Consider the reaction described by the following equation

Question 12.6

We are fortunately given the rate law, which will make this question much less tedious than it could be. Consider the data for run 1, which we can plug into the rate law as follows:

rate = k[C₂H₄Br][I^-]

0.00114 M s^-1 = (5.33 x 10^-3 M^-1 s^-1)[x][0.231 M]

Solving for x, we get x = 0.926 M

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Now we do the same thing to find y, we just need to use run 2's data:

0.000569 M s^-1 =  (5.33 x 10^-3 M^-1 s^-1)[0.231 M][y]

This gives y = 0.462 M

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Again, use run 3's data to find z.

rate = (5.33 x 10^-3 M^-1 s^-1)[0.231 M][0.231 M] = 0.000284 M s^-1 = z

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Question 12.12

We must determine the order of reaction first. This can be done by using the relation:

Let's use data from run's 1 and 2 as follows to solve for n, the order of reaction:

Thus n = 1, so the reaction is first order with respect to C₂H₅Cl. Then the rate law is:

rate = k[C₂H₅Cl].

Now we can use the data from any run to determine k. Let's use the data from run #1:

0.560 x 10^-30 M/s = k(0.100 M)

k = 5.6 x 10^-30 s^-1

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Question 12.25

We can use the two-point Arrhenius equation to find the value of a rate constant:

Let k₂ be the rate constant we are solving for. That means k₁ = 6.1 x 10^-8 s^-1 with T₁ = 600.0 K and T₂ = 815.0 K. So:

k₂ = 0.0634 s^-1

This answer ought to make sense because the rate of reaction increases with temperature.

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Question 12.26

The Arrhenius equation can also take the form of

or

Which can be written as:

Notice that this equation is in the form y = mx + b, where x = 1/T and m = -E_a/R.

So the points you need to use are ln(0.868) = -0.141563 and ln(0.380) = -0.96758 for your y-values. For your x values, you need to use 1/725 K = 0.0013793 K^-1 and 1/325 K = 0.0030769 K^-1. So the points are:

(0.0013793 K^-1, -0.141563) and (0.0030769 K^-1, -0.96758)

The rise is given by:

The run is given by:

The slope is just the rise over the run, so m = -0.826017/0.0016976 K^-1 = -486.58 K

The activation energy form the Arrhenius equation above has the relation:

m = -E_a / R

-mR = E_a

E_a = -(-486.58 K)(8.314 J/mol K) = 4045.426 J/mol