# Thermodynamic favorability versus rate

> AP Chemistry · Unit 9: Applications of Thermodynamics
> Source: https://www.owlsprep.com/study/ap-chemistry-u9-thermodynamic-favorability-versus-rate/

This module covers the key AP Chemistry distinction between thermodynamic favorability (spontaneity, determined by ΔG) and reaction rate (determined by activation energy Ea), including control types and catalyst effects for Unit 9.

**Prerequisites:** [Gibbs free energy change (ΔG) and spontaneity](https://www.owlsprep.com/study/ap-chemistry-gibbs-free-energy/); [Reaction rate theory and activation energy](https://www.owlsprep.com/study/ap-chemistry-collision-theory-activation-energy/)

## Learning objectives

- Distinguish thermodynamic favorability from reaction rate
- Explain kinetic vs thermodynamic control of competing reactions
- Predict catalyst effects on favorability and reaction rate
- Identify and avoid common AP exam misconceptions on this topic

## Core Distinction: Favorability vs Rate

Thermodynamic favorability (or spontaneity) describes whether a reaction can proceed without continuous external energy input, determined solely by the overall difference in Gibbs free energy between reactants and products. Reaction rate describes how fast a reaction proceeds to products, determined by the height of the activation energy barrier. Favorability tells you only if a reaction *can* occur, not how fast it will occur.

**Thermodynamic favorability** — A reaction that proceeds without continuous external energy input, dependent only on the free energy difference between reactants and products, independent of reaction pathway.

*Notation:* $\Delta G < 0$ = favorable

*Example:* Diamond to graphite conversion at 25°C is thermodynamically favorable.

Reaction rate, by contrast, depends on the reaction pathway, not just the initial and final states. Rate is governed by activation energy, the minimum energy colliding reactants need to reach the transition state. From the Arrhenius relationship, rate decreases exponentially as $E_a$ increases: even a very negative $\Delta G$ can result in an immeasurably slow reaction if $E_a$ is very large.

$$\Delta G = G_{\text{products}} - G_{\text{reactants}}$$

**Worked example:** For the reaction $2 \text{H}_2(g) + \text{O}_2(g) \rightarrow 2 \text{H}_2\text{O}(l)$ at 25°C, $\Delta G^\circ = -474$ kJ/mol and $E_a \approx 400$ kJ/mol. Which statement correctly describes the reaction?
1. It is thermodynamically unfavorable and kinetically fast
2. It is thermodynamically favorable and kinetically slow at 25°C without a catalyst
3. It is thermodynamically favorable and kinetically fast at all conditions
4. It is thermodynamically unfavorable and kinetically slow

1. First, assess thermodynamic favorability: $\Delta G^\circ$ is negative, so the reaction is favorable. Eliminate options 1 and 4.
2. Next, relate $E_a$ to rate: typical $E_a$ for a fast reaction at 25°C is < 50 kJ/mol. An activation energy of 400 kJ/mol is extremely high.
3. Without a catalyst to lower $E_a$, very few collisions between H₂ and O₂ have enough energy to overcome the barrier at 25°C.
4. The correct description is option 2: thermodynamically favorable, kinetically slow without a catalyst.

> **Exam tip:** On any AP question asking about rate vs favorability, always check ΔG first for favorability, then Ea for rate. Never assume a negative ΔG means a fast reaction—this is the most common exam trap.

## Kinetic vs Thermodynamic Control of Competing Reactions

When the same starting materials can form two different products via two competing reaction pathways, the final product mixture depends on whether the reaction is under kinetic or thermodynamic control, determined by reaction conditions and reversibility.

**Kinetic Control** — Reaction conditions where only lower activation energy barriers are accessible, and reactions are not reversible. The major product is the faster-forming product, regardless of thermodynamic stability.

*Example:* Typically occurs at low temperatures

**Thermodynamic Control** — Reaction conditions where all activation barriers are accessible, and all reactions are reversible. The system reaches equilibrium, so the major product is the more thermodynamically stable (lower ΔG) product.

