Isolation method

Isolation methods are used for reactions with multiple reactants, e.g.

A+B\rightarrow C+D

rate=k\left [ A \right ]^{i} \left [ B \right ]^{j}\; \; \; \; \; \; \; \; 35

There are two isolation methods to determine the rate of a reaction. The first, which is used together with the initial rate method, involves varying the concentration of one of the reactants, e.g. A, while keeping the concentration of the other reactant, B, constant. The initial rates of these reactions are then determined. Since the concentration of B is constant for all the experiments and that initial rates are used, eq35 becomes

initial\: rate=k\, '\left [ A \right ]_0^{\: i}\; \; \; \; \; \; \; \; 36

where  k\, '=k\left [ B \right ]_0^{\: j}

By isolating the reactant of interest, A, eq35 has changed from an (i + j) order equation to a pseudo-i order equation. Taking the natural logarithm of both sides of eq36 and plotting the experimental results in a ln(initial rate) versus ln[A]0 graph, we can find the gradient of the curve, which is the order with respect to A, and the vertical intercept of the curve, which corresponds to ln(k[B]0 j). To find j and hence the value of k, we repeat the series of experiments by varying concentrations of B while keeping the concentration of A constant, and carrying out the same graphical analysis as before.

The second isolation method involves using an excess amount of one reactant, e.g. B, such that its concentration remains unchanged during the prolonged course of the reaction. Eq35 becomes

rate=k''\left [ A \right ]^{i}\; \; \; \; \; \; \; \; 37

ln\left ( rate \right )=iln\left [ A \right ]+lnk''\; \; \; \; \; \; \; \; 38

where k''=k\left [ B \right ]^{j}

With just a single experiment, the gradients at various points on the curve of a [A] versus time graph correspond to the reaction rates at different [A]. These data are then used to construct another graph with eq38 to determine i and lnk”. Similarly, to find k and j, we repeat the experiment, this time with [A] in excess and carry out the same graphical analysis as before.



Can the first isolation method be used without the initial rate method, i.e. can we, with the first isolation method, let the reaction run its course as per the situation in eq37?


No. This is because the concentration of the reactant that is kept constant is not in excess. The concentration of that reactant will change during the course of the reaction, rendering k” a variable. In other words, the concentration of the reactant that is kept constant in the first method is only constant during the duration necessary for the initial rate of the reaction to be taken.



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