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Consider a reaction, $a G + b H ⟶ Products.$
When concentration of both the reactants G and H is doubled, the rate increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. The overall order of the reaction is :

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$3$

$0$

$2$

$1$

answer is D.

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Detailed Solution

$ϑ_{0} = k [6]^{a} [H]^{b}$

$ϑ_{1} = k [6]^{a} [H]^{b} 2^{a + b}$

$ϑ_{2} = k [6]^{a} [H]^{b} 2^{a}$

$\{\frac{ϑ_{1}}{ϑ_{0}} = 2^{a + b} = 8 ⟶ (1) \frac{ϑ_{2}}{ϑ_{0}} = 2^{a} = 2 ⟶ (2)\}$

A linear equation system is created by solving (1) and (2):

$a = 1, b = 2$

$∴ net order = 2 + 1 = 3 .$

Hence, option D is correct.

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