Question

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?


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Answer 1

Answer:

Dealing with your second question first (as it is easier!):

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

So 37.7%

Now for your first question

Quoting the equation F = e^(-kt)

where F is the fraction remaining; k is the rate constant; t is time.

Also using the fact that F=0.85 when t=10

0.85 = e^(-10k)

So -10k = ln(0.85)

and k = -0.1 ln(0.85) = 0.0163 (3 s.f.)

As time was in minutes, the units of this answer are “per minute”.

0.0163 per minute = 0.000271 per second