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CivilSigma
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Homework Statement
My problem deals with understanding why we substitute in the reaction kinetics equivalent into mass conservation equation instead of dealing with differentials
Homework Equations
From the conservation of mass law about an envelope:
$$\frac{dm}{d t} = \sum m_{in} - \sum m_{out} + Generation - Consumption$$
Assuming there is a consumption of some compound, then:
$$Consumption = -\frac{dc}{dt} = kC^n$$
The Attempt at a Solution
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Why is that when we go to solve the mass balance equation, usually for the unknown concentration that varies with time (in this case for a complete mix reactor), we make the following substitution:
$$\frac{dm}{d t} = \sum m_{in} - \sum m_{out} - kVC^n$$
Why can't we do this:
$$\frac{dm}{d t} = \sum m_{in} - \sum m_{out} + -\frac{dc}{dt} \cdot V$$
$$ V \cdot \frac{dc}{dt} = \sum m_{in} - \sum m_{out} -\frac{dc}{dt} \cdot V$$
and then isolate for the differential terms, and integrate to get the final concentration??
Thank you.