The reaction rate involving reactants A and B is -k[A][B]. Which condition gives a first-order reaction?

GATE 2017 CE (CE1) – Question 23

Water and Waste Water Quality and Treatment · Unit processes and operations · 1 mark · Multiple choice

The reaction rate involving reactants A and B is $-k[A]^\alpha[B]^\beta$. Which condition gives a first-order reaction?

$\alpha=0,\beta=0$
$\alpha=1,\beta=0$
$\alpha=1,\beta=1$
$\alpha=1,\beta=2$

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Show answer and explanation

Correct answer: (B) $\alpha=1,\beta=0$

Explanation

The overall order of this power-law rate expression is $\alpha+\beta$. The four options have orders 0, 1, 2 and 3, respectively. Only $\alpha=1,\beta=0$ makes the rate first order, proportional to A and independent of B. Hence B.

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