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  • During the kinetic study of the reaction 2A + B  C + D, following results were obtained <ta

During the kinetic study of the reaction 2A + B  \rightarrow C + D, following results were obtained

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 [A]/mol L-1 [B]/ mol L-1

Initial rate of formation of D/mol L-1 min-1
I 0.1 0.1

6.0 x 10-3
II 0.3 0.2

7.2 x 10-2
III 0.3 0.4

2.88 x 10-1
IV 0.4 0.1

2.40 x 10-2

Based on the above data which one of the following is correct?

Option: 1

rate = k[A][B]2


Option: 2

rate = k[A]2[B]


Option: 3

rate = k[A][B]


Option: 4

rate = k[A]2[B]2


Answers (1)

best_answer

For a reaction, 

Rate=k[A]^x[B]^y

For the 4 different reaction setups

Rate_1=k[0.1]^x[0.1]^y=6\times 10^{-3}\quad ...1)\\ Rate_2=k[0.3]^x[0.2]^y=7.2\times 10^{-2}\quad ...2)\\ Rate_3=k[0.3]^x[0.4]^y=2.88\times 10^{-1}\quad ...3)\\ Rate_1=k[0.4]^x[0.1]^y=2.4\times 10^{-2}\quad ...4)\\

Dividing equation 4 by equation 1

\frac{Rate_4}{Rate_1}=\frac{2.4\times 10^{-2}}{6\times 10^{-3}}=\frac{k[0.4]^x[0.1]^y}{k[0.1]^x[0.1]^y}\\ 4=4^x\\ x=1

Dividing equation 2 by equation 1 ,

\frac{Rate_2}{Rate_1}=\frac{7.2\times 10^{-2}}{6\times 10^{-3}}=\frac{k[0.3][0.2]^y}{k[0.1][0.1]^y}\\ 12=3\times 2^y\\ 4=2^y \\ y=2

Hence, the rate law expression for the reaction is Rate = k[A][B]^2

The Correct answer is option 1.

Posted by

Devendra Khairwa

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