Spontaneity and Feasibility

students, imagine a reaction like a student deciding whether to walk uphill or downhill 🚶‍♂️⬆️⬇️. Some changes happen naturally, while others need a push from outside. In chemistry, that idea helps explain whether a reaction is spontaneous and whether it is feasible. These words are important in IB Chemistry HL because they help predict if a reaction can happen under given conditions.

Learning objectives:

Explain the main ideas and terminology behind spontaneity and feasibility.
Apply IB Chemistry HL reasoning to judge whether reactions are feasible.
Connect spontaneity and feasibility to energetics, entropy, and reactivity.
Summarize how these ideas fit into the topic of what drives chemical reactions.
Use examples and evidence to support chemical reasoning.

A key idea is this: a reaction can be spontaneous without being fast, and it can be feasible under one set of conditions but not another. That means chemistry is not just about whether something is possible in theory, but whether it is likely to happen on its own in a real situation.

What Spontaneity Means

In thermodynamics, a reaction is spontaneous if it can proceed in the given direction without continuous external energy being supplied. This does not mean it happens instantly. For example, iron rusting is spontaneous in moist air, but it is slow enough that you can see the metal for a long time before major rust appears 🧲.

A common mistake is to think spontaneous means “explosive” or “fast.” That is incorrect. Some spontaneous reactions are extremely slow, such as the formation of diamond from graphite at room conditions. The reverse conversion is also not spontaneous under normal conditions. So spontaneity tells us about the direction a process favors, not its rate.

The word feasible is often used in IB chemistry to mean a reaction can occur under specified conditions. A reaction may be feasible because the overall change in Gibbs free energy is favorable. However, feasibility depends on conditions such as temperature, concentration, and pressure.

Entropy, Enthalpy, and the Big Picture

To understand spontaneity, students, you need two major ideas: enthalpy and entropy.

Enthalpy change, $\Delta H$, tells us whether heat is absorbed or released. If $\Delta H < 0$, the reaction is exothermic and releases heat to the surroundings. If $\Delta H > 0$, it is endothermic and absorbs heat.

Entropy, $\Delta S$, measures the dispersal of energy and matter, often described as the degree of disorder or randomness. A system usually has higher entropy when particles are more spread out or when there are more possible arrangements.

For example:

A gas generally has higher entropy than a liquid.
A liquid generally has higher entropy than a solid.
A reaction that produces more gas particles often has a positive $\Delta S$.

Think about melting ice. Solid water has a very organized structure, while liquid water has particles with more freedom of movement. So melting increases entropy. That is why the sign of $\Delta S$ matters when deciding whether a reaction is favored.

Gibbs Free Energy and Feasibility

The most important equation for spontaneity in IB Chemistry HL is the Gibbs free energy relationship:

$$\Delta G = \Delta H - T\Delta S$$

Here, $\Delta G$ is the Gibbs free energy change, $\Delta H$ is enthalpy change, $T$ is absolute temperature in kelvin, and $\Delta S$ is entropy change.

This equation combines energy and entropy into one useful quantity.

If $\Delta G < 0$, the process is spontaneous in the forward direction and feasible under those conditions.
If $\Delta G > 0$, the forward process is non-spontaneous, so the reverse direction is favored.
If $\Delta G = 0$, the system is at equilibrium.

The term $T\Delta S$ is especially important because temperature can change the outcome. A reaction with a positive $\Delta S$ may become more feasible at higher temperature, because the $T\Delta S$ term becomes larger.

For example, consider a reaction where $\Delta H > 0$ and $\Delta S > 0$. At low temperature, the $\Delta H$ term may dominate, making $\Delta G > 0$. At high temperature, the $T\Delta S$ term may become large enough to make $\Delta G < 0$. So the same reaction can switch from non-spontaneous to spontaneous as temperature rises 🌡️.

Four Common Sign Combinations

students, a strong HL skill is predicting spontaneity from the signs of $\Delta H$ and $\Delta S$.

1. $\Delta H < 0$ and $\Delta S > 0$

This is the most favorable combination. Both terms help make $\Delta G$ negative, so the reaction is spontaneous at all temperatures.

Example: many combustion reactions release heat and produce gases, so they often fit this pattern.

2. $\Delta H > 0$ and $\Delta S < 0$

This is the least favorable combination. Both terms work against spontaneity, so $\Delta G$ is positive at all temperatures.

Example: reactions that absorb heat and create more ordered structures are usually not spontaneous.

3. $\Delta H < 0$ and $\Delta S < 0$

Here, enthalpy helps but entropy opposes. The reaction may be spontaneous at low temperature, where the $\Delta H$ term dominates, but not at high temperature.

