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The blue curve is the plot of the data. The orange line is tangent to the blue curve at t = 40 s.?

for the reaction

A-->products

t(s) [A] (M)

0 0.52

20 0.43

40 0.35

60 0.29

80 0.24

100 0.20

Approximate the instantaneous rate of this reaction at time t = 40 s.

________? M/s

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let's build on your basics a bit. read through my answer here

https://thebasicanswers.com/1337/rate-law-from-concentration-vs-time-data

note this table of equations

.. .. .order.. .. .. . non-integrated.. .. .. . ..integrated

.. .. . .. 0.. . .. . ...rate = k x [A]°... .. .. . . ..[At] = -kt + [Ao]

.. . .. .. 1.. . .. . ...rate = k x [A]¹... .. .. . . ln[At] = -kt + ln[Ao]

.. . .. . .2... . .. .. .rate = k x [A]²... .. .. . . 1/[At] = +kt + 1/[Ao]

note the difference between non-integrated and integrated

.. non-integrated... RATE vs concentration

.. .. . .integrated... .TIME vs concentration

and from calculus, we know that the derivative of a function at a given point = the tangent at that point on the curve. and we can see that the non-integrated rate law is the derivative of the integrated curve.

meaning...

.. the rate of reaction = the slope of the tangent line at the given t value on the

.. time vs concentration plot.

***********

so.. do this

.. (1) draw the plot

.. (2) draw the tangent line

.. (3) pick two points on the tangent line and calculate slope.

.. .. ..I chose (20,0.42) and (60,0.28)

.. (4) rate = -1 * that slope... (it's negative because -d[A] / dt = rate... it's decreasing)

***********

I get

.. rate = - (0.42 - 0.28) / (0.20 - 0.60) = 0.0035 M/sec

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You just need to determine the slope of the orange line by calculating it:

slope = (y2-y1) / (x2-x1)

Pick any two points on that tangent line to use to determine the slope.

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