$\begin{array}{1 1}(a)\;300sec&(b)\;315sec\\(c)\;212.5sec&(d)\;312.5sec\end{array}$

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$2HBr\rightarrow H_2+Br_2$

At $t=0$ $2HBr\Rightarrow a$

At $t=t$ $2HBr\Rightarrow a-x,H_2\Rightarrow x/2,Br_2\Rightarrow x/2$

Rate $=\large\frac{dx}{2dt}$$=K(a-x)^2$

$\large\frac{dx}{(a-x)^2}$$=2Kdt$

$\large\frac{dx}{(a-x)^2}$$=K'dt$

$2K=K'$

$K'$=rate constant=0.08$Lmol^{-1}s^{-1}$

$-\large\frac{1}{a-x}\bigg]_0^{a/2}$$=K't\big]_0^{t_{1/2}}$

$-\big[\large\frac{1}{a}-\frac{1}{a/2}\big]$$=k't_{1/2}$

$t_{1/2}=\large\frac{1}{k'a}$

$t_{1/2}=\large\frac{1}{0.08\times 0.04}$

$t_{1/2}=312.5sec$

Hence (d) is the correct answer.

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