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Question 56

During Kinetic study of reaction $$2A + B \to C + D$$, the following results were obtained :
I: A = 0.1 M, B = 0.1 M, initial rate of formation of D = $$6.0 \times 10^{-3}$$
II: A = 0.3 M, B = 0.2 M, initial rate = $$7.20 \times 10^{-2}$$
III: A = 0.3 M, B = 0.4 M, initial rate = $$2.88 \times 10^{-1}$$
IV: A = 0.4 M, B = 0.1 M, initial rate = $$2.40 \times 10^{-2}$$
Based on above data, overall order of the reaction is ______


Correct Answer: 3

For the reaction $$2A + B \rightarrow C + D$$, let $$\text{Rate} = k[A]^a[B]^b$$.

From experiments I and IV (where B is constant at 0.1 M):

$$ \frac{r_{IV}}{r_I} = \left(\frac{0.4}{0.1}\right)^a = 4^a = \frac{2.40 \times 10^{-2}}{6.0 \times 10^{-3}} = 4 $$
$$ 4^a = 4 \Rightarrow a = 1 $$

From experiments II and III (where A is constant at 0.3 M):

$$ \frac{r_{III}}{r_{II}} = \left(\frac{0.4}{0.2}\right)^b = 2^b = \frac{2.88 \times 10^{-1}}{7.20 \times 10^{-2}} = 4 $$
$$ 2^b = 4 \Rightarrow b = 2 $$

Thus, the overall order of the reaction is $$a + b = 1 + 2 = 3$$.

Answer: 3.

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