Example 5:
 Determine the rate law for the following reaction--- NH4+(aq) + NO2-(aq) 
N2(g) + 2H2O(l)
Experiment
[NH4+]initial
[NO2-]initial
Rate initial
1
5 x 10-2 M
2 x 10-2 M
2
5 x 10-2 M
4 x 10-2 M
2.70 x 10-7
M/s
5.40 x 10-7
M/s
3
1 x 10-1 M
2 x 10-2 M
5.40 x 10-7
M/s
Zero-Order Reactions
 Rate is NOT dependent on reactant concentration
 Graph of [A] vs. time gives STRAIGHT LINE
 If no straight line, reaction is NOT zero order
 Slope = -k
Zero-Order Graph
Integrated Rate Law
 Enables the determination a reactant’s concentration at any
moment in time
 Enables the determination of the time it takes to reach a
certain reactant concentration
 Enables the determination of the rate constant or reaction
order
st
1
Order Reactions
 Integrated Rate law
 ln[A]t – ln[A]0 = - kt
 ln[A] vs. time graph yields STRAIGHT LINE
 If no straight line, reaction is NOT 1st order
 Slope = -k
st
1
Order Graph
1st Order Integrated Rate
Law
 Only used with 1st order reactions
 Focus on initial concentration and ΔC for one reactant
 Initial concentration of reactant known---- can determine
reactant concentration at any time
 Initial and final reactant concentrations known---can
determine rate constant
1st Order Integrated Rate
Law
 Rate = -Δ[A]
= k [A]
Δt
-take equation and integrate with calculus to get….
 ln[A]t – ln[A]0 = - kt
 [A]0 = initial concentration (t = 0)
 [A]t = concentration after a period of time
Example 1: A  B + 2D
 Using the data provided for a 1st order reaction,
determine the rate constant and [A] at time = 5.0 x
102s.
Time (s)
[A] (M)
0
0.020
5.0 x 10
0.017
1.0 x 102
0.014
1.5 x 102
0.012
2.0 x 102
0.010
Example 1: continued
Example 1: A  B + 2D
 Using the data and graph provided, determine the rate
constant and [A] at time = 5.0 x 102s.
Time (s)
[A] (M)
0
0.020
5.0 x 10
0.017
1.0 x 102
0.014
1.5 x 102
0.012
2.0 x 102
0.010
Half-life
 Radioactive decay is a 1st order process
 Half-life (t1/2)—
 Time it takes for half of a chemical compound to decay or
turn into products
 Focus on reactant
 Constant, not dependent on [ ]
 Rate changes with temperature so half-life varies based on
temperature
Example 2:
 Find the half-life for the following reaction with a rate
constant (k) of 1.70 x 10-3 s-1
nd
2
Order Reactions
 Integrated Rate Law
 1___ -
[A]t
1__ = kt
[A]0
 1/[A] vs. time graph yields STRAIGHT LINE
 If no straight line, reaction is NOT 2nd order
 Slope = k
nd
2
Order Graph
2nd Order Integrated Rate
Law
 Used only for second order reactions
 Focus on initial concentration and ΔC for one reactant with
reaction 2nd order with respect to it.
 Initial concentration of reactant known---- can determine
reactant concentration at any time
 Initial and final reactant concentrations known---can
determine rate constant
2nd Order Integrated Rate
Law
 Rate = -Δ[A]
= k [A]2
Δt
-take equation and integrate with calculus to get….

1 __ [A]t
1__ = kt
[A]0
 [A]0 = initial concentration (t = 0)
 [A]t = concentration after a period of time
Example 3:
2NO2(g)  2NO(g) + O2(g)
 Using the data provided, find the rate constant if the
rate law = k[NO2]2.
Time (s)
[NO2]
0.0
0.070
1.0 x 102
0.0150
2.0 x 102
0.0082
3.0 x 102
0.0057
Example 3:
2NO2(g)  2NO(g) + O2(g)
 Using the data and graphs provided, find the rate law
and rate constant.
Time (s)
[NO2]
0.0
0.070
1.0 x 102
0.0150
2.0 x 102
0.0082
3.0 x 102
0.0057
Example 3: continued
Example 4:
 NO2 reacts to form NO and O2 by second-order
kinetics with a rate constant = 32.6 L/molmin. What
is the [NO2] after 1 minute if the initial [NO2] =
0.15M?
Concentration and Time Data
 Use data to construct all graphs for zero, 1st, and 2nd
reaction orders
 Determine which graph yields a straight line.
[A] vs. Time
Zero Order
ln[A] vs. Time
1st Order
1/[A] vs. Time
2nd Order
Homework
 Read over lab procedure