Question

A certain reaction is known to have a \(\Delta G^{\circ}\) value of \(-122 \mathrm{~kJ} / \mathrm{mol}\). Will the reaction necessarily occur if the reactants are mixed together?

Short answer

While \(\Delta G^{\circ}\) value of -122 kJ/mol shows the reaction as spontaneous, it doesn't necessarily mean the reaction will occur instantly when the reactants are mixed. Factors such as kinetics, concentration, temperature, and potential activation energy can determine if a reaction will actually occur or not.

Step-by-step solution

Understanding Gibb's free energy (ΔG°)

Before examining the aforementioned reaction, it's crucial to understand what \(\Delta G^{\circ}\) signifies. Gibb’s free energy (\(\Delta G\)) is a thermodynamic potential that measures the maximum reversible work a system can perform at constant temperature and pressure. If \(\Delta G\) is negative, the reaction is spontaneous, if it's equal to zero, the reaction is at equilibrium and if it's positive, the reaction is non-spontaneous.

Analyzing the given reaction

The given reaction has a \(\Delta G^{\circ}\) of -122 kJ/mol, which implies that it's spontaneous.

Determining the spontaneity of reaction

Though the given \(\Delta G^{\circ}\) indicates a theoretically spontaneous reaction, it doesn't necessarily guarantee that the reaction will occur when the reactants are mixed. Kinetic factors, including temperature and the concentrations of the reactants, can influence the reaction. Also, some reactions need an initial energy input or 'Activation Energy' to start, despite of being spontaneous. Hence, the mention of 'Necessarily occur' isn't guaranteed by just knowing \(\Delta G^{\circ}\).

Key concepts

Spontaneous Reaction

A spontaneous reaction is a process that occurs without needing continuous external energy input once it has begun. In chemical thermodynamics, a reaction is considered spontaneous if it leads to a decrease in the system's free energy — indicated by a negative Gibbs free energy change (\rg\(\Delta G < 0\)). However, it's essential to clarify that 'spontaneous' does not necessarily mean 'instantaneous'. The rate at which a spontaneous reaction proceeds is governed by its reaction kinetics, not the \rg\(\Delta G\) value alone.

For the reaction with \rg\(\Delta G^{\circ} = -122 \mathrm{~kJ} / \mathrm{mol}\), although \rg\(\Delta G\) indicates a tendency to occur spontaneously, we must consider factors such as activation energy and reaction conditions. Sometimes, a barrier in the form of activation energy must be overcome before the reaction can proceed. Thus, a negative \rg\(\Delta G\) value is a thermodynamic prerequisite for spontaneity but not a guarantee of a reaction's immediate occurrence.

Chemical Thermodynamics

Chemical thermodynamics is the study of the relationship between heat, work, temperature, and chemical reactions or with the physical changes of state within a chemical system. The central concept is the energy change associated with chemical reactions, especially in terms of enthalpy (\rg\(\Delta H\)), entropy (\rg\(\Delta S\)), and the Gibbs free energy (\rg\(\Delta G\)).

The Gibbs free energy is particularly important because it indicates the maximum amount of work a chemical reaction can perform and also dictates the direction and spontaneity of the chemical process under constant pressure and temperature. The formula \rg\(\Delta G = \Delta H - T\Delta S\) brings together these concepts. If \rg\(\Delta G\) is negative after we plug in the values for \rg\(\Delta H\), \rg\(\Delta S\), and the temperature (T), the reaction is thermodynamically favorable. While \rg\(\Delta G^{\circ}\) gives us a snapshot of a reaction's thermodynamic potential at standard conditions, the actual conditions under which a reaction takes place can significantly modify this potential.

Reaction Kinetics

Reaction kinetics is the study of the rate at which chemical processes occur and the factors that affect these rates. It's a field that focuses on how quickly a reaction reaches its final equilibrium state, not just whether the reaction is thermodynamically favorable. An essential concept in kinetics is the activation energy (Ea), which is the energy barrier that must be overcome for reactants to transform into products.

In kinetics, the presence of a catalyst, the concentration of reactants, temperature, and the physical state of the reactants can all impact the reaction rate. For a reaction with a given \rg\(\Delta G^{\circ}\) value, kinetics will determine how rapidly the reaction will approach equilibrium — if at all. For instance, even with a highly negative \rg\(\Delta G^{\circ}\), a reaction may be kinetically hindered if the activation energy is too high or if the temperature is too low, effectively leading to a situation where the reaction rate is negligible.