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

The reaction is thermodynamically favorable but may not occur due to kinetic barriers.

Step-by-step solution

Understanding Gibbs Free Energy

The sign of \( \Delta G^{\circ} \) tells us about the spontaneity of a reaction. A negative \( \Delta G^{\circ} \) indicates that a reaction is favorable under standard conditions.

Identify Reaction Conditions

Since \( \Delta G^{\circ} = -122 \) kJ/mol is negative, the reaction is thermodynamically favorable under standard conditions. However, whether a reaction will occur when mixed depends on more than just the thermodynamics;kinetic factors and reaction mechanisms can inhibit the reaction despite Gibbs free energy being negative.

Consider Kinetics

Even if a reaction is thermodynamically favorable, it may not occur if it faces kinetic barriers. For a reaction to proceed, it needs an appropriate pathway with sufficient energy to overcome any activation barrier.

Conclusion

The \( \Delta G^{\circ} \) value suggests the reaction is spontaneous, but it does not guarantee the reaction will happen as other factors such as reaction rates must be considered.

Key concepts

Thermodynamics

Thermodynamics is the science of energy and its transformations. A core aspect is understanding how energy changes in a chemical reaction. Gibbs Free Energy (\( \Delta G^{\circ} \)) is central to this. It helps predict whether a reaction can occur on its own under standard conditions. When \( \Delta G^{\circ} \) is negative, the reaction is deemed thermodynamically favorable.

This means that, in theory, the products have lower energy than the reactants, releasing energy to the surroundings.

• A negative \( \Delta G^{\circ} \) indicates spontaneity at constant temperature and pressure.
• Changes in temperature, pressure, and concentration can influence Gibbs Energy.
• Thermodynamics doesn’t account for how quickly a reaction proceeds.

Reaction Kinetics

Kinetics deals with the speed of a reaction and the steps it follows. While thermodynamics tells us if a reaction can occur, kinetics tells us how fast it will happen. It's about the pathway from reactants to products.

Each step in this pathway has its own rate, dictated by several factors:

• The concentration of reactants: More collisions occur at higher concentrations, influencing speed.
• Temperature: Higher temperatures increase the energy of the particles, hence speeding up reactions.
• Presence of a catalyst: Catalysts provide a different pathway that requires less activation energy.

To predict reaction rates accurately, understanding the mechanism is vital as every reaction has unique kinetic properties.

Activation Energy

Activation energy is the threshold that reactants must surpass to transform into products. Think of it as a hill that molecules must "climb" for the reaction to proceed. This energy barrier must be overcome by reactants for the reaction to start.

The difference between the energy of the activated state and the energy of the reactants is the activation energy \( E_a \).

• A high activation energy implies that few molecules have enough energy to react, slowing down the reaction.
• Catalysts can lower this barrier, allowing more reactant molecules to have enough energy to overcome it.
• Even thermodynamically favorable reactions might not occur without sufficient activation energy.

Understanding activation energy is crucial, especially for designing chemical processes where speed is essential.

Spontaneity of Reactions

Spontaneity in chemistry refers to a process that proceeds on its own without external influence, but not necessarily instantly. A spontaneous reaction under standard conditions means \( \Delta G^{\circ} \) is negative, but spontaneity doesn't imply an immediate reaction.

Factors affecting spontaneity include:

• Entropy: Increased disorder typically favors spontaneous processes.
• Enthalpy: Exothermic reactions often enhance spontaneity.

In real-world scenarios, both thermodynamic favorability and kinetic reality dictate whether a spontaneous reaction will actually occur. Just because a reaction is thermodynamically possible doesn't mean it will happen quickly or obviously. Maintaining a balance between these factors is key for efficient reactions.