Ask Question
27 June, 17:06

A certain reaction has the following general form.

aA → bB

At a particular temperature and [A]0 = 2.80 ✕ 10-3M, concentration versus time data were collected for this reaction, and a plot of 1/[A] versus time resulted in a straight line with a slope value of + 3.00 ✕ 10-2 L mol-1 s-1.

(a) Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. (Rate expressions take the general form: rate = k. [A]a. [B]b.)

+3
Answers (1)
  1. 27 June, 17:33
    0
    rate law = k [A]

    Integrated rate law: ln [A] = - kt + ln[A]₀

    m = - 3.00 x 10⁻² Lmol⁻¹ s⁻¹

    Explanation:

    To determine the rate law we need to know the order of the reaction respect to the concentration of A.

    In general, the rate law for a given equation is:

    r = K [A ]^n

    where rate, r, is the change in time of the concentration of A, and n is the order of the reaction.

    So what we need to solve this question is find out which order of reaction conforms with the fact that a plot of 1/[A] versus time resulted in a straight line.

    If zero order:

    ΔA/Δt = - k [A]º = - k ⇒ ΔA = - k Δt

    From calculus:

    ∫ [A] d[A] = - ∫ kdt ⇒ [A] = - kt + [A]₀

    A graph of this this equation will result in a straight line only graphing [A] versus time, and not 1/[A] vs time as stated in the question.

    If first order.

    r = - k[A] ⇒ ΔA/Δt = - k[A]

    Δ[A]/[A] = - kΔt

    A plot of 1/[A] vs t will result in a straight, so we now know the reaction is first order.

    from calculus we know that this integrated gives us:

    ∫d[A]/[A] = - ∫k dt

    and the integral is:

    ln [A] = - kt + ln[A]₀ where [A]₀ is the intial concentration of A.

    you can see this equation has the form y = mx + b

    So our reaction is first order, the integrated rate law is ln [A] = - kt + ln[A]₀, and the values of the rate constant is the negative of the slope:

    m = - k ⇒ k = - m = - 3.00 x 10⁻² Lmol⁻¹ s⁻¹

    In case you are wondering about the units for k : we are plotting 1/[A] vs time so it follows k will have the units of L/mol per s.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “A certain reaction has the following general form. aA → bB At a particular temperature and [A]0 = 2.80 ✕ 10-3M, concentration versus time ...” in 📗 Chemistry if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers