Spontaneous Reactions: Enthalpy and Entropy Chemistry Tutorial

Key Concepts

A spontaneous chemical reaction or physical change is one that, once started, will continue without any outside help.

A nonspontaneous chemical reaction or physical change is one that requires assistance to keep going.

There are two forces which drive chemical reactions and physical changes:
⚛ enthalpy

⚛ entropy

Chemical reactions and physical changes proceed spontaneously in order to:
⚛ minimise enthalpy

⚛ maximise entropy

Comparison of spontaneous and nonspontaneous chemical reactions:

	Enthalpy Change (ΔH)	AND	Entropy Change (ΔS)
Always Spontaneous	negative (exothermic)	AND	positive (increased entropy)
Always Nonspontaneous	positive (endothermic)	AND	negative (decreased entropy)

Comparison of reversible and irreversible reactions:

		ΔH = - (exothermic)	ΔH = + (endothermic)
		enthalpy change
entropy change	ΔS = + (increase)	irreversible forward reaction	reversible reaction
entropy change	ΔS = - (decrease)	reversible reaction	does not proceed

We cannot predict the rate of a chemical reaction by determining whether the reaction is spontaneous or nonspontaneous.
Some spontaneous reactions are fast, others are slow.

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Enthalpy as a Driving Force of Chemical Reactions

Chemical reactions tend to proceed spontaneously in the direction that allows for

enthalpy of the system to be minimised

entropy of the system to be maximised

The enthalpy of a chemical system will be minimised when the enthalpy of the products (H_products) is less than the enthalpy of the reactants (H_reactants), that is:

H_products < H_reactants

The enthalpy change of a chemical system (ΔH) is defined as:

ΔH = H_products - H_reactants

so for a reaction in which H_products < H_reactants

ΔH = H_products - H_reactants = a negative number = - kJ mol^-1

A reaction in which the sign of the enthalpy change, ΔH, for the reaction is negative, is called an exothermic reaction.
Heat energy is a product of the exothermic reaction.

A reaction is therefore more likely to be driven in the forward direction, be spontaneous in the forward direction, if it is an exothermic reaction (that is, if it releases heat energy).

But what about entropy? Entropy is the other driving force of a chemical reaction.

Entropy as a Driving Force of Chemical Reactions

Chemical reactions tend to proceed spontaneously in the direction that allows for

enthalpy of the system to be minimised

entropy of the system to be maximised

The second law of thermodynamics tells us that the entropy of the universe is constantly increasing.
Therefore chemical reactions should proceed spontaneously in the direction that increases the entropy of the system.

We can recognise an increase in the entropy of a chemical system if:

there are more moles of gaseous product than there are gaseous reactants

there are more moles of ions in solution on the product side than on the reactant side⁽¹⁾

If there is an increase in entropy then the entropy of the products (S_products) is greater than the entropy of the reactants (S_reactants):

S_products > S_reactants

Entropy change for the system (ΔS) is defined as the entropy of the products minus the entropy of the reactants:

ΔS = S_products - S_reactants

Reactions are driven towards maximum entropy, that is, S_products > S_reactants, then

ΔS = S_products - S_reactants = a positive number = +

A reaction is most likely to be spontaneous if it is exothermic AND there is an increase in entropy of the system.
Put another way, a reaction is most likely to be spontaneous if ΔH is negative AND ΔS is positive.

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Spontaneous and Nonspontaneous Reactions

A reaction which is exothermic (ΔH negative) and results in an increase in the entropy of the system (ΔS positive) will always be spontaneous.

Consider the combustion of a fuel like ethanol (C₂H₅OH_(l)) in oxygen gas (O_2(g)) in air. The products of the combustion reaction are carbon dioxide gas (CO_2(g)) and water (H₂O_(g) at temperatures above 100°C). This combustion reaction releases 1368 kJ of heat energy per mole of ethanol consumed in the reaction. We can represent the combustion of ethanol in a balanced chemical reaction as shown below:

C₂H₅OH_(l) + 3O_2(g) → 2CO_2(g) + 3H₂O_(g) ΔH = -1368 kJ mol^-1

The combustion of ethanol is a spontaneous chemical reaction because, as the reaction proceeds from left to right:

enthalpy is minimised because heat is a product of the reaction
(enthalpy of product molecules < enthalpy of reactant molecules, so ΔH is negative)

entropy has increased
(there are 3 moles of gas on the left side of the equation and 2 + 3 = 5 moles of gas on the right hand side of the equation)

Ethanol can be used successfully as a fuel because once the combustion reaction begins (using a spark for instance to overcome the activation energy) it will keep going without any further help (until the ethanol fuel runs out, or, the oxygen gas runs out!), and this is the definition of a spontaneous reaction!

