Problem 24 - Chemistry for Allied Health

Question

Explain how free energy is used to determine whether or not a reaction is spontaneous.

Step-by-Step Solution

Answer

A reaction is spontaneous if the Gibbs free energy change (G) is negative.

Step 1: Understanding Free Energy

Free energy, specifically Gibbs free energy (G), is a thermodynamic quantity that combines enthalpy (H) and entropy (S) factors into a single value to determine the spontaneity of a reaction at constant temperature and pressure. The formula is: G = H - TS, where T is the temperature in Kelvin.

Step 2: Condition for Spontaneity

A reaction is considered spontaneous if it can proceed without any input of energy from an external source. For a process to be spontaneous, the change in Gibbs free energy (G) must be negative (G < 0), indicating that the energy of the system decreases, making the process favorable.

Step 3: Analyzing the Formula Components

In G = H - TS, H is the change in enthalpy, which can be negative (exothermic) or positive (endothermic). TS is the temperature multiplied by the change in entropy; this term becomes more significant at higher temperatures. A favorable (positive) change in entropy (increases in disorder) contributes to a negative G.

Step 4: Applying Formula to Determine Spontaneity

Evaluate the signs and magnitudes of H and S at the temperature of interest. For instance, a reaction with a negative H and positive S will always result in a negative G, indicating spontaneity. Conversely, reactions with negative S or high positive H may not be spontaneous, especially at low temperatures.

Key Concepts

Thermodynamic Spontaneity

Thermodynamic spontaneity refers to a process that can occur naturally without continuous external intervention. It means that once a spontaneous reaction starts, it can proceed without needing extra energy. This is where Gibbs Free Energy (G) plays a crucial role. By calculating G, we can predict whether a reaction will be spontaneous. When G is negative (G < 0), the reaction is considered spontaneous.
A negative G signifies that the system loses energy during the reaction. This loss of energy makes the process favorable and allows it to occur readily. Understanding thermodynamic spontaneity helps us determine which chemical reactions can happen under given conditions, giving us valuable insights into reaction feasibility.

Enthalpy

Enthalpy (H) represents the total heat content of a system. In the context of chemical reactions, changes in enthalpy indicate the energy exchanged with the surroundings.
Enthalpy can either be:

• Negative: Exothermic reaction, heat is released to the environment.
• Positive: Endothermic reaction, heat is absorbed from the environment.

When considering Gibbs Free Energy, H is one of the components used to calculate G. A negative H, indicating an exothermic reaction, often contributes to a negative G, suggesting spontaneity. However, it's important to remember that enthalpy alone doesn't determine spontaneity; it's part of a greater equation that includes entropy and temperature.

Entropy

Entropy (S) is a measure of the disorder or randomness within a system. During any thermodynamic process, systems tend to move towards increased disorder. A positive change in entropy (S) indicates an increase in disorder, which is typically favorable for spontaneity.
Entropy is critical in calculating the Gibbs Free Energy (G), where it is multiplied by the system's temperature (G = H - TS).

• When S is positive, and TS is large enough, it decreases G, supporting spontaneity.
• A negative S can make G positive unless compensated by a very negative H.

Essentially, entropy contributes to the system's energy balance and affects whether a reaction will proceed spontaneously.

Temperature Effect on Spontaneity

Temperature plays a significant role in determining a reaction's spontaneity. It's part of the Gibbs Free Energy equation as TS, which means both temperature and entropy changes influence spontaneity.
At high temperatures:

• The entropy term (TS) becomes more impactful in the equation.
• A positive S will have a larger influence, often leading to a negative G and thus spontaneity.

Conversely, at lower temperatures:

• The impact of TS decreases.
• Enthalpy (H) has a more dominant effect on G.
• Reactions may require a negative H to be spontaneous.

Thus, evaluating temperature alongside enthalpy and entropy is essential to predict reaction spontaneity under varying conditions.