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Consider the hypothetical reaction : $A + 2 B \to C$ The rate remains constant when the concentration of A is doubled and the concentration of B is held constant. The reaction rate doubles when the concentration of B is doubled and the concentration of A is held constant. What are the orders of A and B in this reaction?

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A= 1,B = 0

A= 1,B = 2

A =0,B = 1

A =0,B = 2

answer is A.

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Detailed Solution

$A + 2 B \to C$

$\begin{array}{l} r = k [A]^{x} [B]^{y} \\ r = k [2 A]^{x} [B]^{y} \\ 2 r = k [A]^{x} [2 B]^{y} \end{array}$

$1 = {(\frac{2 x}{A})}^{x} = 2^{x} = 2^{0} x = 0$

$2 = {(\frac{2 B}{B})}^{y} = 2^{y} = 2^{1} y = 1$

$Y = K [A]^{0} [B]^{1}$

Order of reaction = 0 + 1 = 1

As a result the orders of A and B in this reaction will be

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