The experimental data for the reaction, \(2 A+B_{2} \longrightarrow 2 A B\) are as follows. Write probable rate expression; \(\begin{array}{ccc}{[A]} & {\left[B_{2}\right]} & \text { Rate } \times 10^{4} \\ \text { mol litre }^{-1} & \text { mol litre }^{-1} & \text { mol litre }^{-1} \text { sec }^{-1} \\ 0.50 & 0.50 & 1.6 \\ 0.50 & 1.00 & 3.2 \\ 1.00 & 1.00 & 3.2\end{array}\)

When studying chemical kinetics, rate laws are fundamental equations that show the relationship between the concentrations of reactants and the rate of a chemical reaction.

Essentially, a rate law expresses the reaction rate as a product of a rate constant (\( k \)) and the reactant concentrations raised to some powers, which represent the respective orders of the reaction. Mathematically, for a reaction where the concentration of reactant A affects the rate, you might see a rate law such as Rate = k[A]^n, where 'n' is the order of the reaction with respect to A.

Determining the rate law requires experimental data, often obtained by holding the concentration of one reactant constant while varying the others. By examining how changes in concentration affect the rate, chemists can deduce the order of reaction for each reactant and calculate the rate constant.

In the context of chemical kinetics, the term 'reaction rate' refers to the speed at which a chemical reaction progresses. It's typically defined as the change in concentration of a reactant or product per unit time.

For example, if a reaction produces a product P, the rate can be expressed as the increase in concentration of P over time: Rate = Δ[P]/Δt. Conversely, for a reactant A being consumed, it's the decrease in concentration over time: Rate = -Δ[A]/Δt.

The negative sign indicates that the quantity of reactant is diminishing. Measuring these changes allows researchers to understand how quickly a reaction occurs under different conditions, which is crucial for controlling industrial processes, pharmaceutical synthesis, and many other applications.

The 'order of reaction' relates to how the rate of the reaction depends on the concentration of the reactants. It is determined by the reaction's stoichiometry and mechanism and can only be determined experimentally.

Each reactant in a reaction can have an order: zero, first, second, or even fractional. When the rate is independent of a reactant's concentration, that reactant's order is zero. A first-order reaction implies that the rate varies linearly with the reactant's concentration, while a second-order means the rate varies with the square of the concentration.

For the exercise at hand, the order with respect to reactant A is zero, as the reaction rate does not change with varying [A]. This means that A's concentration does not influence the rate at which the reaction proceeds.

The concentration dependence in chemical kinetics is essential for understanding how the concentrations of reactants influence the speed of the reaction. It's clear from the rate law that each reactant's concentration could affect the reaction rate differently, depending on the reaction order with respect to each reactant.

If a reactant appears in the rate law with a higher order, even a small change in its concentration can significantly impact the rate. On the other hand, a reactant that appears with a zero-order in the rate law has no effect on the rate—increasing or decreasing its concentration doesn't change how fast the reaction proceeds.

As seen in the provided exercise, increasing the concentration of B2 leads to a proportional increase in the reaction rate, indicating a direct dependency of rate on the concentration of B2, illustrating the fundamental concept of concentration dependence in chemical kinetics.