Question

What conditions are necessary for the free-energy change to be used to predict the spontaneity of a reaction?

Short answer

\( \triangle \text{G} < 0 \) and the knowledge of temperature, enthalpy, and entropy changes are necessary.

Step-by-step solution

Identify Free Energy

Free energy, denoted as \( \text{G} \), is a thermodynamic quantity equivalent to the capacity of a system to do work.

Understand Free Energy Change

The free-energy change (\( \triangle \text{G} \)) of a reaction is the difference in free energy between the products and the reactants: \( \triangle \text{G} = \text{G}_{\text{products}} - \text{G}_{\text{reactants}} \).

Spontaneity and Free Energy Change

A reaction is spontaneous if \( \triangle \text{G} \) is negative. This means the system releases free energy.

Condition: Negative Free Energy Change

To predict the spontaneity of a reaction, it is necessary that \( \triangle \text{G} < 0 \). This indicates that the reaction can proceed without any input of external energy.

Temperature Dependency

Temperature can affect \( \triangle \text{G} \) since \( \triangle \text{G} = \triangle \text{H} - T \triangle \text{S} \), where \( \triangle \text{H} \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \triangle \text{S} \) is the change in entropy. Both \( \triangle \text{H} \) and \( \triangle \text{S} \) need to be known to predict spontaneity at a given temperature.

Summary of Conditions

The necessary conditions to use free-energy change to predict the spontaneity of a reaction are: (1) \( \triangle \text{G} < 0 \), (2) Knowing the temperature \( T \), and (3) Knowing the enthalpy change \( \triangle \text{H} \) and entropy change \( \triangle \text{S} \) for the reaction.

Key concepts

Thermodynamic Quantities

Thermodynamic quantities are values used to describe the thermodynamic state of a system. These include properties like free energy, enthalpy, and entropy.

Understanding these quantities is crucial for predicting how chemical reactions and processes occur. Thermodynamic quantities help us understand whether a reaction will happen spontaneously or if it requires external energy.

Free energy, often denoted as G, represents the amount of work a system can perform. It helps in predicting the spontaneity of a reaction. The change in free energy (ΔG) indicates whether a process will proceed by itself or not. For spontaneity, ΔG must be negative.

Enthalpy

Enthalpy (H) is a thermodynamic quantity that represents the total heat content of a system. It reflects the energy needed to create a system and the energy needed to make space for it by displacing its surroundings.

Enthalpy change (ΔH) in a chemical reaction is the difference between the enthalpy of the products and the reactants: \[ \triangle H = H_{\text{products}} - H_{\text{reactants}} \]

A reaction can either absorb heat (endothermic), indicated by a positive ΔH, or release heat (exothermic), indicated by a negative ΔH. Enthalpy change is essential in determining the overall energy change in a reaction.

Entropy

Entropy (S) is a measure of the disorder or randomness in a system. Higher entropy means greater randomness. The change in entropy (ΔS) during a reaction is the difference in the entropy of the products and reactants: \[ \triangle S = S_{\text{products}} - S_{\text{reactants}} \]

Entropy plays a vital role in determining spontaneity. For a spontaneous process, the total entropy change (considering both the system and the surroundings) must be positive. An increase in entropy often favors the spontaneity of reactions.

Temperature Dependency

Temperature significantly affects the spontaneity of reactions. The relationship between free energy change (ΔG), enthalpy change (ΔH), entropy change (ΔS), and temperature (T) is given by the equation: \[ \triangle G = \triangle H - T \triangle S \]

Here, T is the temperature in Kelvin. This equation combines all three thermodynamic quantities and shows how temperature influences free energy change.

At higher temperatures, the term \( T \triangle S \) becomes more significant, potentially driving the free energy change to become negative even if ΔH is positive. Understanding this temperature dependency helps in predicting how changing conditions affect the free energy and spontaneity of a reaction.