In dynamic equilibrium:

The forward and reverse rates are equal

The concentrations of reactants and products are equal

Only the forward reaction happens

Static and Dynamic Equilibrium | HSC Chemistry Module 5

In short: In a reversible reaction in a closed system, equilibrium is reached when the forward and reverse reactions go at the same rate. This is dynamic equilibrium: both reactions keep going, but the amounts of each substance stay the same. In static equilibrium, all reactions have stopped.

Reversible reactions

Most reactions you met in Year 10 go one way. Burn a match and you cannot turn the ash and smoke back into a match.

A reversible reaction can go both ways. We write it with a double arrow:

$N_{2} O_{4} (g) ⇌ 2N O_{2} (g)$

The forward reaction goes left to right.
The reverse reaction goes right to left.

Colourless $N_{2} O_{4}$ breaks into brown $N O_{2}$ , and brown $N O_{2}$ joins back up into $N_{2} O_{4}$ , at the same time.

Open and closed systems

An open system swaps both matter and energy with its surroundings. An open beaker of fizzy drink loses carbon dioxide gas into the air.
A closed system swaps energy but not matter. A sealed bottle keeps all its gas inside but can still warm up or cool down.

Equilibrium can only be reached in a closed system. If a product escapes (like a gas bubbling out of an open beaker), the reverse reaction cannot happen, so the reaction just runs to the end.

Dynamic equilibrium

Put $N_{2} O_{4}$ in a sealed flask and watch what happens:

At the start, only the forward reaction can happen, and it is fast because there is lots of $N_{2} O_{4}$ .
As $N_{2} O_{4}$ is used up, the forward reaction slows down.
As $N O_{2}$ builds up, the reverse reaction speeds up.
Soon the two rates become equal. From then on, the amounts of each gas stay the same.

This state is dynamic equilibrium:

The forward and reverse reactions are both still happening.
Their rates are equal.
The concentrations stay constant (but are usually not equal to each other).
Macroscopic properties (colour, pressure, temperature) stay constant.

	Static equilibrium	Dynamic equilibrium
Are reactions happening?	No, they have stopped	Yes, both directions
Rates	Both zero	Forward = reverse, not zero
Example	A fully burnt-out fire	$N_{2} O_{4}$ and $N O_{2}$ in a sealed flask

In static equilibrium, nothing is reacting at all. A finished combustion, or diamond slowly "turning into" graphite at room temperature (far too slow to notice), is static.

Non-equilibrium systems

Some reactions are reversible on paper but never reach equilibrium in real life:

Combustion gives out lots of energy and the gases escape. It is effectively one way.
Photosynthesis and respiration are the reverse of each other, but they happen in different places, with different enzymes, so they are not an equilibrium.

Heating blue hydrated copper(II) sulfate turns it white as the water leaves. Adding water turns it blue again. This shows the reaction is reversible, but because the water escapes as steam in an open tube, it is not an equilibrium. Cobalt(II) chloride crystals (pink when hydrated, blue when dry) show the same thing.

Enthalpy and entropy

Two things decide whether a reaction happens by itself.

Enthalpy change $Δ H$ is the heat energy taken in or given out.

Exothermic: $Δ H$ is negative. Heat is given out. Nature favours this.
Endothermic: $Δ H$ is positive. Heat is taken in.

Entropy $S$ measures how spread out (disordered) energy and particles are. Nature favours more disorder, so a positive entropy change $Δ S$ helps a reaction happen.

Entropy goes up ( $Δ S > 0$ ) when:

a solid melts, or a liquid boils (solid < liquid < gas),
a solid dissolves,
a reaction makes more moles of gas than it uses.

Gibbs free energy

Gibbs free energy combines both ideas:

$Δ G = Δ H - T Δ S$

where $T$ is the temperature in kelvin ( $T = ° C + 273$ ).

$Δ G < 0$ : the reaction is spontaneous (it can happen by itself).
$Δ G > 0$ : it is not spontaneous. It needs a steady supply of energy.
$Δ G = 0$ : the system is at equilibrium.

$Δ H$	$Δ S$	Spontaneous?
−	+	Always
+	−	Never
−	−	Only at low temperature
+	+	Only at high temperature

Watch the units. $Δ H$ is usually in kJ, but $Δ S$ is in J/K. Divide $Δ S$ by 1000 before you use the formula.

