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So from the two experiments lets summarize the important information. We did the same reaction for each experiment, at the same temeprature and other conditions. The only thing different between the two experiments was the initial concentration of [NO₂].

Experiment	[NO₂]	Initial Rate (M min^-1)
1	0.350 M	3.7 x 10^-2 M min^-1
2	0.700 M	1.5 x 10^-1 M min^-1

The data clearly says the initial rate of the reaction is dependent on the initial concentration of NO₂. From this knowledge of the dependence of the initial rate of a reaction on the initial concentration of NO₂ it is possible to determine the rate equation for the reaction. The rate equation gives the mathematical relationship between the reaction rate and the concentration of one or more reactants. Here is an animation of the data and how to obtain an average, instantaneous and initial rate.

From the data we see going from Exp 1 to Exp 2 we doubled the [NO₂].

Whan happened to the ratio of the initial rates?

Had we tripled the initial concentration of NO₂ the initial rate would have increased by a factor of nine.

So how do we interpret this information...;

[NO₂] increase by factor of 2 the rate increases by a factor of 4

[NO₂] increase by factor of 3 the rate increases by a factor of 9

So the rate increases by the square of the concentration. We could write a relationship mathematically that reflects the experimental data;

The exponent used with the [NO₂] is called the order for NO₂. We say the order of the reaction with respect to NO₂ is 2. Or we say the reaction is second order in NO₂.

To convert the relationship from a proportionality to an equality we need to add a constant. We will use 'k' to represent the constant and we will call the constant the rate constant. The new equation now becomes;

This is called the rate law equation for the reaction. It reflects the relationship betwen the initial rate, the rate constant and the order for each reactant.

For this reaction, under these experimental condition we need to know what the magnitude and the units of k, the rate constant. To determine the rate constant for the reaction we substitute for the [NO₂] and the initial rate from either of the experiments.

So;

Substituting for Experiment 1

and

So from the two experiments lets summarize the important information. We did the same reaction for each experiment, at the same temeprature and other conditions. The only thing different between the two experiments was the initial concentration of [NO2].

Experiment

[NO2]

Initial Rate (M min-1)

1

0.350 M

3.7 x 10-2 M min-1

2

0.700 M

1.5 x 10-1 M min-1

From the data we see going from Exp 1 to Exp 2 we doubled the [NO2].

Whan happened to the ratio of the initial rates?

Had we tripled the initial concentration of NO2 the initial rate would have increased by a factor of nine.

So how do we interpret this information...;

[NO2] increase by factor of 2 the rate increases by a factor of 4

[NO2] increase by factor of 3 the rate increases by a factor of 9

So the rate increases by the square of the concentration. We could write a relationship mathematically that reflects the experimental data;

The exponent used with the [NO2] is called the order for NO2. We say the order of the reaction with respect to NO2 is 2. Or we say the reaction is second order in NO2.

To convert the relationship from a proportionality to an equality we need to add a constant. We will use 'k' to represent the constant and we will call the constant the rate constant. The new equation now becomes;

This is called the rate law equation for the reaction. It reflects the relationship betwen the initial rate, the rate constant and the order for each reactant.

For this reaction, under these experimental condition we need to know what the magnitude and the units of k, the rate constant. To determine the rate constant for the reaction we substitute for the [NO2] and the initial rate from either of the experiments.

So;

Substituting for Experiment 1

and

So from the two experiments lets summarize the important information. We did the same reaction for each experiment, at the same temeprature and other conditions. The only thing different between the two experiments was the initial concentration of [NO₂].

[NO₂]

Initial Rate (M min^-1)

3.7 x 10^-2 M min^-1

1.5 x 10^-1 M min^-1

From the data we see going from Exp 1 to Exp 2 we doubled the [NO₂].

Had we tripled the initial concentration of NO₂ the initial rate would have increased by a factor of nine.

[NO₂] increase by factor of 2 the rate increases by a factor of 4

[NO₂] increase by factor of 3 the rate increases by a factor of 9

The exponent used with the [NO₂] is called the order for NO₂. We say the order of the reaction with respect to NO₂ is 2. Or we say the reaction is second order in NO₂.

For this reaction, under these experimental condition we need to know what the magnitude and the units of k, the rate constant. To determine the rate constant for the reaction we substitute for the [NO₂] and the initial rate from either of the experiments.