By G. Hadley
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Extra resources for Linear Programming.
Example text
For most reactions that occur in the liquid phase, such changes in volume are small and normally can be neglected. Conversely, in gas-phase reactions the volume/molal relation is governed in the limit by the ideal gas law and volume changes must be taken into account. For the simple reactions we have been discussing, it is possible to write the volume change directly in terms of the amount of reaction in a convenient form using the fractional conversion. First de®ne an expansion (or contraction) factor , which represents the dierence in reaction system volume at the completion of the reaction and at the start of the reaction divided by the initial value: VI À V0 =V0 1-51 where V0 is the initial volume and VI the ®nal volume.
Eng. 4 The Type III reaction system discussed consisted of irreversible individual steps; however, a more realistic model for many series reactions might be: A6B6C with k1 , k3 forward, and k2 , k4 reverse rate constants, respectively. Derive an expression for the concentration of B as a function of time of reaction under isothermal, constant-volume conditions. Solution The kinetic relationships are: dCA =dt Àk1 CA k2 CB i dCB =dt k1 CA À k2 k3 k4 CC ii dCC =dt k3 CB À k4 CC iii The most convenient approach to obtaining a solution in the time domain for a sequence of reversible rate equations was detailed a long time ago [A.
Apparent Reaction Kinetics 49 which has the interesting property of approaching in®nity as the magnitudes of rt and rb become the same. Physically this means an explosion, so rt rb de®nes an explosion limit for the branching chain reaction. The branching chain theory has been used to interpret explosions in the low-pressure region for reactions such as H2 NO2 and CONO2 . This sort of explosion is dierent from the normal thermal explosion in which the heat evolved in a reaction cannot be removed from the system, leading to increasing temperatures, rates of reaction, heat evolution, noise, and a pu of greasy blue smoke.
Linear Programming. by G. Hadley
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