Photosynthesis has $Δ H > 0$ and $Δ S < 0$ (six gas molecules become one solid sugar and six gas molecules, and energy is stored). So $Δ G$ is always positive. That is why plants need a constant supply of light energy.

Equilibrium

Reversible reactions

Double arrow
Forward and reverse

Systems

Open: matter and energy escape
Closed: energy only
Equilibrium needs closed

Dynamic

Rates equal, not zero
Concentrations constant
Properties constant

Static

Reactions stopped

Spontaneity

ΔH negative helps
ΔS positive helps
ΔG = ΔH − TΔS
ΔG < 0 spontaneous

Year 12The turning temperature

When $Δ H$ and $Δ S$ have the same sign, the reaction changes from not spontaneous to spontaneous at the temperature where $Δ G = 0$ :

$T = \frac{Δ H}{Δ S}$

Example. Heating limestone: $CaC O_{3} (s) \to CaO (s) + C O_{2} (g)$ , with $Δ H = + 178$ kJ and $Δ S = + 161$ J/K.

$T = \frac{178 000}{161} = 1106$ K, or about 833 °C. Above this, $Δ G < 0$ and the limestone breaks down by itself.

Entropy change from tables. $Δ S = \sum S (products) - \sum S (reactants)$ , multiplying each value by its number in the equation. For $2S O_{2} + O_{2} \to 2S O_{3}$ with $S$ values 248, 205 and 257 J/K/mol:

$Δ S = 2 (257) - [2 (248) + 205] = 514 - 701 = - 187$ J/K. Three gas molecules become two, so entropy falls, as expected.

Below or above? If $Δ H$ and $Δ S$ are both negative, the reaction is spontaneous below $T = \frac{Δ H}{Δ S}$ . For $Δ H = - 50.0$ kJ and $Δ S = - 150$ J/K, that is below 333 K.

Reading a graph of $Δ G$ against $T$ . $Δ G = Δ H - T Δ S$ is a straight line. Its intercept at $T = 0$ is $Δ H$ and its gradient is $- Δ S$ . A line falling from positive values means $Δ S > 0$ , and where it crosses zero the reaction becomes spontaneous.

Two values of $Δ G$ . If $Δ G = - 20$ kJ at 300 K and $- 40$ kJ at 500 K, then $Δ S = \frac{- 20 - ( - 40 )}{500 - 300} = 0.10$ kJ/K, and $Δ H = - 20 + 300 \times 0.10 = + 10$ kJ.

Concentrations from a graph. Use the mole ratio. In $A ⇌ 2B$ , if $[A]$ falls by 0.10 mol/L, $[B]$ rises by 0.20 mol/L.

Heat from a fuel. The heat needed is $q = m c Δ T$ . Heating 2.0 kg of water by 60 °C needs $2.0 \times 4.18 \times 60 = 502$ kJ. Carbon gives 394 kJ per mole, so $\frac{502}{394} = 1.27$ mol, or 15.3 g of carbon.

Quick summary

A reversible reaction goes both ways. Equilibrium needs a closed system.
Dynamic equilibrium: forward rate = reverse rate (not zero), concentrations and properties stay constant.
Static equilibrium: all reactions have stopped.
Combustion and photosynthesis/respiration are not equilibrium systems.
$Δ H < 0$ (exothermic) and $Δ S > 0$ (more disorder) both favour a reaction.
$Δ G = Δ H - T Δ S$ , with $T$ in kelvin and $Δ S$ in kJ/K. $Δ G < 0$ means spontaneous.

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In dynamic equilibrium:
1. A Both reactions have stopped
2. B The forward and reverse rates are equal
3. C The concentrations of reactants and products are equal
4. D Only the forward reaction happens
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B: The forward and reverse rates are equal
Both reactions keep going at the same rate, so the amounts stay constant.
Equilibrium can only be reached in:
1. A An open system
2. B A closed system
3. C A system with no reactants
4. D A system that is being heated
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B: A closed system
If matter can escape, the reverse reaction cannot keep up.
A closed system can exchange:
1. A Matter only
2. B Energy only
3. C Both matter and energy
4. D Neither matter nor energy
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B: Energy only
A sealed flask can warm up or cool down but keeps its chemicals inside.

Static and Dynamic Equilibrium

Reversible reactions

Open and closed systems

Dynamic equilibrium

Non-equilibrium systems

Enthalpy and entropy

Gibbs free energy

Quick summary

Quiz

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