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Chemistry More complicated rate expressions

You can use the computer model below to explore how the concentration of nitrogen dioxide, NO₂, affects the rate of the reaction:

2NO₂(g) --> 2NO(g) + O₂(g)

Make a measurement of initial rate of reaction (i.e. at time = 0 seconds) for various starting concentrations of nitrogen dioxide, [NO₂]. The model is set to work at a temperature of 573K.

Carry out the following steps: (Model)

set the starting concentration of NO₂ to 0.1 M.
set the rate to be measured at a time at 0 seconds.
run the model. The gradient and inital rate of reaction will be displayed.
enter the concentration value, [NO₂], and the rate into the text fields for the graph plotting program below the computer model
clear the reaction model but not the graph plotting program.
repeat this procedure for 4 other starting concnetrations of NO₂
choose [NO₂] on the x-axis
press plot to see the relationship between starting concentration and initial rate of reaction
on the graph plotting program, clear the graph only and then choose [NO₂] x [NO₂] on the x-axis
which plot, an x-axis of [NO₂] or [NO₂]², gives the best fit to a straight line?

Reaction Model: Decomposition of nitrogen dioxide at 573K.

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Graph Plotting: Rate of reaction against concentration.

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Back to instructions.

You should have found that there is a straight line relationship between the initial rate of reaction and the square of starting concentration of reactant, [NO₂]², with a gradient of about 5.0 x 10^-1 L mol^-1 s^-1.
This can be more generally expressed as saying there is a linear relationship between the rate of reaction and the reactant concentration squared. Mathematically this is:

rate of reaction is proportional to the reactant concentration squared
In the case you have been studying:

rate[NO₂]²
or
rate = k[NO₂]²
where k is the constant of proportionality, the rate constant, with units in this case of L mol^-1 s^-1 and the equation relating rate to concentration is the rate expression for this reaction.
The value of the rate constant varies with the temperature, so the value of about k = 5.0 x 10^-1 s^-1 for the decomposition of nitrogen dioxide is specific to the temperatue at which the measurements were made, in this case 573K.
Move on to the next page to summarise the learning from this tutorial.