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
- How long does it take to react?
- What concentration remains after a given time?
- What was the initial concentration?
The Common Integrated Rate Laws
For a zero order reaction:
A
products , rate = k
The integrated rate law is [A] = -kt + [Ao]For a first order reaction: A
products , rate = k[A]
The integrated rate law is ln [A] = -kt + ln [Ao]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/[Ao]
To determine t, the time required for the initial concentration of a reactant to be reduced to some final value, we need to know:
- The initial concentration, [Ao].
- The final concentration, [A].
- The order of the reaction or enough information to determine it.
- The rate constant, k, for the reaction or enough information to determine it.
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:
- The initial concentration, [Ao].
- The length of time the reaction ran, t.
- The order of the reaction or enough information to determine it.
- The rate constant, k, for the reaction or enough information to determine it.
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 [Ao], the initial concentration of a reactant, we need to know:
- The final concentration, [A].
- The length of time, t, the reaction ran to reach the final concentration.
- The order of the reaction or enough information to determine it.
- The rate constant, k, for the reaction or enough information to determine it.
Substitute this information into the integrated rate law for a reaction with this order and solve the equation for [Ao]. The integrated rate laws are given above.
