Gibbs Free Energy: Videos & Practice Problems

Gibbs free energy (ΔG) indicates the spontaneity of a reaction, where ΔG = 0 signifies equilibrium. A positive ΔG indicates a non-spontaneous reaction with an equilibrium constant (K) less than 1, while a negative ΔG indicates spontaneity with K greater than 1. When ΔG is unknown, spontaneity can be inferred from enthalpy (ΔH) and entropy (ΔS) signs: both positive leads to spontaneity at high temperatures, both negative at low temperatures, and mixed signs indicate non-spontaneity. Understanding these relationships is crucial for predicting reaction behavior.

Spontaneity of Reactions

Gibbs free energy, denoted as ΔG, is a crucial concept in thermodynamics that quantifies the energy change in a chemical or physical process capable of doing work. The sign and value of ΔG, along with the equilibrium constant (K), are essential in determining the spontaneity of a reaction. A reaction is considered spontaneous if ΔG is negative (ΔG < 0), indicating that the products are favored and K is greater than 1, meaning there are more products than reactants. Conversely, if ΔG is positive (ΔG > 0), the reaction is non-spontaneous, suggesting that reactants dominate and K is less than 1.

At equilibrium, ΔG equals 0, which corresponds to K being equal to 1, indicating that the concentrations of products and reactants are balanced. Understanding the relationship between ΔG and K allows for the prediction of a reaction's behavior: a negative ΔG signifies spontaneity, while a positive ΔG indicates non-spontaneity. This interplay is vital for predicting the direction of chemical reactions and their feasibility under given conditions.

ΔG and Spontaneity Example

In the context of reversible reactions, the Gibbs free energy change (ΔG) provides insight into the spontaneity of a reaction. When ΔG is small and positive, it indicates that the reaction is non-spontaneous in the forward direction, meaning that the reactants are favored over the products. This small positive value suggests that the system is close to equilibrium, as ΔG approaches zero at equilibrium.

In this scenario, since the forward reaction is non-spontaneous, the reverse reaction becomes spontaneous. Therefore, while the forward reaction does not proceed readily, the reverse reaction can occur with relative ease. The key takeaway is that a small positive ΔG signifies that the system is near equilibrium, and the reverse reaction is favored.

In summary, when ΔG is small and positive, the reaction is non-spontaneous in the forward direction but spontaneous in the reverse direction, indicating that the system is near equilibrium.

Spontaneity and Temperature

In thermodynamics, the spontaneity of a chemical reaction can be assessed using the signs of enthalpy change (ΔH) and entropy change (ΔS). When both ΔH and ΔS are positive, the reaction is spontaneous at high temperatures. Conversely, if both ΔH and ΔS are negative, the reaction is spontaneous at low temperatures. This indicates that temperature plays a crucial role in determining spontaneity based on the signs of these thermodynamic quantities.

In scenarios where ΔH is positive and ΔS is negative, the reaction is always non-spontaneous, regardless of temperature. On the other hand, if ΔH is negative and ΔS is positive, the reaction is spontaneous. This relationship can be summarized as follows: for reactions to be spontaneous, the combination of ΔH and ΔS must align with the temperature conditions. Understanding these principles allows for predicting the feasibility of reactions under varying thermal conditions.

Spontaneity and Temperature Example

In the reaction between phosphorus trichloride (PCl₃) and chlorine gas (Cl₂) to form phosphorus pentachloride (PCl₅), the enthalpy change (ΔH) is reported as -92.50 kJ at 25 degrees Celsius. This negative value indicates that the reaction is exothermic, meaning it releases heat rather than absorbing it, which contradicts the notion of it being an endothermic reaction.

When considering the equilibrium expression, the ratio of products to reactants is represented by the equilibrium constant (K). As temperature increases, the behavior of K can be influenced by the signs of ΔH and ΔS. In this case, since ΔH is negative and the reaction involves two reactants forming one product, the change in entropy (ΔS) is negative as well. This is because the formation of a single product from multiple reactants typically results in a decrease in disorder or randomness.

At lower temperatures, the reaction is more spontaneous due to the negative ΔH and ΔS, favoring the formation of products. However, as the temperature rises, the spontaneity decreases, making the reaction less favorable and favoring the reverse direction, where reactants are favored over products. Consequently, the equilibrium constant K decreases as the concentration of reactants increases relative to products.

To summarize, the key points are that the reaction is exothermic (ΔH < 0), the change in entropy is negative (ΔS < 0), and the reaction is spontaneous at low temperatures but becomes non-spontaneous as temperature increases. Therefore, the only true statement regarding this reaction is that ΔS for the reaction is negative, confirming the decrease in entropy associated with the formation of a single product from multiple reactants.

The chemical reaction 2 NO₂Br (g) → 2 NO₂ (g) + Br₂ (g) has a K_eq = 4.50 × 10⁵.
Does the reaction increase the entropy of the Universe? Explain.

