[n11101]

Hello,
I am hoping someone can help me understand what I seem to be doing wrong. 

Looking at the graph in my textbook that I have posted, it says that the rate of change is -.28, divide that by the time, and you have the inst rate.


So where is the number of .28 coming from?  Using the numbers from the graph..  calculating where the tangent crosses the y axis would be points t=40, and t=60, and the respective values would be .44, .36, and the delta would be -.08.   If you look at the entire tangent line, a ball park estimate would say that the top line roughly hits .58, bottom is close to .23, again with a delta of roughly -.35.  How and where is this -.28 coming from. 

Is there a way to not have to rely on the viewing graphs for this material? 

I can't seem to solve any HW problems, because I appear to be unable to determine how the values of instantaneous velocity are determined...

[mjc123]

calculating where the tangent crosses the y axis would be points t=40, and t=60,

This is nonsense, any line crosses the y axis at t = 0. what are you talking about?
If you look at the tangent line as drawn, it extends over a range of 40 s (from t = 30 to 70), over which the concentration changes by -0.28 M (from ca. 0.50 at t = 30 to 0.22 at t = 70). I think your value of 0.35 comes from misreading the axes.

[n11101]

Obviously.. I took the values at t40 and t60 because the lines of y axis can clearly be seen, with a dot where they intersect. 

At thos values, I don't see the ones you get.  The tangent line spans 40s.  at t70, y.23 and t30, y.55, giving what I see as a value if .32 which is closer to the .28 that they have, but using the .32 value gets me the wrong answers.

Is there a way to determine this value without using the graph?  I'm actually good with calculus, actually far more comfortable with calculus than with algebra.  The first derivitave of this should be:
[A] + [ B ] -> 2[C]
and

derivitave [A] / derivative t    =  -k [A]^n   , where n is the rate order, often the same as the stoichometrical value of the coefficient of A. 

Can I not solve for k, and at that point having a set k value, be able to plug in any time t so my answers don't have to rely on what value I think I see on the graph?

Thanks for your help btw. 

[Borek]

0.28 is the length of the shorter leg of the right triangle drawn on the plot. -0.28, as the concentration decreases.

How are you going to find a derivative if you are not given the function? In typical situation you have just the experimental data, set of points. The best approach is the some kind of numerical differentiation, that's more or less of what they are trying to do.

[mjc123]

Obviously..

Not obvious at all.

I took the values at t40 and t60

Looking at the numbers, I think you took the values at t40 and t50.

because the lines of y axis can clearly be seen

You mean the vertical grid lines? They are not the y axis. The y axis is the line t=0.

with a dot where they intersect

A dot where they intersect the green curve. But that doesn't give you the values you need. You want the values where they intersect the tangent line.

at t70, y.23 and t30, y.55

Again you are getting the values from the curve, not from the tangent. These values will give you the average rate over the interval t= 30 to 70 s. To get the instantaneous rate at 50s, you need the slope of the tangent line.