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Elementary reactions are single-step reactions that proceed via a single transition state, with the rate law being directly related to the balanced equation. The rate of an elementary reaction is directly proportional to the product of the concentrations of each reactant raised to the power of their stoichiometric coefficients.

Non-elementary reactions consist of multiple elementary reactions, each with its own rate law and reaction order. The overall rate law of a non-elementary reaction cannot be determined directly from its balanced equation because the reaction involves multiple steps, each with different reaction orders. The overall rate of the reaction is usually determined by the slowest elementary reaction, or the rate-determining step.

To construct the rate law for a non-elementary reaction, we need to establish the reaction mechanism, which consists of a series of elementary reactions that lead to the overall reaction. The rate law for each elementary reaction can be written based on its balanced equation, but the rate law for the overall reaction must be determined experimentally or through analyzing the reaction mechanism.

Under certain circumstances, the overall rate law for a non-elementary reaction can be related to the balanced equation. If the rate-determining step (the slowest step) has a direct relation between its rate law and its balanced equation, then the overall rate law resembles the balanced equation for the reaction. However, such a situation is very rare, and it's important to remember that you cannot assume the rate law directly follows the balanced equation without understanding the reaction mechanism. In conclusion, rate laws generally cannot be written from balanced equations because the stoichiometry of the reaction does not necessarily define the reaction order, which depends on the reaction mechanism. The rate law is directly related to the balanced equation only under the specific circumstance where the rate-determining step within a reaction mechanism resembles the balanced equation, which is relatively rare.