Consider a chemical system containing species A, B, and C; and that A and B can react to make C in a bimolecular reaction with rate constant of k1, and C can decompose to make A and B in a first order reaction with rate constant of k-1. If the instantaneous amounts of A, B, and C are represented as a, b, and c, and the initial amounts are given as A0, B0, and C0, the change in C can be represented with the differential equation ![Consider a chemical system containing species A, B, and C; and that A and B can react to make C in a bimolecular reaction with rate constant of k<sub>1</sub>, and C can decompose to make A and B in a first order reaction with rate constant of k<sub>-1</sub>. If the instantaneous amounts of A, B, and C are represented as a, b, and c, and the initial amounts are given as A<sub>0</sub>, B<sub>0</sub>, and C<sub>0</sub>, the change in C can be represented with the differential equation . If A<sub>0</sub> = 2 , B<sub>0</sub> = 2, C<sub>0</sub> = 0, k<sub>1</sub> = 0.04, and k<sub>-1</sub> = 0.04, solve the differential equation for c and graph the solution. [Note: c can never be larger than C<sub>0</sub> plus the smaller of A<sub>0</sub> or B<sub>0</sub>. Nor can it be smaller than 0.]](https://d2lvgg3v3hfg70.cloudfront.net/TB2342/11eaa948_cce7_2035_84bc_9b5b210a4914_TB2342_11.jpg)
. If A0 = 2 , B0 = 2, C0 = 0, k1 = 0.04, and k-1 = 0.04, solve the differential equation for c and graph the solution. [Note: c can never be larger than C0 plus the smaller of A0 or B0. Nor can it be smaller than 0.]
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