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Types of Elementary Reactions

When the conc...

Question

When the concentration of a reactant in reaction $A \to B$ is increased by 8 times but rate increases only 2 times, the order of the reaction would be 1/n.
value of n is ?

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Solution

$r_{1} = k [A]^{n}$
$r_{2} = 2 r_{1} = k [8 A]^{n}$
$∴ \frac{2 r_{1}}{r_{1}} = (8)^{n}$
$(2)^{1} = (2)^{3 n}$
$∴ 3 n = 1$
$n = \frac{1}{3}$

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