t Print Calculator L Periodic Table Question 8 of 12 Incorrect incorrect Incorre

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t Print Calculator L Periodic Table Question 8 of 12 Incorrect incorrect Incorrect University Science Books Map Donald McQuarrie .Peter A. Rock Ethan Gallogly presented by Sapling Learnin Consider the first-order reaction described by the equation H H (g) CH2 cyclopropane propene At a certain temperature, the rate constant for this reaction is 5.24x 10 4 s-1 Calculate the half-life of cyclopropane at this temperature. 0.693 Number Incorrect. The half-life of a first-order reaction is 1" k 6.19 x 10 s Given an initial cyclopropane concentration of 0.00340 M, calculate the concentration of cyclopropane that remains after 1.70 hours. Number 1.38 x 10 M Preyous Again o Next Exit

Explanation / Answer

For the first order reaction, the half life is given by the equation:

t1/2 = 0.693 / k

Given, k = rate constant = 5.24 x 10^-4 s^-1

So, t1/2 = 0.693 / (5.24 x 10^-4 s^-1) = 1322.52 s

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The integral equation for first order kinetics is

ln[A]t - ln [A]o = -kt

Given,

Initial concentration = [A]o = 0.00340 M

k = rate constant = 5.24 x 10^-4 s^-1

t = time = 1.70 hrs = 1.70 x 60 x 60 = 6120 s

Plugging in the values,

ln[A]t - ln [0.00340] = -(5.24 x 10^-4) ( 6120)

ln[A]t = -8.891

[A]t = 1.376 x 10^-4 M

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