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(B) The rate law is given by $R = k[A]^x [B]^y$.From experiments $I$ and $II$,$[A]$ is constant and $[B]$ changes,but the rate remains constant. Thus,

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$10$

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(B) The rate law is given by $R = k[A]^x [B]^y$.From experiments $I$ and $II$,$[A]$ is constant and $[B]$ changes,but the rate remains constant. Thus,$y = 0$ (zero order with respect to $B$).From experiments $I$ and $III$,when $[A]$ doubles ($0.10$ to $0.20$),the rate doubles ($6.93 	imes 10^{-3}$ to $1.386 	imes 10^{-2}$). Thus,$x = 1$ (first order with respect to $A$).The rate equation is $R = k[A]$.Using experiment $I$: $6.93 	imes 10^{-3} = k(0.10) \Rightarrow k = 6.93 	imes 10^{-2} \ min^{-1}$.For a first-order reaction,the half-life is $t_{1/2} = \frac{\ln(2)}{k} = \frac{0.693}{6.93 	imes 10^{-2}} = 10 \ min$.

Experiment	$[A]$ $(mol \ L^{-1})$	$[B]$ $(mol \ L^{-1})$	Initial rate $(mol \ L^{-1} \ min^{-1})$
$I$	$0.10$	$0.20$	$6.93 \times 10^{-3}$
$II$	$0.10$	$0.25$	$6.93 \times 10^{-3}$
$III$	$0.20$	$0.30$	$1.386 \times 10^{-2}$

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