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Instantaneous rates: Chemistry

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I'm trying to figure out how to do instantaneous rates, but it seems like I need to know calculus to do this. I don't know calculus, and it wasn't listed as a prerequisite; I wasn't told the first day I need to know anything beyond basic algebra.


Anyway, I'm suppose to find the "slope of a line tangent to the curve at any point."


I don't really understand that. I tried searching for hours about this stuff, and I couldn't really find anything to help me; well, I tried analyzing stuff, but I couldn't see how it applied to what I was doing.


The book didn't have that information.


I know how to find the slope of something. But drawing this line against the curve... I don't know how to do that.


Therefore, I decided to come here.


Here is an image giving an example of instantaneous rate:

click here



Thing is, I don't exactly understand how the authors were able to get that line next to the point (t=600) on the graph.


No equation has been giving to figure out how to do that.


The book also tells me this:


I'm not very sure about how it obtained those top variables. It seems like it picked them out of thin air. If I'm correct, though, those variables come from the points that the slope comes across. However, I couldn't know those points unless I had done all of this in a graphing calculator, right?


I haven't the slightest clue how those top variables were obtained, nor do I have the slightest clue how to make that line go against the point of the curve.


How do I do these things?


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The blue/grey triangle shaded on the graph is the clue.

The slope of that tangent is the change in y divided by the change in x. In this case its the change in concentration of butyl chloride divided by the time over which that change took place.

The values can be found by reading off the axes. Look at the line drawn as a tangent to the graph. At 400 sec the concentration is 0.042M at 800 sec its 0.018M and so the difference is 0.024M. Divide that by the difference in time and you get the rate of change.

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How would you find the triangle if it's instanteous rate was 300?


This was a question in the book:

Using Figure 14.4(the graph), determine the instantaneous rate of disappearance of

C4H9cl at T = 300s.


I couldn't figure out this problem because I couldn't find the range in Time and Molarity. I suppose I need the triangle's to figure it out but I don't know how to aquire them.


P.S. - The equation is Rate= - Change of [C4H9cl]/change of Temperature


The answer sheet said 1.1 * 10-4 M/s

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