Using Integrated Rate Laws
We use integrated rate laws, and rate constants to relate concentrations and time. The rate law to use depends on the overall order of the reaction.
The Common Integrated Rate Laws
For a zero order reaction: A products , rate = k
The integrated rate law is [A] = -kt + [A_{o}]For a first order reaction: A products , rate = k[A]
The integrated rate law is ln [A] = -kt + ln [A_{o}]For a second order reaction: 2A products or A + B products (when [A] = [B]) , rate = k[A]^{2}
The integrated rate law is 1/[A] = kt + 1/[A_{o}]
To determine t, the time required for the initial concentration of a reactant to be reduced to some final value, we need to know:
Substitute this information into the integrated rate law for a reaction with this order and solve for t. The integrated rate laws are given above.
How Much Remains After a Given Time?
To determine [A], the concentration of a reactant remaining after some time, t, we need to know:
Substitute this information into the integrated rate law for a reaction with this order and solve for [A]. The integrated rate laws are given above.
What Concentration Was Present Initially?
To determine [A_{o}], the initial concentration of a reactant, we need to know:
Substitute this information into the integrated rate law for a reaction with this order and solve the equation for [A_{o}]. The integrated rate laws are given above.