The first-order decomposition of cyclopropane has a rate constant of 6.7 times 1

Question

The first-order decomposition of cyclopropane has a rate constant of 6.7 times 10^-4 s^-1. If the initial concentration of cyclopropane is 1.33 M, what is the concentration of cyclopropane after 644 s? The first-order decay of radon has a half-life of 3.823 days. How many grams of radon decomposes after 5.55 days if the sample initially weighs 100.0 grams? The second-order decomposition of NO_2 has a rate constant of 0.255 M^-1s^-1. How much NO_2 decomposes in 4.00 s if the initial concentration of NO_2 (1.00 L volume) is 1.33 M? The first-order rearrangement of CH_3NC is measured to have a rate constant of 3.61 times 10^-15 s^-1 at 298 K and a rate constant of 8.66 times 10^-7 s^-1 at 425 K. Determine the activation energy for this reaction.

Explanation / Answer

Question 21

k = 6.7 x 10-4 S-1

Initial concentration = 1.33 M

ln A = -kt + ln Ao

Ao =Initial concentration = 1.33

A = Concentration at the time of t

ln A = -644 x 6.7 x 10-4 + ln 1.33

ln A = -0.1463

A = 0.8639 M

The concentration after 644 S is 0.8639 M

Question 22

We can find the rate constant from half life by using following formula

thalf = 0.693 / k

k = 0.693 / 3.823 = 0.1812 day-1

ln A = -kt + ln Ao

ln A = - 0.1812 x 5.55 + ln 100

A = 36.55 gram

Hence the amount of radon decomposed = 100 - 36.55 = 63.44 grams

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