If 15% of a substance decomposes in first 10 minutes in a first order reaction. Derive the rate constant of the 1st order reaction with graphical presentation and calculate how much of it would remain undecomposed after one hour?

lnA – lnAo = -kt

ln(A/Ao) = -kt

A/Ao = e^(-kt)

A = Ao e^(-kt) …(i)

Since graphical analysis is requested:

Assume Ao = 1 M (t = 0). Then at t= 10 min, A = 1-.15Ao or A = 0.85Ao. = 0.85 M

The equation of the best fit line shown on the plot is y=-0.0163x-4E-17. Consequently, we now have a value for k in units of M/min. The y-intercept should be lnAo = ln (1) = 0; due to internal calculation errors in the best fit algorithm, a value of -4E-17 is displayed, but this is essentially equal to 0.

To get A at t = 1 hr. = 60 min, one can use (i). Simply plug in known value of k, Ao = 1 M and t = 60 min and then calculate A. To help you know whether or not you have done this correctly, your answer should lie somewhere between 0.35M and 0.40M for an assumed starting concentration of 1M. As a percentage, the answer would be between 0.35 % and 0.40 %.

After 10 minutes, 85% is undecomposed.

After 20 minutes, 85% of 85% is undecomposed.

After 30 minutes, 85% of 85% of 85% is undecomposed

After 60 minutes, 85% of 85% of 85% of 85% of 85% of 85% is undecomposed.

0.85^6 = 0.377

=37.7%

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