Question

(a) What is the meaning of the standard free-energy change, \(\Delta G^{\circ}\), as compared with \(\Delta G ?\) (b) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0 ?(c)\) For a certain process, \(\Delta G\) is large and negative. Does this mean that the process necessarily occurs rapidly?

Short answer

(a) \(\Delta G\) is the actual Gibbs free energy change for a reaction, indicating the energy available to do work when the reaction occurs, while \(\Delta G^{\circ}\) is the Gibbs free energy change under standard conditions (1 M, 25°C, 1 atm). (b) When \(\Delta G=0\), it signifies that the process has reached equilibrium at constant temperature and pressure, with no net change in the concentrations of reactants and products. (c) Although a large and negative \(\Delta G\) signifies that the process is highly spontaneous, it does not necessarily imply that the process will occur rapidly. The rate of the process depends on the activation energy and the presence of catalysts.

Step-by-step solution

a) Difference between \(\Delta G^{\circ}\) and \(\Delta G\)

The Gibbs free energy change, denoted as \(\Delta G\), is a thermodynamic quantity that measures the maximum reversible work that can be performed by a system at constant temperature and pressure. In other words, it indicates how much energy is available to do work when a reaction occurs. On the other hand, the standard free-energy change, \(\Delta G^{\circ}\), refers to the Gibbs free energy change under standard conditions, that is, when the reactants and products are present at 1 M concentration, 25°C temperature, and 1 atm pressure. So, the main difference between \(\Delta G\) and \(\Delta G^{\circ}\) is that \(\Delta G\) is the actual Gibbs free energy change for a reaction, while \(\Delta G^{\circ}\) is the Gibbs free energy change under standard conditions.

b) Significance of \(\Delta G=0\) for a constant temperature and pressure process

For a process occurring at constant temperature and pressure, the Gibbs free energy change (\(\Delta G\)) determines whether the process is spontaneous, non-spontaneous, or at equilibrium. The significance of \(\Delta G=0\) can be understood as follows: 1. If \(\Delta G < 0\), the process is spontaneous and favors the formation of products. 2. If \(\Delta G > 0\), the process is non-spontaneous and favors the formation of reactants. 3. If \(\Delta G = 0\), the process is at equilibrium, meaning that the rates of the forward and reverse reactions are equal, and there is no net change in the concentrations of reactants and products. Hence, when \(\Delta G=0\), it signifies that the process has reached equilibrium at constant temperature and pressure.

c) Large negative \(\Delta G\) and rate of a process

A large and negative value of \(\Delta G\) indicates that the process is highly spontaneous and thermodynamically favorable, meaning that there is a considerable amount of energy available to do work. However, the rate of the process (how fast the process occurs) is determined by the activation energy and not by the spontaneity of the reaction (\(\Delta G\)). The activation energy is the minimum amount of energy required for the process to proceed. A reaction with a high activation energy will have a slower rate, while a reaction with a low activation energy will have a faster rate. The presence of catalysts can also affect the rate of a reaction by lowering the activation energy. In conclusion, although a large and negative \(\Delta G\) signifies that the process is highly spontaneous, it does not necessarily imply that the process will occur rapidly. The rate of the process depends on the activation energy and the presence of catalysts.