4. $\Delta H > 0$ and $\Delta S > 0$

Here, entropy helps but enthalpy opposes. The reaction may become spontaneous at high temperature, where $T\Delta S$ becomes large enough.

This pattern is common in reactions where gases are formed or when a solid becomes more dispersed.

Feasibility Is Condition-Dependent

Feasibility is not a fixed label. It depends on the conditions you choose.

A good example is the Haber process for making ammonia:

$$\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}$$

This reaction is exothermic, so lowering the temperature helps favor ammonia formation. But lower temperatures also slow the reaction rate. Industrial chemists choose a compromise temperature and pressure to make the process practical and economically feasible.

This shows that real chemistry often balances thermodynamics with kinetics. A reaction may be thermodynamically feasible, but if it is too slow, it may not be useful in practice.

Another example is ice melting above $0^\circ\mathrm{C}$. At normal pressure, melting becomes spontaneous because the temperature is high enough for the entropy term to matter. But below $0^\circ\mathrm{C}$, freezing is favored instead.

Spontaneity vs Rate: Why They Are Not the Same

A reaction can be spontaneous and still need a long time to happen because of activation energy. Activation energy is the energy barrier that must be overcome before reactants can form products.

For example, hydrogen and oxygen can react to form water:

$$\mathrm{2H_2(g) + O_2(g) \rightarrow 2H_2O(l)}$$

This reaction is strongly spontaneous under normal conditions, but it does not start by itself in an empty flask because the activation energy is high. Once started with a spark, it can proceed rapidly.

This is why catalysts matter. A catalyst lowers activation energy and increases rate, but it does not change $\Delta G$ or the position of equilibrium. So catalysts do not make a non-spontaneous reaction spontaneous. They only help the reaction reach equilibrium faster.

Using Evidence and Reasoning in IB Chemistry HL

When answering exam questions, students, you should use evidence and chemical reasoning rather than memorized phrases alone.

A strong explanation may include:

the sign of $\Delta H$
the sign of $\Delta S$
the temperature dependence shown by $\Delta G = \Delta H - T\Delta S$
whether the reaction is spontaneous or non-spontaneous under stated conditions
whether the process is fast or slow, if rate is relevant

For example, if a reaction is endothermic but produces more gas molecules, you can explain that $\Delta H > 0$ but $\Delta S > 0$. At high enough temperature, $T\Delta S$ may outweigh $\Delta H$, making $\Delta G < 0$. That is a clear HL-style argument.

If data are provided, always use them. For instance, if a reaction has $\Delta H = -100\,\mathrm{kJ\,mol^{-1}}$ and $\Delta S = -200\,\mathrm{J\,mol^{-1}\,K^{-1}}$, you must convert units before using the equation. Since $\Delta S$ is in joules, convert it to kilojoules:

$$-200\,\mathrm{J\,mol^{-1}\,K^{-1}} = -0.200\,\mathrm{kJ\,mol^{-1}\,K^{-1}}$$

Then at $T = 300\,\mathrm{K}$:

$$\Delta G = -100 - 300(-0.200) = -40\,\mathrm{kJ\,mol^{-1}}$$

Because $\Delta G < 0$, the reaction is spontaneous at $300\,\mathrm{K}$.

Conclusion

Spontaneity and feasibility help chemists predict whether a reaction is thermodynamically favored under specific conditions. The key idea is that $\Delta G = \Delta H - T\Delta S$ combines enthalpy and entropy into one test for spontaneity. A reaction with $\Delta G < 0$ is feasible in the forward direction, but that does not mean it is fast. students, this distinction is central to understanding reactivity in IB Chemistry HL. By using the signs of $\Delta H$ and $\Delta S$, and by considering temperature, you can make strong predictions about whether a reaction is likely to proceed.

Study Notes

Spontaneous means a process can happen in a given direction without continuous external energy input.
Spontaneous does not mean fast.
Feasibility means a reaction can occur under stated conditions.
Entropy, $\Delta S$, describes energy and matter dispersal; higher entropy often means more disorder.
Enthalpy, $\Delta H$, shows whether heat is absorbed or released.
Gibbs free energy is given by $\Delta G = \Delta H - T\Delta S$.
If $\Delta G < 0$, the forward reaction is spontaneous.
If $\Delta G > 0$, the forward reaction is non-spontaneous.
If $\Delta G = 0$, the system is at equilibrium.
Temperature changes feasibility because it affects the $T\Delta S$ term.
Catalysts change reaction rate, not $\Delta G$.
Thermodynamic feasibility and reaction rate are different ideas, and both matter in real chemistry.