# Answered Essay: Chapter 12| Kinetics 702 5. A study of the rate of the reaction represented as 2A → B gave the

Hello, I’m confused on number 5 part b and c. I know how to make the graph on part b but am having trouble figuring out how to estimate the instaneous rate of dissaperence of A at 15.0 s. also then on part c using all the answers together. The first pic is the textbook question. The second pic is what I have so far. the third pic is the answers in the back of the book. this is my second time posting this question… Thank you!

Chapter 12| Kinetics 702 5. A study of the rate of the reaction represented as 2A → B gave the following data: 0.0 5.0 10.0 15.0 20.0 25.0 35.0 1.00 0.952 0.625 o.465 0.370 0.308 0.230 Time (s) A] (M) (a) Determine the average rate of disappearance of A between 0.0 s and 10.0 s, and between 10.0 s and 20.0 s. (b) Estimate the instantaneous rate of disappearance of A at 15.0 s from a graph of time versus IAl. What are the units of this rate? (c) Use the rates found in parts (a) and (b) to deternine the average rate of formation of B between 0.00 s and 10.0s and the instantaneous rate of formation of B at 15.0 s

To find the instataneous rate of reaction you must do a graph and then draw a tangent line, this line must touch the point (time = 15 s) but must not cross the line graph, then you have to choose some points from it and read the x values and the y values, then you have to do

$\frac{y2 - y1}{x2 - x1}$

In your example I´m focussing and graphing the points where time is 10 , 15 and 20 secs.

The brown line is the tangent, it has values of y

y2 = 0.4

y1 = 0.5

X:

x1 = 13.7

x2 = 17.7

Calculate the slope

slope = (0.4 – 0.5 ) / (17.7-13.7 = – 0.025

the – sign is because the reactant is dissapearing, so it is correct to say that the instantaneous rate of dissapearance is 0.025 M/s

C. To calculate the average rate of reaction remember that:

$\frac{1}{a}\frac{\Delta A}{\Delta T} = \frac{1}{b}\frac{\Delta B}{\Delta T}$

in this case a = 2 and b = 1 so:

$\frac{1}{2}\frac{\Delta A}{\Delta T} =\frac{\Delta B}{\Delta T}$

So we just need to divide the average rate of reaction you got in the first part (which is correct by the way)

Average rate of formation of B = 0.0375 / 2 = 0.01875 M/s

Instantaneous rate of formation, it follows the same stoichiometrical rule I wrote before:

$\frac{1}{2}\frac{\mathrm{d} A}{\mathrm{d} t} =\frac{\mathrm{d} B}{\mathrm{d} T}$

so the instantaneous rate of formation of B is 0.025 / 2 = 0.0125 M /s

As an extra for you to see the formation of B, i calculated the formation of B from A, the ammount of A that dissapeared is the ammount of B formated dividided by 2.

 Time B 0 0 5 0.024 10 0.1875 15 0.2675 20 0.315 25 0.346 30 0.385

If you want to practice, try to get the instantaneous rate of formation of B by drawing a tangent line as I did in part b, you should be gettin the slope value of 0.0125 M

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