If the forward reaction is spontaneous, does that mean the reverse reaction is nonspontaneous?
The reverse reaction would require carbon dioxide gas and water vapor reacting to produce ethanol and oxygen gas.
When we reverse the chemical equation we must also reverse the sign of the enthalpy change for the reaction, that is, this reaction will absorb 1368 kJ of energy per mole of ethanol produced:

2CO_2(g) + 3H₂O_(g) → C₂H₅OH_(l) + 3O_2(g) ΔH = +1368 kJ mol^-1

This reaction is NOT spontaneous, it is nonspontaneous, because:

enthalpy has increased NOT decreased
(the reaction absorbs energy so H_products > H_reactants, reaction is endothermic, ΔH is positive)

entropy of the system has decreased NOT increased
(5 gaseous molecules on the left side but only 3 on the right hand side).

It's probably just as well that this reaction is nonspontaneous, if lightning during a thunderstorm could supply enough energy to start the reaction then the carbon dioxide gas and water vapor in the atmosphere would begin to form ethanol, and it would rain alcohol!

To summarise,

(i) A reaction will always be spontaneous if:

ΔH is negative (exothermic reaction)

AND

ΔS is positive (entropy increases)

(ii) A reaction will always be nonspontaneous if:

ΔH is positive (endothermic reaction)

AND

ΔS is negative (entropy decreases)

	Enthalpy Change (ΔH)	AND	Entropy Change (ΔS)
Always Spontaneous	negative (exothermic)	AND	positive (increased entropy)
Always Nonspontaneous	positive (endothermic)	AND	negative (decreased entropy)

Driving Forces and Spontaneity

Chemical reactions tend to proceed spontaneously in the direction that allows for

enthalpy of the system to be minimised

entropy of the system to be maximised

(i) A reaction will always be spontaneous if:

ΔH is negative (exothermic reaction)

AND

ΔS is positive (entropy increases)

(ii) A reaction will always be nonspontaneous if:

ΔH is positive (endothermic reaction)

AND

ΔS is negative (entropy decreases)

Can an endothermic reaction (ΔH positive) ever be spontaneous?

Yes, IF the driving force towards increased entropy is great enough!

For example, sodium nitrate dissolves SPONTANEOUSLY in water to form an aqueous solution, even though the reaction is endothermic, that is, the vessel holding the solution gets cooler as the dissolution reaction absorbs heat energy from its surroundings.

NaNO_3(s) → Na⁺_(aq) + NO₃^-_(aq) ΔH = +20.50 kJ mol^-1

We expect the forward reaction to proceed spontaneously on the basis that the entropy of the system has increased due to the formation of mobile ions in solution (ΔS is positive).
But, the forward reaction is not favoured energetically, that is, the enthalpy of the products will be greater than the enthalpy of the reactant molecules because energy has been absorbed (ΔH is also positive).
Because we know the reaction occurs spontaneously, we can watch the sodium nitrate crystals dissolve in the liquid water, this tells us that the main driving force for this reaction is the tendency to maximise entropy.

Can a reaction be spontaneous if there is a decrease in entropy (ΔS is negative)?

Yes, if the driving force towards minimum enthalpy is great enough!

For example, iron has a tendency to rust under normal atmospheric conditions, that is, the reaction between solid iron (Fe_(s)) and oxygen gas (O_2(g)) in moist air to produce iron oxides (Fe₂O_3(s)) occurs spontaneously:

4Fe_(s) + 3O_2(g) → 2Fe₂O₃ ΔH = -1644 kJ mol^-1

Because the reaction is exothermic we are not surprised that the reaction occurs spontaneously, except that the entropy of the system will be decreased in the forward direction!
On the left hand side of the equation there are 3 gaseous molecules, and there are no gaseous molecules on the right hand side of the equation, so the entropy of the system has decreased.
So why is this reaction spontaneous? Because the main driving force for this reaction is the minimisation of energy.

If a reaction is endothermic, it can still be spontaneous IF the tendency towards maximum entropy is the main driving force for the reaction.

If a reaction results in a decrease in the entropy of the system, it can still be spontaneous IF the tendency towards minimum enthalpy is the main driving force for the reaction.

And this brings us to the idea of reversible chermical reactions...

Driving Forces and Reversible Reactions

Chemical reactions tend to proceed spontaneously in the direction that allows for

enthalpy of the system to be minimised

entropy of the system to be maximised

(i) A reaction will always be spontaneous if:

ΔH is negative (exothermic reaction)

AND

ΔS is positive (entropy increases)

This reaction will proceed to completion and will not be reversible to any appreciable extent.

Example:
2HCl_(aq) + Mg_(s) → MgCl_2(aq) + H_2(g) ΔH = -
Reaction is spontaneous and goes to completion because:
(i) enthalpy is minimised (ΔH -)
(ii) entropy increases (ΔS +)

(ii) A reaction will always be nonspontaneous if:

ΔH is positive (endothermic reaction)

AND

ΔS is negative (entropy decreases)

This reaction will not proceed.