*Example:* Typically occurs at high temperatures

**Worked example:** Starting from 1 mol of reactant A, two competing reactions occur: $A \rightarrow B$ ($\Delta G = -12$ kJ/mol, $E_a = 30$ kJ/mol) and $A \rightarrow C$ ($\Delta G = -45$ kJ/mol, $E_a = 75$ kJ/mol). Predict the major product at low temperature (only barriers < 40 kJ/mol are accessible, no reversal) and at high temperature (all barriers accessible, fully reversible).

1. First, identify the kinetically favored product: this is the product with lower $E_a$. B has $E_a = 30$ kJ/mol < 75 kJ/mol for C, so B forms faster and is kinetically favored.
2. Identify the thermodynamically favored product: this is the product with more negative $\Delta G$. C has $\Delta G = -45$ kJ/mol < -12 kJ/mol for B, so C is more stable and thermodynamically favored.
3. At low temperature: only barriers < 40 kJ/mol are accessible, so only B can form, and no reversal occurs. Major product = B, under kinetic control.
4. At high temperature: all barriers are accessible, and reactions are reversible. The system reaches equilibrium, so the more stable C is the major product, under thermodynamic control.

> **Exam tip:** On FRQ, always explicitly connect control type to conditions: kinetic control = low temperature, irreversibility, only low Ea barriers accessible. Do not just state "low T gives kinetic product" without this reasoning to earn full points.

## Catalyst Effects on Favorability vs Rate

A common misconception repeatedly tested on the AP exam is what properties catalysts change versus what they do not. A catalyst works by providing an alternative reaction mechanism (pathway) from reactants to products, with a lower activation energy than the uncatalyzed pathway. Lower $E_a$ increases the rate constant $k$, so the reaction proceeds faster for both the forward and reverse reactions equally.

Because a catalyst does not change the chemical identity or free energy of the starting reactants or final products, it does not change the overall $\Delta G$ for the reaction. This means a catalyst cannot change the thermodynamic favorability of a reaction: it cannot make a non-spontaneous ($\Delta G > 0$) reaction become spontaneous, and it does not change the equilibrium constant or the final product yield at equilibrium. It only makes the reaction reach equilibrium faster.

**Worked example:** The decomposition of hydrogen peroxide is $2 \text{H}_2\text{O}_2(aq) \rightarrow 2 \text{H}_2\text{O}(l) + \text{O}_2(g)$, with $\Delta G^\circ = -234$ kJ/mol at 25°C. The uncatalyzed activation energy is 71 kJ/mol, and the enzyme catalase lowers $E_a$ to 8 kJ/mol. Which statement is correct after adding catalase?
A) ΔG becomes more negative, and the rate increases
B) The rate increases, and ΔG remains unchanged
C) ΔG becomes positive, and the rate decreases
D) The rate remains unchanged, and ΔG remains unchanged

1. Recall the core rule for catalysts: catalysts change the reaction pathway (lower $E_a$) but do not change the free energy of reactants or products.
2. Therefore, $\Delta G$ for the reaction stays at -234 kJ/mol, so the reaction remains thermodynamically favorable. Eliminate options A and C.
3. Lowering $E_a$ from 71 kJ/mol to 8 kJ/mol means far more colliding H₂O₂ molecules have enough energy to react, so the reaction rate increases dramatically. Eliminate D.
4. The correct answer is B.

> **Exam tip:** Any multiple-choice option that claims a catalyst changes ΔG, spontaneity, or the equilibrium constant K is automatically wrong. Only rate and activation energy are changed.

