We have learned from previous chapters that equilibrium and reaction constants are affected by temperature. The length of time that a disinfection process proceeds is a function of the constants of the underlying reaction between the microorganism and the disinfectant; thus, it must also be a function of temperature. The variation of the contact time to effect a given percentage kill with respect to temperature can therefore be modeled by means of the Van't Hoff equation. This equation was derived for the equilibrium constants in Chapter 11, which is reproduced next:
KT1 and KT2 are the equilibrium constants at temperatures T1 and T2, respectively. AH°98 is the standard enthalpy change of the reaction and R is the universal gas constant. If KT1 is replaced by contact time tT1 at temperature T1 and KT2 is replaced by contact time tT2 at temperature T2, the resulting equation would show that as the temperature increases, the contact time to kill the same percentage of microorganisms also increases. Of course, this is not true. Thus, the replacement should be the other way around. Doing this is the same as interchanging the places in the difference term between T1 and T2 inside the exp function. Thus, doing the interchanging,
Table 17.1 shows the standard enthalpy change as a function of pH for both aqueous chlorine and chloramines, and Table 17.2 shows the various possible values of the universal gas constant.
Example 17.2 The contact time for a certain chlorination process at a pH of 7.0 and a temperature of 25°C is 30 min. What would be the contact time to effect the same percentage kill if the process is conducted at a temperature 18°C?
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