Zn + 2H^{+} to Zn^{2+} + H_2The half-life per | vedclass

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(C) $(I)$ Since $t_{1/2}$ is independent of concentration of $Zn$ at constant $pH$,the order with respect to $[Zn]$ is $1$.$(II)$ Let the rate law be

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$B, C$ and $D$

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(C) $(I)$ Since $t_{1/2}$ is independent of concentration of $Zn$ at constant $pH$,the order with respect to $[Zn]$ is $1$.$(II)$ Let the rate law be $r = k[Zn]^1[H^{+}]^x$.When $pH = 3$,$[H^{+}] = 10^{-3} \ M$. When $pH = 2$,$[H^{+}] = 10^{-2} \ M$.Given that for constant $[Zn]$,the rate increases by $100$ times when $pH$ changes from $3$ to $2$:$\frac{r_2}{r_1} = \frac{k[Zn][10^{-2}]^x}{k[Zn][10^{-3}]^x} = 100$$10^x = 100 \Rightarrow x = 2$.Thus,the rate law is $\frac{dx}{dt} = k[Zn][H^{+}]^2$. Statement $(B)$ is correct.$(III)$ Checking statement $(C)$: If $[Zn]$ becomes $4[Zn]$ and $[H^{+}]$ becomes $\frac{[H^{+}]}{2}$,then $r' = k[4Zn][\frac{H^{+}}{2}]^2 = k[4Zn][\frac{[H^{+}]^2}{4}] = k[Zn][H^{+}]^2 = r$. Thus,$(C)$ is correct.$(IV)$ Checking statement $(D)$: If $[H^{+}]$ is doubled at constant $[Zn]$,then $r' = k[Zn][2H^{+}]^2 = 4k[Zn][H^{+}]^2 = 4r$. Thus,$(D)$ is correct.Therefore,statements $(B)$,$(C)$,and $(D)$ are correct.

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