Gibbs Free Energy and Spontaneity

What Makes a Process Spontaneous?

Definition

Spontaneity

A chemical reaction or physical process is spontaneous if it occurs without external intervention under a given set of conditions.

To determine spontaneity, we use the Gibbs free energy equation:

$Δ G = Δ H - T Δ S$

Where:

$Δ G$ : Gibbs free energy change ( $k J m o l^{- 1}$ )
$Δ H$ : Enthalpy change ( $k J m o l^{- 1}$ )
$Δ S$ : Entropy change ( $k J K^{- 1} m o l^{- 1}$ )
$T$ : Temperature (K)

Spontaneity and $Δ G$ :

If $Δ G < 0$ : The process is spontaneous.
If $Δ G = 0$ : The system is at equilibrium.
If $Δ G > 0$ : The process is non-spontaneous under the given conditions.

Example

Combustion of methane ( ${CH}_{4} + 2 O_{2} \to {CO}_{2} + 2 H_{2} O$ ) is highly exothermic ( $Δ H < 0$ ) and increases disorder ( $Δ S > 0$ ).
Hence, $Δ G$ is negative, making the reaction spontaneous at all temperatures.

Common Mistake

Many students mistakenly assume that all exothermic reactions ( $Δ H < 0$ ) are spontaneous. While this is often true, you must also consider $Δ S$ and $T$ . For example, freezing water is exothermic but non-spontaneous above 0°C because the entropy decreases ( $Δ S < 0$ ).

Temperature Dependence of Spontaneity

The interplay between $Δ H$ , $Δ S$ , and $T$ determines whether a reaction is spontaneous. Let’s break this down into four scenarios:

$Δ H$	$Δ S$	$Δ G$	Spontaneity
< 0	> 0	Always negative	Always spontanous
> 0	< 0	Always positive	Always non-spontaneous
< 0	< 0	Negative at low $T$ , positive at high $T$	Spontaneous at low $T$
> 0	> 0	Negative at high $T$ , positive at low $T$	Spontaneous at high $T$

Determining the Temperature at Which $Δ G = 0$

At the threshold temperature, $Δ G = 0$ , and the system is at equilibrium.
Rearranging the Gibbs free energy equation gives:

$T = \frac{Δ H}{Δ S}$

This temperature marks the transition between spontaneity and non-spontaneity.

Example

Consider the decomposition of calcium carbonate ( ${CaCO}_{3} \to CaO + {CO}_{2}$ ) with $Δ H = 178 {kJ mol}^{- 1}$ and $Δ S = 161 {J K}^{- 1} {mol}^{- 1}$ .

Convert $Δ S$ to kJ: $161 {J K}^{- 1} = 0.161 {kJ K}^{- 1}$ .

Threshold temperature: $T = \frac{Δ H}{Δ S} = \frac{178}{0.161} = 1106 K$ .

The reaction becomes spontaneous above 1106 K.

Tip

Always convert entropy values from J to kJ when using the Gibbs free energy equation to maintain consistent units.

Reflection

Theory of Knowledge

The term spontaneous can be misleading—while a negative $Δ G$ predicts feasibility, external factors like temperature or catalysts can alter outcomes. This raises questions:

How reliable are scientific models in predicting natural behavior?
Can complex systems be fully described by mathematical formulas?

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R1.4.3 Spontaneity and Gibbs free energy (Higher Level Only)

Gibbs Free Energy and Spontaneity

What Makes a Process Spontaneous?

Spontaneity and $Δ G$ :

Temperature Dependence of Spontaneity

Determining the Temperature at Which $Δ G = 0$

Reflection

You've read 2/2 free chapters this week.

Introduction to Gibbs Free Energy

R1.4.3 Spontaneity and Gibbs free energy (Higher Level Only)

Gibbs Free Energy and Spontaneity

What Makes a Process Spontaneous?

Spontaneity and ΔG:

Temperature Dependence of Spontaneity

Determining the Temperature at Which ΔG=0

Reflection

You've read 2/2 free chapters this week.

Introduction to Gibbs Free Energy

Spontaneity and $Δ G$ :

Determining the Temperature at Which $Δ G = 0$