---
title: "ΔG°reaction = ΣΔG°f Equation — AP Chem Definition & Guide"
description: "ΔG°rxn = ΣΔG°f(products) − ΣΔG°f(reactants) calculates standard Gibbs free energy from formation values, the fastest way to judge thermodynamic favorability in Unit 9."
canonical: "https://fiveable.me/ap-chem/key-terms/g-reaction-g-f-products-g-f-reactants"
type: "key-term"
subject: "AP Chemistry"
unit: "Unit 9"
---

# ΔG°reaction = ΣΔG°f Equation — AP Chem Definition & Guide

## Definition

ΔG°reaction = ΣΔG°f(products) − ΣΔG°f(reactants) is the products-minus-reactants equation that calculates a reaction's standard Gibbs free energy change from tabulated standard free energies of formation; if the result is negative, the process is thermodynamically favored (AP Chem Topic 9.3).

## What It Is

This equation lets you calculate ΔG° for any reaction using a table of standard Gibbs free energies of formation (ΔG°f). You add up the ΔG°f values of the [products](/ap-chem/key-terms/products "fv-autolink") (each multiplied by its coefficient), do the same for the reactants, and subtract reactants from products. It's the same products-minus-reactants logic you used with ΔH°f values back in [Unit 6](/ap-chem/unit-6 "fv-autolink"), just with free energy instead of enthalpy.

The "standard" part matters. ΔG° only applies when everything is in its [standard state](/ap-chem/unit-9/gibbs-free-energy-thermodynamic-favorability/study-guide/hCJVI2XJaSGmj1c3zvrO "fv-autolink"), meaning pure substances, 1.0 M solutions, or gases at 1.0 atm (or 1.0 bar), per essential knowledge 9.3.A.1. The payoff is one number that tells you whether the reaction is thermodynamically favored. ΔG° < 0 means favored, ΔG° > 0 means not favored. The CED prefers "thermodynamically favored" over "spontaneous" because spontaneous wrongly suggests the reaction happens fast. ΔG° says nothing about speed; that's kinetics' job. Also remember that ΔG°f for any element in its most stable form is zero by definition, which saves you a step in calculations.

## Why It Matters

This equation lives in Topic 9.3 (Gibbs Free Energy and Thermodynamic Favorability) in [Unit 9](/ap-chem/unit-9 "fv-autolink"): Thermodynamics and Electrochemistry. It directly supports learning objective 9.3.A, which asks you to explain whether a physical or chemical process is thermodynamically favored based on an evaluation of ΔG°. Before you can evaluate ΔG°, you usually have to calculate it, and this equation is one of the two main routes (the other is ΔG° = ΔH° − TΔS°). It's also where [AP Chem](/ap-chem "fv-autolink") cashes in the big idea that thermodynamic data is composable. Because G is a state function, you can build the ΔG° of any reaction from formation values without ever running the reaction.

## Connections

### [ΔG° = ΔH° − TΔS° (Unit 9)](/ap-chem/key-terms/g-h-t-s)

This is the other route to the same answer. The formation-values equation works when you're handed a ΔG°f table; the ΔH° − TΔS° equation works when you have enthalpy and entropy data, and it's the one to use when temperature changes the verdict. Both should give matching ΔG° values at [298 K](/ap-chem/key-terms/k "fv-autolink"), which makes them a great self-check.

### Enthalpy Change and ΔH°f calculations (Unit 6)

You've already done this exact math with enthalpies of formation. ΔG°rxn = ΣΔG°f(products) − ΣΔG°f([reactants](/ap-chem/key-terms/reactants "fv-autolink")) is the Hess's-law pattern copied over to free energy, because G, like H, is a state function. If you can do a ΔH°f problem, you can do this one. Just swap the table you're reading from.

### Thermodynamic favorability (Unit 9, Topic 9.3)

The number this equation spits out is the whole point of Topic 9.3. A negative ΔG° means thermodynamically favored; a positive ΔG° means not favored. But favored does not mean fast. A reaction with ΔG° = −500 kJ/mol can still sit there for years if the [activation energy](/ap-chem/key-terms/activation-energy "fv-autolink") is huge.

