Complex reactions. The hydrogen-bromine reaction

The rate of the reaction is equal to the rate at which the activated molecules are formed, since the activated molecule decomposes immediately. The kinetics are second order, since the collision is a second-order process. 

Case 2. A Ca A 2. If after activation there is an appreciable time lag before the molecule falls apart, then there is opportunity for the activated molecule to make a number of collisions that may deactivate it. If the time lag is long, then the rate of deactivation, A iCaCa, is much greater than the rate of decomposition, k2Cp. This means that A 2, and A iCa + k2 A iCa. This brings Eq. (32.61) to the form 

In a gas-phase reaction, high pressures increase the number of collisions so that /c Ca is large and the rate is first order. The supply of activated molecules is adequate, and the rate at which they fall apart limits the rate of the reaction. At lower pressures the number of collisions decreases, k Ca is small, and the rate is second order. The rate then depends on the rate at which activated molecules are produced by collisions. 

The apparent first-order rate constant decreases at low pressures. Physically the decrease in value of the rate constant at lower pressures is a result of the decrease in number of activating collisions. If the pressure is increased by addition of an inert gas, the rate constant increases again in value, showing that the molecules can be activated by collision with a molecule of an inert gas as well as by collision with one of their own kind. Several first-order reactions have been investigated over a sufficiently wide range of pressure to confirm the general form of Eq. (32.61). The Lindemann mechanism is accepted as the mechanism of activation of the molecule. 

The kinetic law for the hydrogen-bromine reaction is considerably more complicated than that for the hydrogen-iodine reaction. The stoichiometry is the same. 

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