A solid, A, crystallizes in rods having a rectangular cross...

A solid, A, crystallizes in rods having a rectangular cross section. Suppose that when $\mathrm{A}$ is heated, the reaction $\mathrm{A}(\mathrm{s}) \rightarrow \mathrm{P}(\mathrm{g})$ occurs only on the ends of the rods. What would be the rate law for the reaction?

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Key Concepts

Surface Area Dependence

The reaction rate for surface reactions directly depends on the available surface area where the reaction can occur. In this scenario, only the ends of the rods are active. This limited and constant reactive surface area means that even as the volume (and overall mass) of the solid increases, the effective area for reaction remains unchanged, thus governing the rate law based on that fixed area.

Zero Order Kinetics

Zero order kinetics describe reactions whose rate is independent of the concentration of the reactant. For a reaction that occurs only on a fixed, geometry-determined portion of a solid, such as the ends of a rod, the reactive surface area remains constant regardless of the amount of solid present. As a result, the rate law reflects a zero order dependence on the solid reactant.

Heterogeneous Reaction Kinetics

This concept involves reactions occurring at the interface between two phases, such as a solid and a gas. In heterogeneous reactions, the rate is determined by the properties of the surface where the reaction takes place, rather than the concentration of the bulk reactant. In this problem, the reaction occurs on the ends of the solid rods, which highlights the importance of surface phenomena in controlling the reaction rate.

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