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A rate law is a mathematical expression describing the relationship between reaction rate and reactant concentrations. It expresses how the rate depends on the concentration of each reactant raised to a specific power, called the reaction order. The rate law includes the rate constant k, which is specific to a particular reaction at a given temperature, and the reaction orders for each reactant, which are determined experimentally.

Reaction orders and the rate constant are determined by observing how the reaction rate changes as reactant concentrations vary. A common experimental approach is the method of initial rates, which involves measuring reaction rates using different initial reactant concentrations. Comparing these measured rates allows chemists to determine the reaction orders and subsequently calculate the rate constant to formulate the rate law.

In a zero-order reaction, the reaction rate remains constant throughout and is independent of reactant concentration. Since the reactant concentration is raised to the zeroth power in the rate law, any number raised to zero equals one, making the rate equal to the rate constant alone. Therefore, even as the reactant concentration decreases, the reaction rate does not slow down.

In a first-order reaction, the reaction rate is directly and linearly proportional to reactant concentration. The reactant concentration is raised to the first power in the rate law, so the rate depends directly on the concentration value. As the reactant concentration decreases, the reaction rate decreases proportionally in a linear manner.

In a second-order reaction, the reactant concentration is raised to the second power in the rate law, making the rate dependent on the square of the concentration. This quadratic relationship means small changes in concentration produce larger changes in rate. As reactant concentration decreases, the reaction rate decreases exponentially rather than linearly, following the squared concentration term.

The overall reaction order is the sum of the individual reaction orders for all reactants in the rate law. For example, in a reaction that is first-order in reactant A and second-order in reactant B, the overall reaction order is three (1 + 2 = 3). The overall order determines the mathematical dependence of the reaction rate on all reactant concentrations combined.

No, reaction orders cannot be reliably predicted from stoichiometric coefficients. Rate laws are determined by experiment only and must be established through direct observation of how reaction rates change with concentration. Reaction orders can be integers, fractions, negative, or zero, and this experimental determination is essential for accurately describing reaction kinetics.