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A waste with a concentration of 0.1 gram per liter is to be

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A waste with a concentration of 0.1 gram per liter is to be introduced to a hazardous waste reactor that is to achieve 90% destruction. A reactant, which is intended to cause an exothermic reaction is to be mixed with the waste stream so that there is only one common/mixed input to the reactor.

If the waste is in excess of the reactant and is modeled with 1st order kinetics equal to k=1000/minute --- what does this mean?

And if the reactant was in excess to the waste stream and was modeled with 2nd order kinetics equal to k = 1000 g-moles per liter minute --- what does this mean?

What is the simple difference between the first and second order kinetics? Is there a benefit to one process over the other?

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Let W be the concentration of the waste
R be the concentration of the reactant
P be the product
We can write the general reaction as below:
W + R = P
Here we're not given the reaction stoichiometry, i.e. how much W will react with how much R. Therefore it is normal in chemistry that a number of assumptions and predictions are made.

First, the waste is in excess of the reactant and is modeled with 1st order ...

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