In an elementary chemical reaction, single molecules of two reactants A and B form a molecule of the product C: A + B → C. The law of mass action states that the rate of reaction is proportional to the product of the concentrations of A and B:




(See Example 4 in Section 3.3) Thus, if the initial concentrations are [A] = a moles/L and [B] b moles/L and we write x = [C], then we have dx/dt = k (a €“ x) (b €“ x)
(a) Assuming that a ≠ b, find as a function of t. Use the fact that the initial concentration of C is 0.
(b) Find x(t) assuming that a = b. How does this expression for x(t) simplify if it is known that [C] = a/2 after 20 seconds?

Transcribed Image Text:

d[C] K[A][B] dt