1. Chemical Kinetics The Zeroth Order Integrated Rate Equation

2. The Rate Law for a general reaction
a X + b Y  products is
k, m, and n are numbers that are determined experimentally!!
This is the differential Rate Law.
The differential rate law relates the rate of reaction to the
concentrations of the various species in the system.
In this form, it isn't useful for predicting how much reactant
remains in solution or how much product has been formed in a given amount of time.
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3. We use the integrated form of the rate law for:
Testing to see whether a set of data follows 0th, 1st, or 2nd order.
Predicting how much reactant remains in solution or how much product has been formed in a given amount of time.
Let’s see what the integrated form of the rate law looks like for: Zeroth, First, and Second Order Rate Laws.
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4. Zeroth Order Rate Law
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5. This is the zero order differential rate law.
Zero Order (m+n=0)
For a general reaction
that obeys zero order rate law.
a X + b Y  products
This is the zero order differential rate law.
The rate of a zero order reaction is independent of the concentration of the reactant.
Increasing the concentration of the reacting species will not speed up the rate of the reaction. (i.e. Doubling concentration has no effect on rate.)
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6. This is the zero order differential rate law.
Zero Order (m+n=0)
For a general reaction
that obeys zero order rate law.
a X + b Y  products
This is the zero order differential rate law.
The reaction is experimentally determined to proceed at a constant rate.
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7. This is the zero order differential rate law.
For a general reaction
that obeys zero order rate law.
a X + b Y  products
This is the zero order differential rate law.
When this equation is rearranged and both sides are integrated we get the following result.
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8. that obeys zero order rate law.
For a general reaction
that obeys zero order rate law.
a X + b Y  products
This is the zero order differential rate law.
Separate the variables
Integrate
This is the zero order integrated rate law.
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9. This is the zero order integrated rate law.
For a general reaction
that obeys zero order rate law.
a X + b Y  products
This is the zero order integrated rate law.
[X]0 is the concentration of X at time=0
[X]t is the concentration of X at time=t
Rearrange,
[X]t = -ak0t + [X]0
A reaction is zeroth order if concentration data is plotted against time and the result yields straight line.
The slope of this resulting line is -ak0
The unit of k0 is M s-1
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10. that obeys zero order rate law.
For a general reaction
that obeys zero order rate law.
a X + b Y  products
Integrated rate law
Differential rate law
Rearrange,
[X]t = -ak0t + [X]0
Slope = -ak0
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11. Zero Order Example: A catalyzed reaction Oxygen atom CO Catalyst CO2
(Pt, Pd or Rh)
CO2
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12. that obeys zero order rate law.
For a general reaction
that obeys zero order rate law.
a X + b Y  products
Integrated rate law
Half-life, 
The half-life, , of a reaction is the time required for the
concentration of the reactant to decrease by half.
When t= ,
Half-life of a zero-order reaction is proportional to the initial concentration of X, [X]0.
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13.  For a general reaction that obeys zero order rate law. Half-life, 
a X + b Y  products
Half-life,  

14. Rate Equations For a general reaction, a X + b Y  products
Zeroth Order
Differential
Rate Law
Integrated Rate Law
Units of k
M s-1
Linear Plot
[X] vs. t
Half-life
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15. Determine the rate constant in M s-1 for a zero order reaction,
The initial concentration is 2.0 M. After one minute, the
concentration is 1.0 M.
What is the initial half-live?
X  products
[X]t = 1.0 M and [X]0= 2.0 M, a = 1
t = (1min) (60. sec/1 min) = 60. s 2.0 M - 1.0M = k (60. sec)     k = rate constant = M s-1
Note: Since it took 1 min for the initial concentration to drop to half its value. The half-life for this reaction is 1 min.

16. Rate Equations For a general reaction, a X + b Y  products
Zeroth Order
First Order
Second Order
Differential
Rate Law
Integrated Rate Law
Units of k
M s-1
s-1
M-1s-1
Linear Plot
[X] vs. t
ln([X]) vs. t
vs. t
Half-life
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