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For Zero order reactions, the linear plot was obtained for $\left[ A \right]$ vs $t$ . The slope of the line is equal to:
A) ${k_o}$
B) $ - {k_o}$
C) $\dfrac{{0.693}}{{{k_0}}}$
D) $ - \dfrac{{{k_0}}}{{2.303}}$

Last updated date: 20th Jun 2024
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Hint:We know that the rate of order is determined by the differential rate law or the integrated rate law, rate of reaction is speed of chemical reaction proceeds measure of the change in concentration product or the change in concentration of the reactants.
If the kinetics of the reaction depends on the concentration of only one reactant then the order of the reaction is first order present, but each reactant will be zeroth-order.

Complete step by step answer:
We need to know that the integrated rate law for a zero-order reaction is frequently written in two different ways: one using exponents and one using logarithms. The exponential form is as follows:
\[\left[ A \right] = {\left[ A \right]_0}{e^{ - kt}}\]
Initial concentration of reactant A at \[t = 0\] is denoted as $\left[ {{A_0}} \right]$ ,
K is that the rate constant, and e is that the base of the natural logarithms, which has the worth \[2.718\] to $3$ decimal places. Integrating on both sides and finding the value of C we get,
\[\left[ A \right] = - {k_0}t + \left[ {{A_0}} \right]\]
$ - {k_o}$ is rate constant.
$\left[ {{A_0}} \right]$ is the initial concentration. So the slope of the line is $ - {k_o}$ .
Hence option B is correct.

Additional information:
We also know that for chemical reaction \[A{\text{ }} + {\text{ }}B{\text{ }}C{\text{ }} \to {\text{ }}E\;\] , the rate of the reaction is doubled when the concentration of B was doubled, if the concentration, of both A and B was doubled rate become doubled and if the concentration of both B and C was doubled rate become quadrupled. The order of the reaction with respect to A, B and C and the total order given as,
The rate reaction is doubled, concentration B is doubled. In this above reaction rate, reaction depends on concentration of reactant B. This shows B is a first-order reaction.
The concentration of Both A and B was doubled, concentration of both B and C was doubled rate quadrupled. This shows B and C is first-order kinetics but the concentration of A does not impact the rate of reactant. This show A is zeroth-order. Thus the order of A is zeroth-order (0), B is First-order (1), and C is First-order (1).
The Total sum of order \[ = 0 + 1 + 1 = 2\]

We have to remember that for zeroth-order kinetics reaction is independent of concentration of reaction, the changing of concentration does not impact the rate of reaction. For second-order kinetics the sum of the order is equal to two in the rate law of chemical reaction.