# Gibbs Free Energy and Spontaneity

Chemistry I · Energy, Equilibrium and Electrochemistry · https://tryals.app/learn/chemistry-i/gibbs-free-energy-and-spontaneity

## Spontaneity Without Looking at the Surroundings

Judging spontaneity by $\Delta S_{universe}$ is correct but inconvenient, it demands information about the surroundings. At constant temperature and pressure, that requirement can be folded into a single property of the system:

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

The criterion becomes wonderfully simple. $\Delta G < 0$ means spontaneous, $\Delta G > 0$ means non-spontaneous (the reverse is spontaneous), and $\Delta G = 0$ means the system is at equilibrium.

Because the entropy term is multiplied by $T$, the two contributions compete, and which one wins can depend on temperature:

| $\Delta H$ | $\Delta S$ | Outcome |
|---|---|---|
| Negative | Positive | Spontaneous at every temperature |
| Positive | Negative | Never spontaneous |
| Negative | Negative | Spontaneous only at low $T$ |
| Positive | Positive | Spontaneous only at high $T$ |

The two mixed cases have a **crossover temperature** where $\Delta G$ passes through zero:

$$T = \frac{\Delta H}{\Delta S}$$

Below it one term dominates, above it the other. Ice melting is the everyday example: $\Delta H > 0$ and $\Delta S > 0$, with a crossover at exactly 273 K.

Gibbs energy also connects to equilibrium. $\Delta G^\circ = -RT\ln K$ links the standard free-energy change to the equilibrium constant, so a strongly negative $\Delta G^\circ$ means a large $K$ and a reaction that runs nearly to completion. But note the word *standard*: $\Delta G^\circ$ describes one specific reference condition, while $\Delta G$ varies as the mixture's composition changes, reaching zero at equilibrium.

> **Common pitfall:** reading $\Delta G < 0$ as "fast". Gibbs energy says only that a reaction *can* proceed, never how quickly. Diamond converting to graphite has $\Delta G < 0$ at room temperature and takes geological time, spontaneity is thermodynamics, rate is kinetics.

## Practice questions

8 of this lesson's 12 practice questions, with answers. The full set is in the app.

### 1. Diamond converts to graphite with $\Delta G < 0$ at room temperature, yet diamonds do not visibly change. What does this show?

A. Spontaneity says nothing about rate
B. The reaction is actually non-spontaneous
C. A high barrier makes $\Delta G$ positive
D. Gibbs energy applies only to gas phases

**Answer:** A. Spontaneity says nothing about rate

**Why:** Thermodynamics says the conversion *can* happen; kinetics says how fast. An enormous activation barrier keeps the rate effectively zero, so a genuinely spontaneous process takes geological time. A barrier affects rate, not $\Delta G$.

Page: https://tryals.app/practice/chemistry-i/gibbs-free-energy-and-spontaneity/diamond-converts-to-graphite-with-g-0-at-room-temperature-yet

### 2. A reaction has $\Delta H = +30$ kJ/mol and $\Delta S = +100$ J/mol/K. Set the temperature in kelvin above which it becomes spontaneous.

**Answer:** 300 (within ±25)

**Why:** The crossover is $T = \Delta H/\Delta S = 30{,}000/100 = 300$ K. Above it the $T\Delta S$ term outgrows the enthalpy penalty and the reaction becomes spontaneous.

Page: https://tryals.app/practice/chemistry-i/gibbs-free-energy-and-spontaneity/a-reaction-has-h-30-kj-mol-and-s-100-j-mol-k-set-the

### 3. Sort each combination of signs by when the reaction is spontaneous.

**Answer:**

- At all temperatures: -ΔH and +ΔS
- At no temperature: +ΔH and -ΔS
- Only at high temperature: +ΔH and +ΔS
- Only at low temperature: -ΔH and -ΔS

**Why:** When enthalpy and entropy agree, temperature is irrelevant. When they disagree, the $T\Delta S$ term grows with temperature, so a positive $\Delta S$ needs high $T$ to win and a negative one needs low $T$ to stay out of the way.