Example:
MgCl_2(aq) + H_2(g) → 2HCl_(aq) + Mg_(s) ΔH = +
Reaction is nonspontaneous and does NOT occur because:
(i) enthalpy is maximised NOT minimised (ΔH +)
(ii) entropy decreases NOT increases (ΔS -)

Other combinations of driving forces lead to a reversible reaction in which a balance is struck, or a compromise is reached, between these two opposing driving forces:

enthalpy increases and entropy increases (ΔH + and ΔS +)
Example: CaCO_3(s) ⇋ CaO_(s) + CO_2(g) ΔH = +
Entropy is maximised, increases, in the forward direction, so the forward reaction is favoured.
Enthalpy is minimised, ΔH = -, in the reverse direction, so the reverse reaction is favoured.
Since the two driving forces act in opposite directions, this reaction is reversible.

enthalpy decreases and entropy decreases (ΔH - and ΔS -)
Example: 2Mg_(s) + O_2(g) ⇋ 2MgO_(s) ΔH = -
Entropy is maximised, increases, in the reverse direction, so the reverse reaction is favoured.
Enthalpy is minimised, ΔH = -, in the forward direction, so the forward reaction is favoured.
Since the two driving forces act in opposite directions, this reaction is reversible.

In summary:

		ΔH = - (exothermic)	ΔH = + (endothermic)
		enthalpy change
entropy change	ΔS = + (increase)	irreversible forward reaction	reversible reaction
entropy change	ΔS = - (decrease)	reversible reaction	does not proceed

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Worked Example of Entropy and Enthalpy as Driving Forces for a Chemical Reaction

(using the StoPGoPS approach to Problem Solving)

Question: Chris the chemist likes to cook. One particular recipe called for the addition of solid sodium hydrogen carbonate (sodium bicarbonate, NaHCO_3(s)) to an aqueous solution of citric acid (H₃C₆H₅O_7(aq)) in a bottle with a lid. Chris added the sodium bicarbonate to the citric acid in the bottle and quickly sealed it. Bubbles of carbon dioxide gas (CO_2(g)) caused the solution to foam up, but not only that! Chris was intrigued to find that the bottle became noticably colder.
Explain what is driving this spontaneous chemical reaction forward.

STOP	STOP! State the Question.
	What is the question asking you to do? Explain which force(s) are driving the chemical reaction forward.
PAUSE	PAUSE to Prepare a Game Plan
	(1) What information (data) have you been given in the question? (a) Reaction absorbs energy from the surroundings (gets cooler) (b) Reaction between the solid and aqueous solution produces a gas (2) What is the relationship between what you know and what you need to find out? (i) Irreversible reaction: minimise enthalpy (exothermic) and maximise entropy (entropy increases) (ii) No reaction: maximise enthalpy (endothermic) and minimise entropy (entropy decreases) (iii) Reversible reactions: (I) forward reaction: minimise enthalpy (exothermic) and minimise entropy: minimising enthalpy drives reaction forward (II) forward reaction: maximise enthalpy (endothermic) and maximise entropy: maximising entropy drives reaction forward
GO	GO with the Game Plan
	(a) Endothermic reaction (ΔH +) because reaction absorbed energy from the surroundings (got cooler) (b) Entropy increases (ΔS +) because gas molecules were produced (there were no gaseous reactants) (iii) (II) reaction is reversible with the drive to maximise entropy in the forward direction greater than the drive to minimise enthalpy in the reverse direction.
PAUSE	PAUSE to Ponder Plausibility
	Is your answer plausible? Since the reaction is endothermic (ΔH +) the forward reaction is not favoured, that is, enthalpy is maximised in the forward direction. Enthalpy will be minimised in the reverse direction, that is, enthalpy drives the reaction in the reverse direction. Enthalpy is NOT the force driving the reaction forward. Therefore, if the reaction is spontaneous (as it must be if you can see bubbles of gas forming), the drive towards maximising entropy must be driving the reaction forward. If entropy also favoured the reverse reaction, then both enthalpy and entropy would drive the reverse reaction and the forward reaction would not be occurring to any appreciable extent (that is, you wouldn't see bubbles of gas forming).
STOP	STOP! State the Solution
	Since this reaction is endothermic, the drive to maximise entropy is forcing the reaction in the forward direction.

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Footnotes:

(1) For some ionic solids, especially those with small highly charged ions like Al³⁺ or Mg²⁺, dissolving in water can actually increase the order (decrease the entropy) of the water molecules more than the increase in the disorder of the ions (ordered lattice to mobile ions in solution), so the entropy of the whole system may decrease overall.