Entropy (1) Determining the direction of chemical change

Edexcel A level Chemistry (2017)

Topic 13B: Entropy:

Here are the first learning objectives:

13B/13. To know that entropy is a measure of the disorder of a system and that the natural direction of change is increasing total entropy (positive entropy change)

13B/14. To understand why entropy changes occur during:

.    i  changes of state 


.    ii  dissolving of a solid ionic lattice 


.    iii  reactions in which there is a change in the number of moles from reactants to products 


.    Students should be able to discuss typical reactions in terms of disorder and enthalpy change, including: 


o dissolving ammonium nitrate crystals in water


o reacting ethanoic acid with ammonium carbonate

o burning magnesium ribbon in air

o mixing solid barium hydroxide, Ba(OH)2.8H2O, with solid ammonium chloride.

Entropy: determining the direction of chemical change

How can chemists decide if a reaction will go or not?

Entropy measures the extent of disorder in a substance.

Lots of non-mathematical analogies of entropy exist as these pictures reveal:

Here is great disorder or high entropy in this picture of Einstein’s desk:

And what about this revealing picture of the high entropy of a student’s room the morning after the night before:

Clearly, both photos reveal a state of chaos or disorder or entropy.

How does this relate to chemical systems?

Example 1: Change of state

We can see from this chart how the disorder of the three states of matter increases from solid through liquid to gas.

This difference in the orderliness of substances at r.t.p is reflected in their standard molar entropies at r.t.p.

Table of standard molar entropies:

Example 2: Dissolving ammonium nitrate in water

Put a mole of aluminium at 20^oC into a vacuum flask containing a litre of water at 40^oC and the temperature of the water will drop and that of the aluminium will rise.

Knowing the heat capacities of the water and the aluminium the final temperature can be calculated.

But if aluminium at 20^oC is put into the water at 20^oC there will be no temperature change at all. 

Repeat the experiment but this time use a mole of a salt like ammonium nitrate and a litre of water both at 20^oC then the temperature does not remain the same instead it falls dramatically by several degrees.

What causes the difference?

In the case of the ammonium nitrate a chemical change occurs in which the ammonium nitrate dissolves. 

The neatly organized structure of ammonium ions and nitrate ions collapses into the chaos of a solution of ions in which their behaviour is random. 

An endothermic change has occurred in which the disorder of the system has increased.

NH₄NO₃(s)   +  aq   ⟶     NH₄⁺(aq)   +    NO₃^—(aq)

The change is spontaneous

A spontaneous chemical change is one in which no external agency is required to make it happen.

Example 3: Spontaneous Endothermic reactions

a) Many other examples of spontaneous endothermic changes in which the disorder of the system increases occur:

2CH₃COOH(l) + (NH₄)₂CO₃(s) ⟶ 2CH₃COONH₄(aq) + CO₂(g) + H₂O(l)

Here 3 moles of reactant in the liquid and solid state become 4 moles of product in the liquid and gaseous state—much more disordered.

b) Another spontaneous endothermic chemical change is that between citric acid and sodium hydrogen carbonate:

C₆H₈O₇  + 3NaHCO₃  ⟶  C₆H₅O₇Na₃   +    3CO₂   +  3H₂O

Here 4 moles of reactant in the solid state (in the presence of a small amount of water) become 7 moles of product in the liquid and gaseous state.

The mixture fizzes like mad and gets really cold.

c) And a really nasty colourful spontaneous endothermic reaction is that between thionyl chloride (SOCl₂) and the violet crystals of cobalt(II)chloride (CoCl₂.6H₂O).

SOCl₂(l)    +    CoCl₂.6H₂O(s)     ⟶    CoCl₂(s)  + 12HCl(g) + 6SO₂(g)                                  Violet                          Blue

And again if we look at the changes in the numbers of moles then there are two moles of reactants and 19 moles of products.

It is clear that the entropy of the products is much greater than the entropy of the reactants. 

There are more moles of product (19) than reactant (2) and the products are in a state (mainly gaseous) inherently more disordered than the reactants (solid and liquid).

d) Here is another spontaneous endothermic reaction that between two solids: ammonium chloride (NH₄Cl) and barium hydroxide (Ba(OH)₂)

2NH₄Cl(s)    +     Ba(OH)₂(s)   ⟶   BaCl₂(s) +   2NH₃(g)  +  2H₂O(l)

Carry this reaction out in a small beaker on a white tile with a drop of water underneath the beaker and the beaker will freeze to the tile during the reaction as the temperature can drop to —20^oC.

Notice again that the number of moles product (5) is greater than the number of moles reactant (3) and that the states of the product (gas and liquid) are more disordered than the states of the reactants (solid).

So it would seem that an increase in entropy propels a reaction to go forward.

And they tell us that the endo– or exo– thermic nature of a chemical change cannot be used to determine if the reaction will go or not.

So here is a puzzle:

e) Magnesium burns in oxygen brilliantly and brightly and leaves behind magnesium oxide.

This reaction is of course spontaneous and exothermic but the system becomes more ordered.

The products are more ordered than the reactants.

The reaction moves from 3 moles of reactants to 2 moles of products.

Furthermore, the state of reactants (solid and gas) is more disordered than the state of the products (solid)!!!

Yet the reaction is spontaneous.

How can this be?

Here the significant increase in entropy does not occur in the system but in the surroundings.

Since the burning of magnesium is so overwhelmingly exothermic the energy gain by the surroundings leads to a massive entropy change there.

It seems that to fully understand how entropy change points to the direction of chemical change we must consider both the entropy change in the system and the entropy change in the surroundings!