• A. Yes, because K_eq > 1 and ΔG < 0.
• B. No, because K_eq > 1 and ΔG > 0.
• C. Yes, because K_eq > 1 and ΔG = 0.
• D. No, because K_eq > 1 and ΔG = 0.

Answer: (A)

What are the signs of ∆H, ∆S and ∆G for the spontaneous conversion of a solid into gas?

• A. ∆H = (+), ∆S = (+), ∆G = (−)
• B. ∆H = (+), ∆S = (+), ∆G = (+)
• C. ∆H = (−), ∆S = (+), ∆G = (−)
• D. ∆H = (+), ∆S = (−), ∆G = (−)

Answer: (A)

Consider the combustion of butane gas and predict the signs of ΔS, ΔH and ∆G.
C₄H₁₀ (g) + 13/2 O₂ (g)  ⟶  4 CO₂ (g) + 5 H₂O (g)

• A. ΔS = (−), ΔH = (+), ∆G = (+)
• B. ΔS = (+), ΔH = (−), ∆G = (+)
• C. ΔS = (+), ΔH = (+), ∆G = (−)
• D. ΔS = (+), ΔH = (−), ∆G = (−)

Answer: (D)

You calculate the value of ΔG for a chemical reaction and get a positive value. Which would be the most accurate way to interpret this result?
a) If a mixture of reactants and products is created and left to equilibrate, the equilibrium mixture will contain more reactant than product.
b) If a mixture of reactants and products is created, we cannot say anything about its composition at equilibrium but we can say it will reach equilibrium very rapidly.
c) The reaction will not occur under any circumstances.
d) If a mixture of reactants and products is created and left to equilibrate, the equilibrium mixture will contain more product than reactant.

• A. If a mixture of reactants and products is created and left to equilibrate, the equilibrium mixture will contain more reactant than product.
• B. If a mixture of reactants and products is created, we cannot say anything about its composition at equilibrium but we can say it will reach equilibrium very rapidly.
• C. The reaction will not occur under any circumstances.
• D. If a mixture of reactants and products is created and left to equilibrate, the equilibrium mixture will contain more product than reactant.

Answer: (A)

Here’s what students ask on this topic:

What is Gibbs free energy and how is it related to spontaneity of a reaction?

Gibbs free energy (ΔG) is a thermodynamic quantity that measures the amount of energy available to do work during a chemical or physical process. It is related to the spontaneity of a reaction. If ΔG is negative (ΔG < 0), the reaction is spontaneous, meaning it can proceed without external input. If ΔG is positive (ΔG > 0), the reaction is non-spontaneous and requires energy input to proceed. At equilibrium, ΔG is zero (ΔG = 0), indicating no net change in the system. The relationship between ΔG and the equilibrium constant (K) also helps determine spontaneity: if K > 1, ΔG is negative and the reaction is spontaneous; if K < 1, ΔG is positive and the reaction is non-spontaneous.

How do the signs of enthalpy (ΔH) and entropy (ΔS) affect the spontaneity of a reaction?

The signs of enthalpy (ΔH) and entropy (ΔS) can predict the spontaneity of a reaction when ΔG is unknown. If both ΔH and ΔS are positive, the reaction is spontaneous at high temperatures. If both ΔH and ΔS are negative, the reaction is spontaneous at low temperatures. If ΔH is positive and ΔS is negative, the reaction is always non-spontaneous. Conversely, if ΔH is negative and ΔS is positive, the reaction is always spontaneous. These relationships help determine the conditions under which a reaction will proceed spontaneously.

What does it mean when Gibbs free energy (ΔG) is zero?

When Gibbs free energy (ΔG) is zero, it means the system is at equilibrium. At this point, there is no net change in the concentrations of reactants and products, and the forward and reverse reactions occur at the same rate. The equilibrium constant (K) is equal to 1, indicating that the ratio of products to reactants is balanced. In this state, the system has reached a point where the free energy is minimized, and no further work can be done without external input.

How can the equilibrium constant (K) be used to determine the spontaneity of a reaction?

The equilibrium constant (K) can be used to determine the spontaneity of a reaction. If K is greater than 1 (K > 1), the reaction is spontaneous, meaning ΔG is negative, and products dominate over reactants. If K is less than 1 (K < 1), the reaction is non-spontaneous, meaning ΔG is positive, and reactants dominate over products. At equilibrium, K is equal to 1 (K = 1), and ΔG is zero, indicating no net change in the system. Thus, the value of K provides insight into the direction and spontaneity of a reaction.

What are the conditions for a reaction to be spontaneous at high or low temperatures?

The conditions for a reaction to be spontaneous at high or low temperatures depend on the signs of enthalpy (ΔH) and entropy (ΔS). If both ΔH and ΔS are positive, the reaction is spontaneous at high temperatures because the positive entropy term (TΔS) outweighs the positive enthalpy term. If both ΔH and ΔS are negative, the reaction is spontaneous at low temperatures because the negative enthalpy term outweighs the negative entropy term. These conditions help predict the temperature range in which a reaction will proceed spontaneously.