Question

Use mathematical software or an electronic spreadsheet to examine thetime dependence of [I] in the reaction mechanism A →I→P (k1,k2). Youmay either integrate eqn 22.39 numerically (seeAppendix2) or use eqn 22.40directly. In all the following calculations, use [A]0=1 mol dm−3and a timerange of 0 to 5 s. (a) Plot [I] against tfork1=10 s−1andk2=1 s−1. (b) Increasethe ratio k2/k1steadily by decreasing the value of k1and examine the plot of [I]againsttat each turn. What approximation about d[I]/dtbecomesincreasingly valid?

Answer 1

Answer:

Here's what I get  

Explanation:

$\rm A \xrightarrow{k_{1}}I \xrightarrow{k_{2}} P$

(a) Plot I against t

I assume that Equation 22.40 is something like

$\text{[I]} = \dfrac{k_{1}\text{[A]}_{0}}{k_{2} - k_{1}} \left(e^{-k_{1}t} - e^{-k_{2}t} \right )$

If the initial conditions are  

[A]₀ = 1.0 mol·dm⁻³; k₁ = 10 s⁻¹; k₂ = 1 s⁻¹

The equation becomes  

$\text{[I]} = \dfrac{10}{-9} \left(e^{-10t} - e^{-t} \right )$

The graph of [I] vs t is shown in Fig 1.

(b) Increasing k₂/k₁ ratio

In Fig. 2, I added the same plots, but with k₂ = 3, 11, and 51 s⁻¹ (black, green and purple).  

The graphs show that, as k₂ becomes increasingly greater than k₁, the maximum concentration of I becomes smaller and the graph becomes (except for the very beginning) a flat line.

Thus, the approximation that

$\mathbf{\dfrac{\text{d[I]}}{\text{d}t}=0}$

becomes increasingly valid.