## Common pitfalls

- **Wrong:** Claiming a thermodynamically favorable reaction will always occur at an observable rate
  - Why it fails: Students associate the everyday definition of 'spontaneous' (happens immediately) with the chemical definition, confusing thermodynamic possibility with kinetic feasibility
  - Correct: Always explicitly separate the two properties: ΔG < 0 means the reaction is possible, but rate depends on Ea, so it may be too slow to observe
- **Wrong:** Claiming a catalyst changes the spontaneity (ΔG) of a reaction
  - Why it fails: Students know catalysts speed up reactions, so they incorrectly extrapolate that catalysts can make a non-spontaneous reaction spontaneous
  - Correct: Remember catalysts only change the reaction pathway (lower Ea) not the free energy of reactants or products, so ΔG and spontaneity are always unchanged
- **Wrong:** Predicting the thermodynamically favorable product as the major product under all conditions
  - Why it fails: Students forget competing reactions can be under kinetic control if equilibrium cannot be reached
  - Correct: Always check whether the reaction is reversible and whether the activation barrier for the thermodynamic product is accessible before predicting the major product
- **Wrong:** Stating a non-thermodynamically favorable reaction can never occur
  - Why it fails: Students confuse 'will not occur on its own' with 'can never occur'
  - Correct: Recall non-spontaneous reactions can occur if driven by external free energy input (e.g. electrolysis) or coupled to a favorable reaction; thermodynamic favorability only means no continuous input is needed, not that it can never happen
- **Wrong:** Assigning kinetic control to high temperature and thermodynamic control to low temperature
  - Why it fails: Students reverse the relationship between temperature and control type
  - Correct: Memorize that low temperature = only low Ea barriers accessible, no reversal = kinetic control; high temperature = all barriers accessible, reversibility = thermodynamic control
- **Wrong:** Using activation energy to determine the sign of ΔG and spontaneity
  - Why it fails: Students mix up kinetic and thermodynamic properties, using Ea (kinetic) to infer favorability
  - Correct: Only use the overall free energy difference between reactants and products to determine thermodynamic favorability; Ea is only used for rate, never for spontaneity

## Cheatsheet

| Category | Rule/Property | Key Notes |
| --- | --- | --- |
| Thermodynamic Favorability | $\Delta G = G_{\text{products}} - G_{\text{reactants}}$ | $\Delta G < 0$ = favorable; $\Delta G > 0$ = unfavorable. Depends only on reactant/product free energy, not pathway. |
| Reaction Rate | Depends on activation energy $E_a$ | Higher $E_a$ = slower rate. Depends on reaction pathway, not overall $\Delta G$. |
| Kinetic Control | Low temperature, irreversible, only low $E_a$ accessible | Major product = faster-forming (lower $E_a$), regardless of stability. |
| Thermodynamic Control | High temperature, reversible, all barriers accessible | Major product = more stable (more negative $\Delta G$), regardless of formation rate. |
| Catalyst Effect | Lowers $E_a$ via alternative pathway | Only increases reaction rate; no change to $\Delta G$, favorability, or equilibrium constant. |

## What's next

Understanding the distinction between thermodynamic favorability and rate is foundational for applying thermodynamics to real-world industrial, biological, and environmental chemistry problems. This concept connects the two core pillars of AP Chemistry: thermodynamics, which describes what reactions can occur spontaneously, and kinetics, which describes how fast those reactions will proceed. Many industrial processes are optimized by using catalysts to speed up thermodynamically favorable reactions that are naturally slow, or tuning reaction temperature to select for specific products via kinetic or thermodynamic control. Mastering this distinction will help you avoid common misconceptions frequently tested on both AP Chemistry MCQ and FRQ sections.

- [Unit 9 Applications of Thermodynamics Overview](https://www.owlsprep.com/study/ap-chemistry-u9-overview/)
- [Free Energy and Equilibrium](https://www.owlsprep.com/study/ap-chemistry-u9-free-energy-and-equilibrium/)
- [Galvanic (voltaic) and electrolytic cells](https://www.owlsprep.com/study/ap-chemistry-u9-galvanic-and-electrolytic-cells/)

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