Above What Temperature Does The Following Reaction Become Nonspontaneous

Above What Temperature Does the Following Reaction Become Nonspontaneous? A Deep Dive into Gibbs Free Energy and Reaction Spontaneity

Determining the temperature at which a reaction transitions from spontaneous to nonspontaneous requires understanding the interplay between enthalpy, entropy, and Gibbs Free Energy. This article will explore this crucial concept, providing a comprehensive guide with practical examples. We'll delve into the mathematical relationships, explore the impact of various factors, and demonstrate how to solve problems related to reaction spontaneity.

Understanding Spontaneity and Gibbs Free Energy

A spontaneous reaction proceeds without external intervention, driven by its inherent thermodynamic properties. The key to predicting spontaneity lies in Gibbs Free Energy (ΔG), defined as:

ΔG = ΔH - TΔS

Where:

• ΔG is the change in Gibbs Free Energy (kJ/mol)
• ΔH is the change in enthalpy (kJ/mol), representing the heat absorbed or released during the reaction. A negative ΔH indicates an exothermic reaction (heat released), while a positive ΔH signifies an endothermic reaction (heat absorbed).
• T is the temperature in Kelvin (K).
• ΔS is the change in entropy (kJ/mol·K), reflecting the change in disorder or randomness of the system. A positive ΔS indicates increased disorder, while a negative ΔS indicates decreased disorder.

Spontaneity Criteria:

• ΔG < 0: The reaction is spontaneous under the given conditions.
• ΔG > 0: The reaction is nonspontaneous under the given conditions. Energy input is required for the reaction to proceed.
• ΔG = 0: The reaction is at equilibrium; the forward and reverse reaction rates are equal.

The Temperature Dependence of Spontaneity

The temperature (T) plays a crucial role in determining the spontaneity of a reaction. Notice that the Gibbs Free Energy equation includes T as a multiplier for ΔS. This means that the influence of entropy becomes increasingly significant at higher temperatures.

Let's analyze the different scenarios based on the signs of ΔH and ΔS:

1. ΔH < 0 (Exothermic) and ΔS > 0 (Increase in disorder):

This is the most favorable scenario. Since both ΔH and -TΔS are negative, ΔG will always be negative, regardless of temperature. The reaction is always spontaneous.

2. ΔH > 0 (Endothermic) and ΔS < 0 (Decrease in disorder):

This is the least favorable scenario. Both ΔH and -TΔS are positive, resulting in a positive ΔG at all temperatures. The reaction is never spontaneous.

3. ΔH < 0 (Exothermic) and ΔS < 0 (Decrease in disorder):

In this case, the spontaneity depends on the temperature. At lower temperatures, the negative ΔH dominates, making ΔG negative and the reaction spontaneous. However, as temperature increases, the -TΔS term becomes more significant, eventually causing ΔG to become positive and rendering the reaction nonspontaneous. The temperature at which the reaction becomes nonspontaneous can be calculated by setting ΔG = 0 and solving for T.

4. ΔH > 0 (Endothermic) and ΔS > 0 (Increase in disorder):

Similar to case 3, the spontaneity depends on the temperature. At lower temperatures, the positive ΔH dominates, making ΔG positive and the reaction nonspontaneous. However, as temperature increases, the -TΔS term becomes more significant, eventually making ΔG negative and the reaction spontaneous. The temperature at which the reaction becomes spontaneous can be calculated by setting ΔG = 0 and solving for T.

Calculating the Temperature of Nonspontaneity

To determine the temperature at which a reaction becomes nonspontaneous (or spontaneous, depending on the scenario), we set ΔG = 0 and solve for T:

0 = ΔH - TΔS

T = ΔH/ΔS

This equation gives us the equilibrium temperature (T_eq). For cases 3 and 4, this is the temperature where the spontaneity changes.

• For Case 3 (ΔH < 0 and ΔS < 0): The reaction is spontaneous below T_eq and nonspontaneous above T_eq.
• For Case 4 (ΔH > 0 and ΔS > 0): The reaction is spontaneous above T_eq and nonspontaneous below T_eq.

Example Problems

Let's illustrate this with a couple of examples:

Example 1:

A reaction has ΔH = -50 kJ/mol and ΔS = -100 J/mol·K. At what temperature does the reaction become nonspontaneous?

First, convert ΔS to kJ/mol·K: ΔS = -0.1 kJ/mol·K

T = ΔH/ΔS = (-50 kJ/mol) / (-0.1 kJ/mol·K) = 500 K

The reaction becomes nonspontaneous above 500 K.

Example 2:

A reaction has ΔH = 25 kJ/mol and ΔS = 100 J/mol·K. At what temperature does the reaction become spontaneous?

Convert ΔS to kJ/mol·K: ΔS = 0.1 kJ/mol·K

T = ΔH/ΔS = (25 kJ/mol) / (0.1 kJ/mol·K) = 250 K

The reaction becomes spontaneous above 250 K.

Factors Affecting Spontaneity Beyond Temperature

While temperature is a significant factor, other aspects influence reaction spontaneity:

• Concentration of Reactants and Products: The reaction quotient (Q) considers the relative amounts of reactants and products. A reaction will proceed spontaneously if Q < K (the equilibrium constant).
• Pressure: Changes in pressure, particularly for gaseous reactions, can shift the equilibrium and affect spontaneity.
• Catalysts: Catalysts accelerate the rate of reaction but do not change the spontaneity; they lower the activation energy, making the reaction faster but not necessarily more favorable thermodynamically.

Conclusion

Understanding the temperature dependence of spontaneity is essential for predicting and controlling chemical reactions. The relationship between Gibbs Free Energy, enthalpy, entropy, and temperature provides a powerful framework for analyzing reaction behavior. By carefully considering the signs of ΔH and ΔS and using the equation T = ΔH/ΔS, we can determine the temperature at which a reaction transitions from spontaneous to nonspontaneous or vice-versa. Remember that while temperature is crucial, other factors like concentration and pressure also play significant roles in determining the overall spontaneity of a reaction. This detailed analysis equips you with the tools to approach more complex thermodynamic problems and offers a firm grasp on the principles governing reaction spontaneity.