For the reaction; \(2 A+B+C \longrightarrow A_{2} B+C\) The rate \(=K[A][B]^{2}\) with \(K=2.0 \times 10^{-6} M^{-2} \mathrm{~s}^{-1} .\) Calculate the initial rate of the reaction when \([A]=0.1 M,[B]=0.2 M\) and \([C]=0.8 M\). If the rate of reverse reaction is negligible then calculate the rate of reaction after \([A]\) is reduced to \(0.06 M\).

Understanding the reaction rate calculation is essential for students studying chemical kinetics. The rate of a chemical reaction measures how fast the reactants are converted into products over time. It is usually expressed in terms of concentration change per unit time, for instance, moles per liter per second (M s^-1).

To calculate the initial rate of a reaction, as in our textbook problem, you use the given rate law expression and substitute the initial concentrations of the reactants. The rate law for the reaction, based on the problem, is given as rate = K[A][B]², where K represents the rate constant — a unique value for each reaction at a specific temperature — and [A] and [B] are the concentrations of the reactants A and B. For the given reaction, you simply plug in the initial concentrations and perform the multiplication to find the initial rate.

The connection between concentration and reaction rate is directly observable in the calculations. For instance, if the concentration of A doubled, and the concentration of B remained the same, the reaction rate would also double, according to the rate law.

Rate law expressions are the mathematical relationship that describes the connection between the concentrations of reactants and the reaction rate. The general form of a rate law is rate = k[Reactant 1]ⁿ[Reactant 2]^m..., where k is the rate constant, and n and m are the reaction orders with respect to each reactant. These orders are determined experimentally and are not necessarily related to the reaction's stoichiometry.

The rate law helps predict how changes in concentration affect the reaction rate. As seen in our exercise, the rate of the reaction depends specifically on the concentration of reactants A and B, each raised to a power that represents their respective reaction order in the equation. The reaction order provides valuable insights into the mechanism of the reaction and how each reactant's concentration affects the rate.

Initial concentration effects are an integral part of understanding how chemical reactions progress over time. The initial concentrations of reactants can significantly influence the reaction rate, which is quantified by the rate law. As the reactants are consumed to form products, their concentrations decrease. This, in turn, causes a change in the reaction rate if the reaction order with respect to a reactant is not zero.

In the case of our practice problem, decreasing the concentration of reactant A from 0.1 M to 0.06 M leads to a decreased rate of reaction. This effect demonstrates the importance of initial concentrations — particularly in reactions where reactants are not in large excess, and their depletion can be practically observed, altering the reaction dynamics. Emphasizing how the rate will change with varying initial concentrations helps students predict the behavior of reaction systems under different conditions and plan experiments accordingly.