A 1st order **consecutive reaction** of the type *A* → *B* → *C* is composed of the reactions:

The rate laws are:

To understand how a 1^{st} order consecutive reaction proceeds over time, we need to develop equations for , and . The expression for is the solution for eq20, i.e. . Substituting this in the 2nd rate law above and rearranging:

Eq21 is a linear first order differential equation of the form *y’* + *P*(*t*)*y* = *f*(*t*). Multiplying eq21 with the integrating factor , we have

The LHS of eq22 is the derivative of the product of and [*B*], i.e. . So,

Integrating both sides with respect to time, noting that [*B*] = 0 at *t* = 0, and rearranging, we have

As *t* → ∞, [*B*] = 0.

At all times, [*A*] + [*B*] + [*C*] = [*A _{0}*], so from eq23,

Substitute in the above equation and rearranging,

As *t* → ∞, [*C*] = [*A _{0}*].