Kinetics : Integrated Forms of the First-Order
Integrated Form of the First-Order Rate Law
The original first-order rate law equation is:
The integrated form of the first-order rate law equation is:
Where X is the concentration of a reactant at any moment in time, (X)o is the initial concentration of this reactant, k is the constant for the reaction, and t is the time since the reaction started.
This equation is useful in calculating how much of a substance remains after a certain amount of time has passed, or to calculate how long it takes until the concentration is at a certain point.
||If the rate law of a reaction is first order
with respect to [A], then the graph of ln[A]
versus time (t) creates a straight line with a
negative slope. The value of the slope of the
line is equal to the negative value of the
rate constant (k).
Integrated Form of the Second-Order Rate Law
The original equation for a second-order rate law with a single reactant is:
The integrated form of the second-order rate law equation is:
||If the rate law for a reaction is second order
with respect to [A], a graph of 1/[A] versus
time (t) creates a straight line with a positive
slope. The value of the slope of the line is
equal to the value of the rate constant (k).