Can someone please please tell me how to calculate the instantaneous rate of a reaction from a graph.?

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Can someone please explain how to calculate the instantaneous rate of a reaction from a graph? 
In the problem, we are given the following reaction: H2(g) + Br2(g) ---> 2HBr(g). The graph below shows the concentration of Br2(g) as a function of time, and it is not linear. 
Part A asks us to calculate the average rate of the reaction between 0 and 25 seconds, which I can do. The average rate of change is simply calculated as (Change in concentration / Change in time). However, it also asks for the instantaneous rate at 25 seconds and at 50 seconds. Since there is no table of values, I can only estimate the concentration at those times by looking at the graph. 
I understand that the instantaneous rate of change is represented by the slope of the tangent line at that point, but how can I find the slope of a tangent line without using calculus or knowing specific values? The book mentioned choosing two values very close to the point of interest, but which two points should I select? For example, would 24 seconds and 26 seconds be appropriate? In the book, they used 30 seconds and 70 seconds to calculate the instantaneous rate at 50 seconds. Is there a general rule for selecting these points?

Anonymous · Accepted Answer

You're pretty much on track. Visualize a line tangent to the function to get the derivative at a point. 
Since 30 seconds and 70 seconds are both 20 seconds away from 50, it is acceptable to use those. 24 seconds and 26 seconds would be acceptable if you were trying to find 25 seconds, because a 2 second interval is pretty small.
The general rule is tangent line is the best, otherwise the line will intersect at two points. You want those two points to be as close together as possible.

Kayley Kunde · Answer

Instantaneous Rate Of Reaction

Anonymous · Answer

Instantaneous Rate Of Change Chemistry

Anonymous · Answer

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Can someone please please tell me how to calculate the instantaneous rate of a reaction from a graph.?
Can someone pleaseee tell me how to calculate the instantaneous rate of a reaction from a graph.
In the problem they give Consider the following reaction:
H2(g) + Br2(g) ---> 2HBr(g)
The graph below shows the concentration of Br2(g) as a function of time. The graph is not linear.
Part a...

Anonymous · Answer

For finding instantaneous rate around 25s, use the two ranges around the point, in this case at time 40 and 10, so you have (.65 - .9)/(40-10) = .0083. The correct answer is .0085, but this answer also works.

Anonymous · Answer

that depends on the reaction. for the reaction A ---> B + C rate = -d[A] / dt = k x [A]^n... where n is the order of the reaction. if n=0 -d[A] / dt = k x [A]^n becomes ∫d[A] = -k∫dt which integrates to [At] - [Ao] = -kt [At] = -kt + [Ao] so a plot of [A] vs t gives you a line with slope = -k in which case.. you can plug in k into this equation rate = k x[A]^0 ********* if n=1, ∫1/[A] d[A] = -k∫dt integrates to ln[A] = -kt + ln[Ao] and a plot of ln[A] vs t gives -k.. and you plug that into rate = k x [A]^1 ******* if n=2 1/[A] = +kt + 1/[Ao] and a plot of 1/[A] vs t gives +k.. and you finish like this rate = k x [A]^2 ********* so without seeing the data or knowing the reaction it's impossible to answer your question.

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Can someone please please tell me how to calculate the instantaneous rate of a reaction from a graph.?

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