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Chemical kinetics

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Here are a few questions puzzling me for a long period of time.

1. If reactant X is converted to product Z through a intermediate Y.

Then, it is unfair to compare the rate constant of (y to z and x to y) just on the basis of the activation energy for the steps, right?

arrhenius equation : k=A *exp(Ea/RT)

What does A mean and under what circumstances does it change.

2. Recently, my class took a laboratory experiment but I am not sure about the validity of theorem behind.

In the experiment, four different set-ups with the concentration of the propanone solution as the sole variable factor are used.

At fixed time interval, the concentration of the remaining iodine concentration was recorded.

The problem is here,

We plot the rate of reaction against the concentration of the propanone which are set in different values in four set-ups.

but the rate of reaction is taken as the slope of the graph of

the concentration of iodine solution VS the time.

Aren't the slopes only the average rate of the reaction, I bet initial rate should be taken, right?

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Yes, this is the method of initial rates. What happens is that at the start of reaction there is insufficient product for any drastic effect a reverse reaction may have, hence initial rate of reaction is taken and it is a tangent at point of time as [math]\Delta t\rightarrow 0[/math]. When you have varied concentrations of different reactants for multiple retries you can get different initial rates of reaction. This will be useful in determining experimental constants a and b in [math] Rate = k[A]^a [ B]^b [/math] where A and B are reactants (in this example only 2 reactants) in that you will be able to use different rates and then comparing each with 2 different experiments. For example; in 2 of the experiments you would've varied concentration of one reactant while keeping other the same, you can use this neatly to do a ratio equation such as:

 

[math] \frac{Rate_1}{Rate_2} = \frac{k[A ]^a [b ]^b}{k_2[A ]_2^a [b ]_2^b} [/math]

 

in which you can cancel out either A's or B's depending on which one you kept the same for those two experiments. You also cancel k's. Then you get fraction of [math]\frac{rate_1}{rate_2} = [A]^a[/math], multiply both sides by natural logarithm, ln, and you'll get your 'a'. After you get your 'a' (which is usually an integer 0, 1, 2 or a half - this also determines the order of reaction with respect to A, but not the overall order) you can use it in conjunction with other 2 experimental retries to figure out 'b'. However, if you have another 2 experiments where you varied concentration of B but kept [A] the same then you can use that as well; again, [A]'s will cancel, along with k's and you get your b. Then you rewrite your rate equation with known constants of a and b, hence you determine the overall order of reaction, and then you can use one of the experimental results (one only!) to find out what constant k is as you will by now know both 'a' and 'b'. When you find k you rewrite the equation again with k in it. You can then test this rate equation to see how it fits by substituting various experimental results.

 

That pretty much sums up the initial rates method for determining the rate equation.. I hope.

 

And as a further note: all of the above is for a plot of concentration vs time. I'm not quite sure what you're referring to, maybe you can clarify.

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