Difficult
For the following rate law,determine the unit of the rate constant: Rate $= -\frac{d[R]}{dt} = k[A]^{\frac{1}{2}}[B]^{2}$
The total order of reaction $n = \frac{1}{2} + 2 = \frac{5}{2} = 2.5$.
Rate $= k[A]^{\frac{1}{2}}[B]^{2} = k[Concentration]^{\frac{5}{2}}$.
$\therefore k = \frac{\text{Rate}}{[Concentration]^{\frac{5}{2}}}$.
$\therefore$ Unit of $k = \frac{\text{mol } L^{-1} s^{-1}}{(\text{mol } L^{-1})^{\frac{5}{2}}} = (\text{mol } L^{-1})^{1 - 2.5} s^{-1} = (\text{mol } L^{-1})^{-1.5} s^{-1}$.
$= \text{mol}^{-1.5} L^{1.5} s^{-1}$ or $L^{1.5} \text{mol}^{-1.5} s^{-1}$.
Rate $= k[A]^{\frac{1}{2}}[B]^{2} = k[Concentration]^{\frac{5}{2}}$.
$\therefore k = \frac{\text{Rate}}{[Concentration]^{\frac{5}{2}}}$.
$\therefore$ Unit of $k = \frac{\text{mol } L^{-1} s^{-1}}{(\text{mol } L^{-1})^{\frac{5}{2}}} = (\text{mol } L^{-1})^{1 - 2.5} s^{-1} = (\text{mol } L^{-1})^{-1.5} s^{-1}$.
$= \text{mol}^{-1.5} L^{1.5} s^{-1}$ or $L^{1.5} \text{mol}^{-1.5} s^{-1}$.
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View SolutionFor the reaction ${H_{2(g)} + I_{2(g)} \to 2HI_{(g)}}$,the possible mechanism is given below:
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${2I + H_2 \xrightarrow{K_2} 2HI}$ (slow step)
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$I_2 \underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons}} 2 I$ (fast step)
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Determine the rate law for the reaction.
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View SolutionFor the reaction $N_2O_5 \rightarrow 2NO_2 + \frac{1}{2} O_2$,given that:
$-\frac{d[N_2O_5]}{dt} = K_1[N_2O_5]$,
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What is the relationship between $K_1$,$K_2$,and $K_3$?
$-\frac{d[N_2O_5]}{dt} = K_1[N_2O_5]$,
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View SolutionWrite the formula for the rate of reaction $R \to P$ for zero-order and first-order reactions.
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View SolutionThe 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.
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