container.|
|There are more ways of arrangement that are spread out than orderly.||
Compare the orderly arrangements (red) with the dispersed arrangements (yellow).
|Thus it is more probable for particles to be in a disordered/dispersed position than in an orderly one.|
|In systems of billions of particles, the probability of disorder is much larger than the probability of order.|
|It can be said that entropy is a measure of the number of disordered ways.|
|Thus, entropy tends to increase in a system unless external energy is put in to make it more ordered.|
|However, the process of providing external energy itself causes entropy in another system.
Thus, the total entropy in the Universe cannot decrease.
This is Newton’s 2nd Law of Thermodynamics.
A video explanation: Jeff Phillips: What is Entropy? (TED Ed)
What is Standard Entropy?
The measure of entropy of a certain substance (compound or element) at standard conditions.
It is denoted as S⦵.
Just as standard enthalpies are listed out, standard entropies can also be listed for each element, like so:
Note that all values of entropy are positive.
There is no such thing as negative entropy, unlike enthalpy which CAN be negative.
What are the Factors affecting Entropy?
|The more possible movement a state has, the higher its entropy.
Generally*, gases have higher entropy than liquids, which have higher entropy than solids.
This is because particles can move more freely in a gas than in a liquid, etc.
S of Η2Ο (g) > S of Η2Ο (l) > S of Η2Ο (s)
|The higher the kinetic energy of a substance, the higher its entropy.
Substances at a higher temperature have a higher entropy than those at a lower temperature.
S of Η2Ο (l) at 350 K > S of Η2Ο (l) at 320 K
Number of particles
|The more particles there are, the more possible arrangements, thus the higher the entropy.
S of 2 moles of Η2Ο (l) > S of 1 mole of Η2Ο (l)
Number of atoms
|The more atoms there are in a molecule, the more possible arrangements for the energy between bonds, thus the higher the entropy.
S of CaCO3 > S of CaO
Hardness of solids
|The softer the solid, the more possible arrangements for particles to have, thus the higher the entropy.
Harder substances have a lower entropy than soft substances.
S of C (graphite) > S of C (diamond)
*These factors do have exceptions!
What is an Entropy Change (ΔS)?
The change in the dispersal of energy between reactants & products in a reaction.
We will look at a few types of processes & their corresponding entropy changes.
Temperature & State changes
|When substances melt/vaporise, their entropy increases.
Here’s a graph of entropy against temperature, as ice is heated, melted, & then boiled:
Reaction with a change in the number of gas particles
|In a reaction, the reactants’ elements reshuffle & form new compounds as products.
We can say entropy INCREASES when the products have
N2 (g) + 3H2 (g) → 2NH3 (g)
How do you calculate entropy changes in a reaction?
First, we need to be aware that every reaction can be divided into 2 parts:
- System: reactants & products
- Surroundings: not involved in the reaction, but can transfer energy to/from the system
Let’s look at each part:
|Entropy change in a system = difference between entropies of products & reactants.
ΔSsystem = ΣSproducts – ΣSreactants
ΔS⦵system = ΣS⦵products – ΣS⦵reactantsSince the exact values of entropy for given substances are known, all we need to do is to substitute the values into the equation!
ΔS⦵system = ΣS⦵products – ΣS⦵reactants
|Entropy change in surroundings = energy transferred to surroundings divided by temperature in Kelvin (at standard conditions, T = 298K)
ΔSsurroundings = –ΔHreaction/T
ΔS⦵surroundings = –ΔH⦵reaction/TNote that the negative sign is part of the equation.
No matter whether ΔHreaction was negative or positive,
you still have to multiply it by -1.
Converting to Jmol-1: ΔH⦵r = – 1270200 Jmol-1
ΔS⦵surroundings = –ΔH⦵reaction/T
|Total entropy change = entropy change of system + entropy change of surroundings
ΔStotal = ΔSsystem + ΔSsurroundings
ΔS⦵total = ΔS⦵system + ΔS⦵surroundingsFor example:
Calculate total entropy change for:
2Ca (s) + O2 (g) → 2CaO (s)
ΔS⦵total = ΔS⦵system + ΔS⦵surroundings
When a question asks to “calculate the entropy change of a reaction”, they usually mean the entropy change of the system, UNLESS you are specifically asked to calculate the total.
- If the S⦵ of each species is given, you can calculate ΔSsystem
- If the ΔΗ⦵ of the reaction is given, you can calculate ΔSsurroundings
- You need both S⦵ & ΔΗ⦵ to calculate ΔStotal
- If only S⦵ is given, the question’s asking for ΔSsystem
What is a feasible/spontaneous reaction?
A reaction that can occur without continuous supply of external energy.
This means that when the reaction is started (which may require a little activation energy), it can continue on its own without external work put in.
A spontaneous reaction MUST have a POSITIVE total entropy change (i.e. the net entropy of the system + surroundings must increase).
If [ΔSsystem + ΔSsurroundings] > 0, a reaction is spontaneous.
- Neutralisation is feasible:
an acid & an alkali will react when their solutions are in contact
- Rusting is feasible:
iron will rust as long as it is in contact with oxygen & water
- Combustion of petrol at room temperature is feasible:
you only need a spark to start it burning, but it will continue to burn on its own
- Charging a battery is NOT feasible:
You need to continuously supply electrical current
There are a few ways to know if a reaction is feasible:
- Calculating Total Entropy Change (as above)
If Total Entropy Change is POSITIVE, it is feasible
- Calculating Gibbs Free Energy Change (see here)
If Gibbs Free Energy Change is NEGATIVE, it is feasible