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$2 X + Y \xrightarrow{i} P$
the rate of reaction is $\frac{ d [ P ]}{ dt }=k[ X ]$. Two moles of $X$ are mixed with one mole of $Y$ to make $1.0 L$ of solution. At $50 s , 0.5$ mole of $Y$ is left in the reaction mixture. The correct statement(s) about the reaction is(are)
(Use: $\ln 2=0.693$ )
$(A)$ The rate constant, $k$, of the reaction is $13.86 \times 10^{-4} s ^{-1}$.
$(B)$ Half-life of $X$ is $50 s$.
$(C)$ At $50 s ,-\frac{ d [ X ]}{ dt }=13.86 \times 10^{-3} mol L ^{-1} s ^{-1}$.
$(D)$ At $100 s ,-\frac{ d [ Y ]}{ dt }=3.46 \times 10^{-3} mol L ^{-1} s ^{-1}$.
