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Understanding reaction rates is essential when analyzing chemical equilibrium. Reaction rates refer to the speed at which reactants convert into products over time. In a chemical reaction like \(3 \mathrm{~A} \rightleftharpoons \mathrm{B}\), the rate at which \(A\) becomes \(B\) and vice versa is crucial for achieving equilibrium.

- **Forward Reaction Rate:** Initially, when only \(A\) is present, \(A\) begins to transform into \(B\). The rate of this conversion is known as the forward reaction rate.

- **Reverse Reaction Rate:** Conversely, the reverse reaction rate represents how \(B\) can convert back into \(A\).

These rates are initially unequal but change as the reaction progresses. They adjust until both rates become equal, indicating the system has reached equilibrium.

Once a chemical reaction reaches equilibrium, the concentrations of the reactants and products become stable. In the exercise of \(3 \mathrm{~A} \rightleftharpoons \mathrm{B}\), establishing equilibrium means the concentrations stop changing with time because the reaction rates are balanced.

- If only \(A\) starts in the system, \(A\) will reduce, and \(B\) will increase until the concentration of \(B\) surpasses that of \(A\), achieving equilibrium conditions specified by the problem.

- When the system begins solely with \(B\), it must transform some of \(B\) back into \(A\), stabilizing at an equilibrium where \(B\) is again higher than \(A\).

- In cases where both \(A\) and \(B\) are present initially, the concentrations shift until \(B\) once again is in greater concentration than \(A\), creating the equilibrium stated for the exercise. Understanding these concentration dynamics is key to analyzing equilibrium states.

Dynamic equilibrium plays a significant role in how equilibrium is maintained in a chemical reaction. When a system reaches this state, reactions continue to occur, but the overall concentrations stay constant.

- **Continuous Reaction Activity:** In dynamic equilibrium, the reactions have not stopped. Instead, the forward and reverse reactions occur at the same rate, meaning that \(3 \mathrm{~A} \rightarrow \mathrm{B}\) and \(\mathrm{B} \rightarrow 3 \mathrm{~A}\) happen simultaneously, keeping concentrations unchanged.

- **Constant Concentrations:** This particular dynamic means that although molecules are continuously reacting, the amounts of \(A\) and \(B\) in the system do not fluctuate.

The concept of dynamic equilibrium helps understand why systems can stay stable externally while remaining active at the molecular level.