Chapter 18: Problem 84
For a reaction with a negative \(\Delta G^{\circ}\) value, which of the following statements is false? (a) The equilibrium constant \(K\) is greater than one. (b) The reaction is spontaneous when all the reactants and products are in their standard states. (c) The reaction is always exothermic.
Short Answer
Expert verified
Statement (c) is false.
Step by step solution
01
Understanding Gibbs Free Energy
Gibbs free energy, \(\Delta G^{\circ}\), is used to predict the spontaneity of a reaction. A negative value suggests that the reaction can occur spontaneously under standard conditions.
02
Analyzing Statement (a)
A negative \(\Delta G^{\circ}\) signifies that at equilibrium, the reaction favors products over reactants, thus the equilibrium constant \(K\) is greater than one. This statement is true.
03
Analyzing Statement (b)
A reaction with a negative \(\Delta G^{\circ}\) indicates that under standard-state conditions (1 atm pressure, 1M concentration, 298K), the reaction is indeed spontaneous. Hence, this statement is true.
04
Analyzing Statement (c)
A negative \(\Delta G^{\circ}\) does not necessarily mean that the reaction is exothermic. \(\Delta G^{\circ}\) involves both enthalpy and entropy changes, so it is possible for the reaction to be endothermic but still spontaneous if the entropy term \(T\Delta S\) is large enough. Thus, this statement is false.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Equilibrium Constant
The equilibrium constant (\( K \)) is a significant factor in understanding chemical reactions. It is a measure of how far a reaction will proceed before reaching a state of balance. At equilibrium, the rates of the forward and reverse reactions are equal. This constant tells us which direction a reaction favors—towards the products or reactants.
- A large (\( K \)) value indicates that the reaction favors the formation of products, meaning that at equilibrium, products are predominant over reactants.
- A small (\( K \)) value means that reactants are favored and are more abundant at equilibrium.
In the context of Gibbs Free Energy, a negative (\( \Delta G^{\circ} \)) implies a large (>1) equilibrium constant, indicating that the reaction favors product formation, as more products than reactants will be present at equilibrium.
- A large (\( K \)) value indicates that the reaction favors the formation of products, meaning that at equilibrium, products are predominant over reactants.
- A small (\( K \)) value means that reactants are favored and are more abundant at equilibrium.
In the context of Gibbs Free Energy, a negative (\( \Delta G^{\circ} \)) implies a large (>1) equilibrium constant, indicating that the reaction favors product formation, as more products than reactants will be present at equilibrium.
Spontaneity
Spontaneity in chemical reactions refers to the potential for a reaction to occur naturally without external input. This is where Gibbs Free Energy (\( \Delta G^{\circ} \)) plays an essential role. A negative (\( \Delta G^{\circ} \)) value signals that a reaction is spontaneous under standard conditions (\( 1 \) atm pressure, \( 1 \) M concentration, \( 298 \) K temperature).
- A spontaneous reaction means that the system has the potential to release free energy and move towards equilibrium without requiring energy input.
- It does not necessarily mean the reaction will occur quickly; some spontaneous reactions can take years to complete.
Understanding spontaneity helps in predicting whether a reaction will occur naturally or will need some external energy to push it forward.
- A spontaneous reaction means that the system has the potential to release free energy and move towards equilibrium without requiring energy input.
- It does not necessarily mean the reaction will occur quickly; some spontaneous reactions can take years to complete.
Understanding spontaneity helps in predicting whether a reaction will occur naturally or will need some external energy to push it forward.
Enthalpy
Enthalpy (\( \Delta H \)) is a measure of the total heat content in a system, reflecting the energy absorbed or released during a reaction at constant pressure. In terms of Gibbs Free Energy, the enthalpy change is one of the components that determine spontaneity.
- An exothermic process releases heat, resulting in a negative (\( \Delta H \)), which can make a reaction more likely to be spontaneous, but only when coupled with favorable entropy changes.
- An endothermic reaction absorbs heat, leading to a positive (\( \Delta H \)). Such reactions can still be spontaneous if the temperature and entropy changes are sufficient to make (\( \Delta G \)) negative.
It is important to note that simply having a negative Gibbs Free Energy does not automatically mean a reaction is exothermic, as interplay with entropy and temperature can offset enthalpy contributions.
- An exothermic process releases heat, resulting in a negative (\( \Delta H \)), which can make a reaction more likely to be spontaneous, but only when coupled with favorable entropy changes.
- An endothermic reaction absorbs heat, leading to a positive (\( \Delta H \)). Such reactions can still be spontaneous if the temperature and entropy changes are sufficient to make (\( \Delta G \)) negative.
It is important to note that simply having a negative Gibbs Free Energy does not automatically mean a reaction is exothermic, as interplay with entropy and temperature can offset enthalpy contributions.
Entropy
Entropy (\( \Delta S \)), often described as a measure of disorder or randomness, is a crucial component when discussing the spontaneity of reactions. In chemical reactions, an increase in entropy (\( \Delta S > 0 \)) typically favors a spontaneous process, especially at high temperatures.
- A positive change in entropy indicates greater disorder in the system's products compared to its reactants.
- Entropy's influence grows as the temperature increases, which is represented in the Gibbs Free Energy equation by the term (\( T \Delta S \)).
When evaluating a reaction's spontaneity, considering both enthalpy and entropy is vital, since a reaction can be spontaneous if a large enough positive (\( T \Delta S \)) can offset a positive (\( \Delta H \)). This emphasizes that even reactions that absorb energy can happen spontaneously when they lead to substantial increases in the system’s entropy.
- A positive change in entropy indicates greater disorder in the system's products compared to its reactants.
- Entropy's influence grows as the temperature increases, which is represented in the Gibbs Free Energy equation by the term (\( T \Delta S \)).
When evaluating a reaction's spontaneity, considering both enthalpy and entropy is vital, since a reaction can be spontaneous if a large enough positive (\( T \Delta S \)) can offset a positive (\( \Delta H \)). This emphasizes that even reactions that absorb energy can happen spontaneously when they lead to substantial increases in the system’s entropy.