## On the AP Exam

Expect this as a calculation step inside a larger thermodynamics question. A typical setup gives you a table of ΔG°f values and a balanced equation, then asks for ΔG°rxn and whether the reaction is thermodynamically favored, with justification. The two classic point-losers are forgetting to multiply each ΔG°f by its stoichiometric coefficient and subtracting in the wrong order (it's always products minus reactants). On FRQs, the favorability claim has to be tied to the sign of ΔG°, not vibes. Write something like "ΔG° = −86 kJ/mol < 0, so the reaction is thermodynamically favored." Also watch the language trap baked into the CED. Saying a reaction with negative ΔG° will "happen quickly" can cost you, because ΔG° measures favorability, not rate.

## ΔG°reaction = ΣΔG°f products - ΣΔG°f reactants vs ΔG° = ΔH° − TΔS°

Both calculate the same quantity, ΔG°, but from different inputs. The formation equation (ΣΔG°f products − ΣΔG°f reactants) uses a table of free energies of formation and only works at the temperature the table was made for, usually 298 K. The ΔH° − TΔS° equation builds ΔG° from enthalpy and entropy, so it lets you plug in different temperatures and figure out when a reaction flips between favored and not favored. On the exam, the data you're given tells you which one to use.

## Key Takeaways

- ΔG°rxn = ΣΔG°f(products) − ΣΔG°f(reactants), and every ΔG°f value must be multiplied by its coefficient from the balanced equation.
- If the calculated ΔG° is negative, the reaction is thermodynamically favored; if positive, it is not favored under standard conditions.
- The ΔG°f of any element in its most stable standard-state form is zero, so those species drop out of the sum.
- Standard state means pure substances, 1.0 M solutions, and gases at 1.0 atm (or 1.0 bar); that's what the ° symbol guarantees (EK 9.3.A.1).
- A negative ΔG° tells you nothing about speed. The CED uses "thermodynamically favored" instead of "spontaneous" specifically to avoid that mix-up.
- This equation and ΔG° = ΔH° − TΔS° are two routes to the same ΔG°; use formation values when given a table, use ΔH° − TΔS° when temperature matters.

## FAQs

### What is the equation ΔG°reaction = ΣΔG°f products − ΣΔG°f reactants?

It's the formula for finding a reaction's standard Gibbs free energy change by summing the standard free energies of formation of the products, summing those of the reactants, and subtracting reactants from products. A negative result means the reaction is thermodynamically favored (Topic 9.3).

### Does a negative ΔG° mean the reaction happens fast?

No. ΔG° < 0 only means the reaction is thermodynamically favored, not that it's fast. Diamond converting to graphite has a negative ΔG° and takes essentially forever. Rate comes from kinetics (Unit 5), not thermodynamics.

### How is ΔG° from formation values different from ΔG° = ΔH° − TΔS°?

Both calculate the same ΔG°. The formation-values equation needs a ΔG°f data table and is locked to the table's temperature (usually 298 K), while ΔG° = ΔH° − TΔS° lets you change T and find where favorability flips. Pick based on what data the problem gives you.

### Why is ΔG°f zero for elements like O2 and Fe?

By definition, forming an element in its most stable standard-state form from itself involves no change, so its ΔG°f is 0 kJ/mol. That means O2(g), N2(g), Fe(s), and similar species contribute nothing to the sum.

### Do I have to multiply ΔG°f values by the coefficients in the balanced equation?

Yes, always. ΔG°f values are per mole, so 2H2O(g) contributes 2 × ΔG°f of water vapor. Skipping coefficients is one of the most common ways to lose the calculation point on an FRQ.

