Question

If a reaction occurs readily but has an endothermic heat of reaction, what must be the driving force for the reaction?

Short answer

The driving force for the given endothermic reaction to occur readily is a significant increase in disorder or entropy (\(\Delta S > 0\)). The positive entropy change in this reaction compensates for the positive enthalpy change, resulting in a negative change in Gibbs free energy (\(\Delta G < 0\)), which means the reaction is spontaneous.

Step-by-step solution

Understanding the key terms

- Endothermic heat of reaction: A reaction that absorbs heat energy from the surroundings is referred to as endothermic. - Enthalpy (H): It is a measure of the total energy of a thermodynamic system, which includes the internal energy and the energy transferred as heat. - Entropy (S): It is a measure of the disorder or randomness of a system. A positive change in entropy corresponds to an increase in disorder. - Gibbs free energy (G): It is a measure of the energy available for a reaction to perform useful work. When the Gibbs free energy is negative, the reaction is spontaneous.

Understand the spontaneous reaction condition

For a reaction to occur spontaneously, the Gibbs free energy change must be negative. The equation for Gibbs free energy change is given by \[ \Delta G = \Delta H - T\Delta S\ , \] where \(\Delta G\) is the change in Gibbs free energy, \(\Delta H\) is the change in enthalpy, \(\Delta S\) is the change in entropy, and \(T\) is the temperature in Kelvin.

Analyze the endothermic heat of reaction

As mentioned earlier, the given reaction has an endothermic heat of reaction, which means it absorbs heat from the surroundings and has a positive \(\Delta H\).

Determine the driving force for the reaction

Since the reaction occurs readily, it means it is spontaneous, implying that the Gibbs free energy change is negative. Based on the Gibbs free energy equation, we can conclude that if \(\Delta H\) is positive (endothermic reaction), the driving force for the reaction to occur spontaneously must be an even larger increase in entropy. In other words, the reaction results in a significantly higher degree of disorder (\(\Delta S > 0\)), which overcomes the endothermic reaction and makes the overall \(\Delta G\) negative.

Conclusion

The driving force for the given endothermic reaction to occur readily is a significant increase in disorder or entropy. The positive entropy change in this reaction compensates for the positive enthalpy change, resulting in a negative change in Gibbs free energy, which means the reaction is spontaneous.

Key concepts

Endothermic Reactions

In an endothermic reaction, the system absorbs heat from the surroundings. This means the reaction requires energy input to proceed. The enthalpy change, denoted as \(\Delta H\), is positive for endothermic reactions. This absorption of energy can often seem counterintuitive when we think about reactions that happen readily. Yet, certain reactions occur naturally even when they are endothermic. To understand why, it's crucial to look beyond just the enthalpy change. We'll need to consider the role of entropy (\(S\)) in helping drive these reactions forward. It's the balance between enthalpy and entropy that influences the direction and favorability of chemical processes. In essence, endothermic reactions can proceed spontaneously if there is another strong driving force at play, which is often an increase in entropy.

Entropy

Entropy is a measure of the disorder or randomness in a system. It's a fundamental concept that helps predict the direction of chemical reactions. When entropy increases, it means the system is becoming more disordered. Unlike enthalpy, which focuses on heat, entropy considers the number of configurations or ways particles can be arranged. An increase in entropy, \(\Delta S > 0\), typically favors the spontaneity of a process. In the context of our original exercise, even though a reaction is endothermic (absorbs heat), the increase in entropy can be substantial enough to drive the reaction forward.

• Positive \(\Delta S\): More disorder, favored in nature
• Negative \(\Delta S\): Less disorder, less favored

Entropy can therefore act as a key driving force, compensating for energy absorbed in endothermic processes.

Spontaneous Reactions

A spontaneous reaction is one that occurs naturally without needing outside energy input, once started. The Gibbs Free Energy change, \(\Delta G\), determines whether a reaction is spontaneous. For a reaction to be spontaneous, \(\Delta G\) must be negative.The equation \(\Delta G = \Delta H - T\Delta S\) highlights how both enthalpy (\(\Delta H\)) and entropy (\(\Delta S\)) interact to affect the spontaneity of a reaction.

• \(\Delta G < 0\): Reaction is spontaneous
• \(\Delta G > 0\): Reaction is non-spontaneous
• \(\Delta G = 0\): Reaction is at equilibrium

In an endothermic reaction, a negative \(\Delta G\) can still be achieved if the increase in entropy is large enough to offset the positive \(\Delta H\). Therefore, even endothermic reactions can proceed spontaneously if they result in a significant increase in entropy, highlighting the balance of forces that can drive chemical transformations.