Question

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, and (c) the reaction is always exothermic.

Short answer

The false statement is (c) the reaction is always exothermic.

Step-by-step solution

Analysis of statement (a)

A negative \(\Delta G^{\circ}\) implies a spontaneous reaction under standard conditions. For such reactions, the Equilibrium Constant, \(K\), is greater than one (since \( K = e^{-\Delta G^ι/RT}\), where R is the gas constant and T is the absolute temperature). Hence, statement (a) is true.

Analysis of statement (b)

As concluded in step 1, a reaction with negative \(\Delta G^{\circ}\) is spontaneous (also known as thermodynamically favorable) when all reactants and products are in their standard states. Hence, statement (b) is also true.

Analysis of statement (c)

A reaction with a negative \(\Delta G^{\circ}\) is spontaneous, but it is not necessarily always exothermic. The \(\Delta G\) value is also affected by the entropy change \(\Delta S\) (since \(\Delta G^ι = \Delta H^ι - T\Delta S\), where \(\Delta H\) is the enthalpy change). So, even endothermic reactions (\(\Delta H > 0\)) may have negative \(\Delta G^{\circ}\) if there is a sufficiently large positive \(\Delta S\), making the reaction spontaneous. Therefore, statement (c) is false.

Key concepts

Spontaneity of Reactions

The spontaneity of reactions is a crucial concept in chemistry and is determined by the Gibbs Free Energy change, \( \Delta G \). If \( \Delta G^{\circ} \) is negative, the reaction is considered spontaneous under standard conditions. This means that the process can occur without outside energy input. Spontaneity is not always linked with speed; a reaction can be slow but still spontaneous.
It's important to remember that spontaneity and being thermodynamically favorable are the same in this context. This means that the reaction tends to proceed forward to reach equilibrium.
While a negative \( \Delta G^{\circ} \) indicates spontaneity, this does not imply the reaction must be exothermic, where heat is released. Instead, the overall thermodynamic equation, \( \Delta G = \Delta H - T\Delta S \), shows that both enthalpy \( \Delta H \) and entropy \( \Delta S \) influence spontaneity. A reaction can still be spontaneous if the entropy change, \( \Delta S \), is significant enough to overcome an endothermic \( \Delta H \).
In summary, while negative \( \Delta G^{\circ} \) means a spontaneous reaction, it does not enforce that the reaction must be exothermic.

Equilibrium Constant

The Equilibrium Constant, \( K \), is a vital factor in understanding chemical equilibria. It is related to the Gibbs Free Energy through the equation \( \Delta G^{\circ} = -RT\ln K \,\) where \( R \) is the gas constant and \( T \) is the temperature in Kelvin. From this relationship, it’s clear that a negative \( \Delta G^{\circ} \) implies \( K > 1 \.\) In essence, when \( K \) is greater than 1, the products of the reaction are favored at equilibrium, indicating a greater tendency for the reaction to occur in the forward direction.
Equilibrium constants give us insight into the position of equilibrium and the extent to which reactants are converted into products. A large \( K \) value indicates that at equilibrium, the concentration of products is much higher than that of reactants. Conversely, a small \( K \) value would mean that reactants dominate at equilibrium.
This relation helps chemists predict whether a reaction will be spontaneous or not. Thus, analyzing \( K \) provides valuable information about the potential yield of products in a given chemical reaction.

Thermodynamics

Thermodynamics is the study of energy transformations, and it plays a pivotal role in determining the direction and spontaneity of chemical reactions. The core of chemical thermodynamics can be summarized by understanding three key concepts: enthalpy \( \Delta H \), entropy \( \Delta S \), and Gibbs Free Energy \( \Delta G \).
Enthalpy assesses the total heat content of a system. It tells us if heat is absorbed or released during a reaction. Entropy, on the other hand, is a measure of the disorder in a system. The second law of thermodynamics asserts that the total entropy of a system and its surroundings always increases in a spontaneous process.
Gibbs Free Energy combines these two concepts into a single criterion that predicts reaction spontaneity. The equation \( \Delta G = \Delta H - T\Delta S \) shows how both enthalpy and entropy contribute to determining \( \Delta G \).
Understanding these relationships allows chemists to manipulate conditions to achieve desired outcomes, such as increasing reaction yields or correcting non-spontaneous reactions. Thus, thermodynamics not only predicts whether reactions will occur but also provides the foundation to control chemical processes effectively.