## Related Study Guides

- [9.3 Gibbs Free Energy and Thermodynamic Favorability](/ap-chem/unit-9/gibbs-free-energy-thermodynamic-favorability/study-guide/hCJVI2XJaSGmj1c3zvrO)

## Structured Data

```json
{"@context":"https://schema.org","@graph":[{"@type":"LearningResource","@id":"https://fiveable.me/ap-chem/key-terms/g-reaction-g-f-products-g-f-reactants#resource","name":"ΔG°reaction = ΣΔG°f Equation — AP Chem Definition & Guide","url":"https://fiveable.me/ap-chem/key-terms/g-reaction-g-f-products-g-f-reactants","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/ap-chem/key-terms/g-reaction-g-f-products-g-f-reactants#term"},"audience":{"@type":"EducationalAudience","educationalRole":"student"},"dateModified":"2026-06-11T05:27:15.442Z","isPartOf":{"@type":"Collection","name":"AP Chemistry Key Terms","url":"https://fiveable.me/ap-chem/key-terms"},"publisher":{"@type":"Organization","name":"Fiveable","url":"https://fiveable.me"}},{"@type":"DefinedTerm","@id":"https://fiveable.me/ap-chem/key-terms/g-reaction-g-f-products-g-f-reactants#term","name":"ΔG°reaction = ΣΔG°f products - ΣΔG°f reactants","description":"ΔG°reaction = ΣΔG°f(products) − ΣΔG°f(reactants) is the products-minus-reactants equation that calculates a reaction's standard Gibbs free energy change from tabulated standard free energies of formation; if the result is negative, the process is thermodynamically favored (AP Chem Topic 9.3).","url":"https://fiveable.me/ap-chem/key-terms/g-reaction-g-f-products-g-f-reactants","inDefinedTermSet":{"@type":"DefinedTermSet","name":"AP Chemistry Key Terms","url":"https://fiveable.me/ap-chem/key-terms"}},{"@type":"FAQPage","mainEntity":[{"@type":"Question","name":"What is the equation ΔG°reaction = ΣΔG°f products − ΣΔG°f reactants?","acceptedAnswer":{"@type":"Answer","text":"It's the formula for finding a reaction's standard Gibbs free energy change by summing the standard free energies of formation of the products, summing those of the reactants, and subtracting reactants from products. A negative result means the reaction is thermodynamically favored (Topic 9.3)."}},{"@type":"Question","name":"Does a negative ΔG° mean the reaction happens fast?","acceptedAnswer":{"@type":"Answer","text":"No. ΔG° < 0 only means the reaction is thermodynamically favored, not that it's fast. Diamond converting to graphite has a negative ΔG° and takes essentially forever. Rate comes from kinetics (Unit 5), not thermodynamics."}},{"@type":"Question","name":"How is ΔG° from formation values different from ΔG° = ΔH° − TΔS°?","acceptedAnswer":{"@type":"Answer","text":"Both calculate the same ΔG°. The formation-values equation needs a ΔG°f data table and is locked to the table's temperature (usually 298 K), while ΔG° = ΔH° − TΔS° lets you change T and find where favorability flips. Pick based on what data the problem gives you."}},{"@type":"Question","name":"Why is ΔG°f zero for elements like O2 and Fe?","acceptedAnswer":{"@type":"Answer","text":"By definition, forming an element in its most stable standard-state form from itself involves no change, so its ΔG°f is 0 kJ/mol. That means O2(g), N2(g), Fe(s), and similar species contribute nothing to the sum."}},{"@type":"Question","name":"Do I have to multiply ΔG°f values by the coefficients in the balanced equation?","acceptedAnswer":{"@type":"Answer","text":"Yes, always. ΔG°f values are per mole, so 2H2O(g) contributes 2 × ΔG°f of water vapor. Skipping coefficients is one of the most common ways to lose the calculation point on an FRQ."}}]},{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"AP Chemistry","item":"https://fiveable.me/ap-chem"},{"@type":"ListItem","position":2,"name":"Key Terms","item":"https://fiveable.me/ap-chem/key-terms"},{"@type":"ListItem","position":3,"name":"Unit 9","item":"https://fiveable.me/ap-chem/unit-9"},{"@type":"ListItem","position":4,"name":"ΔG°reaction = ΣΔG°f products - ΣΔG°f reactants"}]}]}
```