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### Topic: Serial reactions or consecutive reactions: rate vs time  (Read 177 times)

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#### Mimic

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##### Serial reactions or consecutive reactions: rate vs time
« on: July 22, 2022, 12:15:33 PM »
Serial reactions, or consecutive reactions, are two or more reactions in which the product of the first reaction becomes the reactant in the next. The simplest case of a serial reaction involves a reagent A turns into B which in turn, again in the reaction environment, turns into P. In the simplest case, all reactions are irreversible reactions of the first order, so we can be write

$$\mathrm{A} \xrightarrow{k_1} \mathrm{B} \xrightarrow{k_2} \mathrm{P}$$

the rates of these reactions will be

$$\begin{equation*} \begin{cases} r_\mathrm{A} = -k_1\ c_\mathrm{A} \\ r_\mathrm{B} = k_1\ c_\mathrm{A} -\ k_2\ c_\mathrm{B} \\ r_\mathrm{P} = k_2\ c_\mathrm{B} \\ \end{cases} \end{equation*}$$

Where $k$ are the kinetics constants, and $c$ is the concentration of the various substances. Plotting $r = f (t)$, I get this

The maximum rate of P formation is reached when $r_\mathrm{B}$ is zero. My hypothesis is that the maximum rate of formation of P must be reached when the concentration of B is maximum, therefore at the minimum of the $r_\mathrm{B}(t)$ curve.
Is my guess right, or is the plot right?

• Mr. pH