Medium
The following are the rate constants of two different reactions. What is the overall order of reaction for each?
$(a)$ $2.418 \times 10^{-5} \ hr^{-1}$
$(b)$ $7.1 \times 10^{-4} \ atm \ s^{-1}$
$(a)$ $2.418 \times 10^{-5} \ hr^{-1}$
$(b)$ $7.1 \times 10^{-4} \ atm \ s^{-1}$
(A) The order of a reaction can be determined from the units of the rate constant $(k)$.
For a reaction of order $n$,the units of the rate constant are $(concentration)^{1-n} \ time^{-1}$.
$(a)$ The unit is $hr^{-1}$,which corresponds to $time^{-1}$. This implies $1-n = 0$,so $n = 1$. Thus,it is a $1^{st}$ order reaction.
$(b)$ The unit is $atm \ s^{-1}$,which corresponds to $(pressure)^1 \ time^{-1}$. This implies $1-n = 1$,so $n = 0$. Thus,it is a $0^{th}$ order reaction.
For a reaction of order $n$,the units of the rate constant are $(concentration)^{1-n} \ time^{-1}$.
$(a)$ The unit is $hr^{-1}$,which corresponds to $time^{-1}$. This implies $1-n = 0$,so $n = 1$. Thus,it is a $1^{st}$ order reaction.
$(b)$ The unit is $atm \ s^{-1}$,which corresponds to $(pressure)^1 \ time^{-1}$. This implies $1-n = 1$,so $n = 0$. Thus,it is a $0^{th}$ order reaction.
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The reaction $CH_{3}COF + H_{2}O \rightleftharpoons CH_{3}COOH + HF$ is studied under two conditions:
Condition $I$: $[H_{2}O]_{0} = 1.00 \ M$,$[CH_{3}COF]_{0} = 0.01 \ M$
Condition $II$: $[H_{2}O]_{0} = 0.02 \ M$,$[CH_{3}COF]_{0} = 0.80 \ M$
Time $(t)$ min (Condition $I$) / $[CH_{3}COF]$ $M$ Time $(t)$ min (Condition $II$) / $[H_{2}O]$ $M$ $0$ / $0.01000$ $0$ / $0.0200$ $10$ / $0.00867$ $10$ / $0.0176$ $20$ / $0.00735$ $20$ / $0.0156$ $40$ / $0.00540$ $40$ / $0.0122$
Determine the overall order of the reaction and calculate the rate constant.
Condition $I$: $[H_{2}O]_{0} = 1.00 \ M$,$[CH_{3}COF]_{0} = 0.01 \ M$
Condition $II$: $[H_{2}O]_{0} = 0.02 \ M$,$[CH_{3}COF]_{0} = 0.80 \ M$
| Time $(t)$ min (Condition $I$) / $[CH_{3}COF]$ $M$ | Time $(t)$ min (Condition $II$) / $[H_{2}O]$ $M$ |
|---|---|
| $0$ / $0.01000$ | $0$ / $0.0200$ |
| $10$ / $0.00867$ | $10$ / $0.0176$ |
| $20$ / $0.00735$ | $20$ / $0.0156$ |
| $40$ / $0.00540$ | $40$ / $0.0122$ |
Determine the overall order of the reaction and calculate the rate constant.
The rate equation for the reaction $2A + B \longrightarrow \text{products}$ is $\text{rate} = k[A][B]^2$. If $k$ at $T \, K$ is $5.0 \times 10^{-6} \, mol^{-2} \, L^2 \, s^{-1}$,the initial rate of the reaction,when $[A] = 0.05 \, mol \, L^{-1}$ and $[B] = 0.1 \, mol \, L^{-1}$ is:
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