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Kinetics and the Initial Rates Method with Multiple Approaches

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See attachment for proper format.
For the hypothetical complex reaction,
OX2 + Cl2 + 2NO --> N2O + 2ClO +X2,
where X is an unknown element, data was obtained from measurement of the initial rate of reaction at varying concentrations. The results of this kinetics investigation under similar temperatures and conditions are summarized in the table below.
Initial concentrations of reactants Initial Rate (in mmol L-1 s-1)
Exp [OX2] [Cl2] [NO] (d[N2O])/dt
1 0.150 M 0.100 M 0.100 M 2.63
2 0.150 M 0.200 M 0.100 M 10.5
3 0.250 M 0.100 M 0.200 M 4.38
4 0.350 M 0.200 M 0.200 M 24.5

Using the initial rates method, find the order with respect to each of the reactants. Then find the rate constant, k, for the overall reaction.

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Solution Preview

See attachment for full solution with written work showing:
Step 1: Pick a set of experiments to compare
There are multiple approaches for the initial rates method that could be used here, but they all have to start in the same place. The initial rates method can be summed up with the statement "Compare how the rate of a reaction changes when changing only one variable (reactant concentration) while holding all other conditions constant". This limits which reactions we can use to start this evaluation. If you look at the concentrations of the reactants in the four different experiments you can see that there is only one set of experiments in which only one react is being changed. This is in experiments 1 and 2. In this case the concentrations of OX2 and NO are being held constant while the concentration of Cl2 is changing. So by using these two experiments we will be evaluating the reaction order for Cl2.

Step 2: Develop a template
This is an optional step, but I like to establish a template for how the final rate law will look. Then assign variables for the orders. So the rate law for the reaction given should look like the following:
Rate = k[OX2]x[Cl2]y[NO]z
Where k is the rate constant, and x, y, and z values would be the orders with respect to each reactant.

Step 3: Set up a ratio of two experiments
Now that we have the rate law and the experiments we want to use we can set up a ratio of two results:

(Written work shown in attachment)

Step 4: Cancel out terms
We now want to cancel out anything that we can. Ideally we want to be left with one variable. If we can't do this we have picked the wrong set of experiments to compare and should go back and pick another set of experimental values to use.

A few things to note:
- k will cancel out as it should be the same value if the conditions are the same (a key to doing this experiment is that we can't change temperatures).
- The units of rate and concentrations are different, but that doesn't matter as we can actually cancel out the units. This makes sinces, ...

Solution Summary

The Initial Rates Method, a common general chemistry method, is applied to a reaction where the initial concentrations and initial rate of the reaction is given for multiple experiments. Using this data the orders of each reactant and the rate constant for the reaction are determined using the full approach with each step written out showing the math. A simplified option is described as well, including details on when you can and cannot use the simplified option.

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