A certain reaction has the following general form.?

Question

A certain reaction has the following general form.aA bBAt a particular temperature and [A]0 = 2.00 multiplied by 10-2 M, concentration versus time data were collected for this reaction, and a plot of ln[A] versus time resulted in a straight line with a slope value of −2.97 multiplied by 10-2 min-1.(a) Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction.rate lawk[A]k[A]2k[A]3k[B]integrated rate lawln[A] = −kt + ln[A]0ln[A] = −kt + ln(1/[A]0)ln[A] = kt − ln[A]0ln[A] = −kt − ln[A]0(b) Calculate the half-life for this reaction.(c) How much time is required for the concentration of A to decrease to 2.80 10-3 M?

Hermina Ferry · Accepted Answer

If a plot of ln[A] vs t gives a straight line, this is a first order reaction for which the equation isln[A] = -kt + ln[A]oNote that the slope of this line is -k and the y-intercept is [A]o.rate law: rate = k[A] (first order)k = 0.0297 min^-1 = -slope of lineb) t 1/2 = 0.693 / k = 0.693 / 0.0297 min^-1 = 23.3 minc) ln[A]t = -kt + ln[A]o ln(0.00280) = -(0.0297)(t) + ln(0.0200)-5.88 = -0.0297 t – 3.91-1.97 = -0.0297 t66.3 min = tDoes the answer make sense? If the concentration of A at time t = 0.0028 and the initial concentration of A was 0.0200, then the fraction remaining is 0.0028 / 0.0200 = 0.14.0.125 is just under that and represents the time when 1/8 of the reactant remains. 1/8 is the same as three half-lives (1/2 x 1/2 x 1/2) which corresponds to 3 x t 1/2 = 3 x 23.3 min = 69.9 min. This is close to the 66.3 that we calculated for our problem, so the answer makes sense.

Kelsie Sawayn

A certain reaction has the following general form.?

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