The rate constants for the following reaction | vedclass

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Question

(C) The unit of the rate constant indicates the order of the reaction. For a reaction $A \rightarrow P$,the rate $r = k[A]^n$. Reaction $1$: $k_1 = 1

Vedclass · Accepted Answer

$r_1 = 100 \ r_3, r_2 = \frac{r_3}{10}$

Vedclass · Answer

(C) The unit of the rate constant indicates the order of the reaction. For a reaction $A ightarrow P$,the rate $r = k[A]^n$. Reaction $1$: $k_1 = 1 \ s^{-1}$,which corresponds to a $1^{st}$ order reaction. Thus,$r_1 = k_1[A]^1 = 1 	imes 1 = 1 \ M \ s^{-1}$. Reaction $2$: $k_2 = 0.1 \ L \ mol^{-1} \ s^{-1}$,which corresponds to a $2^{nd}$ order reaction. Thus,$r_2 = k_2[A]^2 = 0.1 	imes 1^2 = 0.1 \ M \ s^{-1}$. Reaction $3$: $k_3 = 0.01 \ L^2 \ mol^{-2} \ s^{-1}$,which corresponds to a $3^{rd}$ order reaction. Thus,$r_3 = k_3[A]^3 = 0.01 	imes 1^3 = 0.01 \ M \ s^{-1}$. Comparing the rates: $r_1 = 1, r_2 = 0.1, r_3 = 0.01$. $r_1 = 10 \ r_2 \implies r_2 = \frac{r_1}{10}$. $r_1 = 100 \ r_3 \implies r_3 = \frac{r_1}{100}$. $r_2 = 10 \ r_3 \implies r_3 = \frac{r_2}{10}$. From the options,$r_1 = 100 \ r_3$ and $r_2 = 10 \ r_3$ (or $r_3 = r_2 / 10$) is consistent with option $C$.

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