13B.12-13B.17 - Entropy And Feasibility | Edexcel A-Level Chemistry

Explain how endothermic changes can occur and why an exothermic reaction can make its reacting particles more ordered. Calculate entropy changes for the system and surroundings, then combine them to judge the direction of change.

Why Enthalpy Is Not Enough

An endothermic process can still happen at room temperature. When ammonium nitrate crystals dissolve in water, the mixture becomes colder, so energy has been taken from the surroundings into the system. The change is not driven by enthalpy release, yet it can still proceed because the particles become much more dispersed.

Keep three ideas separate from the start:

Term	Meaning in this lesson	Sign clue
$\Delta H$	enthalpy change of the system at constant pressure	negative for exothermic, positive for endothermic
$\Delta S_{\mathrm{system}}$	entropy change of the reacting chemicals or dissolving substance	often follows particle dispersal and moles of gas
$\Delta S_{\mathrm{surroundings}}$	entropy change caused by heat entering or leaving the surroundings	positive when the surroundings gain heat

The natural direction of chemical change is the direction in which total entropy increases. That does not mean the system entropy must increase on its own. A reaction such as burning magnesium can make the system more ordered by using up oxygen gas, but the large heat release can make the surroundings much more disordered.

Endothermic does not mean impossible

Enthalpy is only the heat-transfer part of the story. An endothermic process can still have a positive total entropy change if particle dispersal in the system is large enough.

Recognising Entropy Changes

Entropy connects the freedom of particles with the number of ways their energy can be distributed.

Entropy, $S$

A measure of disorder: how spread out the particles and their energy are, not whether a substance looks messy. Standard molar entropies are in $\mathrm{J\,mol^{-1}\,K^{-1}}$ .

Three common patterns decide the sign of $\Delta S_{\mathrm{system}}$ :

Change	Entropy reasoning	Typical sign for $\Delta S_{\mathrm{system}}$
Change of state	particles have more freedom in solid → liquid → gas	positive for melting, boiling and subliming; negative for condensing and freezing
Dissolving an ionic lattice	fixed ions in a solid lattice separate and disperse among water molecules	often positive, although hydration can order nearby water molecules
Reaction with changing moles	more independent particles, especially more gas molecules, gives more disorder	positive if gas moles increase; negative if gas moles decrease

The word "system" matters. If ice melts, the system entropy increases because water molecules can move more freely in liquid water. If steam condenses, the system entropy decreases because gaseous water molecules lose freedom and become closer together.

Now apply the same model to the specification examples:

Example	Main entropy point	Enthalpy link
Ammonium nitrate dissolving in water	solid ions become dispersed aqueous ions, so $\Delta S_{\mathrm{system}}$ is positive	the process is endothermic, so $\Delta S_{\mathrm{surroundings}}$ is negative
Ethanoic acid reacting with ammonium carbonate	carbon dioxide gas is produced and particles become more dispersed	the total result depends on both particle dispersal and heat transfer
Magnesium burning in air	oxygen gas is used up to form solid magnesium oxide, so $\Delta S_{\mathrm{system}}$ is negative	the reaction is very exothermic, so $\Delta S_{\mathrm{surroundings}}$ is large and positive
Barium hydroxide octahydrate mixed with ammonium chloride	two solids produce ammonia gas and liquid/aqueous material, so $\Delta S_{\mathrm{system}}$ increases greatly	the reaction is strongly endothermic, so the surroundings lose heat

The ethanoic acid–ammonium carbonate reaction is also endothermic: the mixture cools while carbon dioxide escapes. The positive system entropy outweighs the negative surroundings term when it proceeds. A simplified equation is

\ce{2CH3COOH(aq) + (NH4)2CO3(s) -> 2CH3COONH4(aq) + H2O(l) + CO2(g)}

For the solid mixture:

\ce{Ba(OH)2.8H2O(s) + 2NH4Cl(s) -> BaCl2(aq) + 2NH3(g) + 10H2O(l)}

Both liquid formation and ammonia dispersal increase entropy. This demonstration needs ventilation and suitable handling of toxic barium compounds; smelling the ammonia directly is not an identification method.

Calculating The System Entropy Change

To calculate the entropy change of the system, use the balanced equation and the standard molar entropies of the substances:

Entropy change of the system

\Delta S_{\mathrm{system}} = \textstyle\sum S(\text{products}) - \sum S(\text{reactants})

Each $S$ in $\mathrm{J\,mol^{-1}\,K^{-1}}$ , multiplied by its coefficient in the balanced equation.

The sigma symbol means "add up". Multiply each entropy value by the balancing number in the equation before subtracting. Standard molar entropy values are normally given in $\mathrm{J\,mol^{-1}\,K^{-1}}$ , so the answer for $\Delta S_{\mathrm{system}}$ has the same unit for the equation as written.

Worked example: magnesium oxide formation.

For the reaction:

\ce{Mg(s) + 1/2O2(g) -> MgO(s)}

Use these standard molar entropies:

Substance	$S$ / $\mathrm{J\,mol^{-1}\,K^{-1}}$
$\ce{Mg(s)}$	32.7
$\ce{O2(g)}$	205.0
$\ce{MgO(s)}$	26.9

Substitute into the equation:

\Delta S_{\mathrm{system}} = S[\ce{MgO(s)}] - (S[\ce{Mg(s)}] + 1/2 S[\ce{O2(g)}])

\Delta S_{\mathrm{system}} = 26.9 - (32.7 + 0.5\times 205.0)

\Delta S_{\mathrm{system}} = 26.9 - 135.2

\Delta S_{\mathrm{system}} = -108.3 \mathrm{J\,mol^{-1}\,K^{-1}}

The negative sign is chemically sensible. The reaction removes half a mole of gas and produces an ordered ionic solid, so the system becomes less disordered.

Continue this lesson.

You’re previewing NovaLearn without an account. Create a free account to read the rest.

Create free account

Last Accessed

Foundation Chemistry (Topics 1-10, shared with AS)

Advanced Chemistry (Topics 11-19)

13B.12-13B.17 - Entropy And Feasibility

Why Enthalpy Is Not Enough

Recognising Entropy Changes

Calculating The System Entropy Change

Continue this lesson.

Learn faster with Nova