Page: https://tryals.app/practice/chemistry-i/gibbs-free-energy-and-spontaneity/sort-each-combination-of-signs-by-when-the-reaction-is-spontaneous

### 4. Gibbs free energy isolates the spontaneity criterion to system properties alone, yet it remains mathematically equivalent to the Second Law. Why does evaluating the system's enthalpy and entropy capture the total entropy change of the universe?

A. Constant pressure conditions ensure system enthalpy equals universe entropy
B. The entropy change of the surroundings is assumed negligible under constant $T$
C. The enthalpy term reflects entropy changes occurring in the surroundings
D. The Gibbs function replaces the need for the universe entropy to increase overall

**Answer:** C. The enthalpy term reflects entropy changes occurring in the surroundings

**Why:** Gibbs energy encapsulates the Second Law because $-\Delta H/T$ quantifies the entropy transferred to surroundings at constant pressure. Assuming surroundings are negligible or redefining universal laws misinterprets how state functions link open boundaries.

Page: https://tryals.app/practice/chemistry-i/gibbs-free-energy-and-spontaneity/gibbs-free-energy-isolates-the-spontaneity-criterion-to-system

### 5. Which statements about Gibbs free energy are correct?

A. It equals zero at equilibrium
B. It relates to the equilibrium constant by $\Delta G^\circ = -RT \ln K$
C. A negative value indicates a spontaneous process at constant T and P
D. It measures how quickly a reaction reaches equilibrium

**Answer:** A. It equals zero at equilibrium; B. It relates to the equilibrium constant by $\Delta G^\circ = -RT \ln K$; C. A negative value indicates a spontaneous process at constant T and P

**Why:** Gibbs energy gives the direction, the equilibrium condition and the link to $K$. It says nothing whatever about rate, which belongs to kinetics.

Page: https://tryals.app/practice/chemistry-i/gibbs-free-energy-and-spontaneity/which-statements-about-gibbs-free-energy-are-correct

### 6. A reaction with a positive enthalpy change can still be spontaneous.

**Answer:** True

**Why:** True, an endothermic reaction becomes spontaneous once $T\Delta S$ exceeds $\Delta H$. Dissolving ammonium nitrate absorbs heat and gets cold, yet happens readily because the entropy gain is large.

Page: https://tryals.app/practice/chemistry-i/gibbs-free-energy-and-spontaneity/a-reaction-with-a-positive-enthalpy-change-can-still-be-spontaneous

### 7. Complete the account of what Gibbs free energy does and does not tell you.

**Answer:** A **negative** value of $\Delta G$ means the reaction is spontaneous, a value of exactly zero means the system is at **equilibrium**, and the magnitude tells you nothing about the reaction **rate**, which is governed instead by the **activation energy**.

**Why:** Negative means spontaneous, zero means equilibrium, and rate is a kinetic question answered by the activation energy. Confusing the size of $\Delta G$ with speed is the most persistent misconception in this topic.

Page: https://tryals.app/practice/chemistry-i/gibbs-free-energy-and-spontaneity/complete-the-account-of-what-gibbs-free-energy-does-and-does-not-tell

### 8. Match each quantity to what it determines.

**Answer:**

- $\Delta H$ → The heat exchanged at constant pressure
- $\Delta S$ → The change in the number of accessible arrangements
- $\Delta G$ → Whether the process can proceed spontaneously
- $E_a$ → How fast the process actually goes

**Why:** Enthalpy handles heat, entropy handles disorder, Gibbs energy combines them into a spontaneity criterion, and activation energy, which appears in none of them, is what sets the rate.

Page: https://tryals.app/practice/chemistry-i/gibbs-free-energy-and-spontaneity/match-each-quantity-to-what-it-determines