A certain reaction has the following general form.?

Question

A certain reaction has the following general form: aA + bB → products. At a particular temperature, with an initial concentration of [A]₀ = 2.00 × 10⁻² M, concentration versus time data were collected for this reaction. A plot of ln[A] versus time resulted in a straight line with a slope value of -2.97 × 10⁻² min⁻¹. 
(a) Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. 
Rate law options: 
1. k[A] 
2. k[A]² 
3. k[A]³ 
4. k[B] 
Integrated rate law options: 
1. ln[A] = -kt + ln[A]₀ 
2. ln[A] = -kt + ln(1/[A]₀) 
3. ln[A] = kt - ln[A]₀ 
4. ln[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?

Anonymous · Accepted Answer

If a plot of ln[A] vs t gives a straight line, this is a first order reaction for which the equation is
ln[A] = -kt + ln[A]o
Note 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 line
b) t 1/2 = 0.693 / k = 0.693 / 0.0297 min^-1 = 23.3 min
c) 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 t
66.3 min = t
Does 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.

Anonymous

A certain reaction has the following general form.?

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