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What is the rate of the reaction $A+B\rightarrow C$ based on the following experiments:

$\begin{array} {cccc} \text{Experiment} & [A]\; \text{in M} & [B]\; \text{in M} & \text{Initial Rate in Ms}^{-1}\\ 1 & 1 & 2 & 0.01\\ 2 & 1 & 8 & 0.64\\ 3 & 0.5 & 8 & 0.32\\ 4 & 1 & 1 & 0.00125\\ \end{array}$

$\begin{array}{1 1}k[A]^3 [B]^3 \\ k[A][B]^3 \\ k[A]^3 [B] \\ k[A][B] \end{array}$

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Answer: k[A][B]$^3$
Comparing experiments 2 and 3, with [B] constant, as [A] is halved, so does the initial rate. Hence rate is first order with respect to [A].
Comparing experiments 1 and 2, with [A] constant, as [B] increases 4 times, the initial rate increases 64 times (4$^3$), which means that the rate is third order with respect to [B].
Hence the Rate = k[A][B]$^3$
answered Dec 16, 2013 by sreemathi.v
edited Jul 26, 2014 by balaji.thirumalai
 

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