Relation of Rate Equation to Mechanism

The rate equation, sometimes called the rate law, relates the rate at time t to the activities (less rigorously, the concentrations) of the reactants remaining at that instant. Unlike the equilibrium expression (cf. Eq. 2.2), 

k is the forward rate constant, and the composition of the transition state is H4ASO4I, although it could contain additionally (or be short of) the elements of one or more water molecules, since we cannot determine the order with respect to the solvent. Equation 2.36 cannot be arrived at from reaction 2.35, but consideration of the concentration factors in the two equations tells us at once the rate law for the reverse reaction (Eq. 2.38, rate constant kr), since, according to reaction 2.35, the equilibrium expression has to be 

It follows that the equilibrium constant K is given by kf/kr- The reverse reaction is inverse second order in iodide, and inverse first-order in H . This means that the transition state for the reverse reaction contains the elements of arsenious acid and triiodide ion less two iodides and one hydrogen ion, namely, H2ASO3I. This is the same as that for the forward reaction, except for the elements of one molecule of water, the solvent, the participation of which cannot be determined experimentally. The concept of a common transition state for the forward and reverse reactions is called the principle of microscopic reversibility. 

However, more than one reaction pathway may exist, in which case the rate equation will contain sums of terms representing the competing reaction pathways. For example, one of the oxidation reactions that convert the atmospheric pollutant sulfur dioxide to sulfuric acid (a component of acid rain) in water droplets in clouds involves dissolved ozone, O3 (see Sections 8.3 and 8.5)  

Rate equations of considerable complexity can result from chain reactions, such as the reaction of bromine with hydrogen in the gas phase between 200 and 300 °C to form hydrogen bromide. These are reactions in which a chain carrier is created in an initiation step (here, a Br- atom from dissociation of Br2) and goes on to create more carriers (Br -t- H2 - HBr -I- H-, followed by H -(- Bra -t HBr -I- Br-, and so on) until a recombination step ends the chain. The rate equation for HBr formation has been shown to be  

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