10. Biomolecules — Chemistry STD 12 Science — Question

$2 X + Y \xrightarrow{i} P$

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 $100 s ,-\frac{ d [ Y ]}{ dt }=3.46 \times 10^{-3} mol L ^{-1} s ^{-1}$.

$A \rightarrow  B; \ \ \ K_1 = 10^{15}\  exp.\ \left( {\frac{{ - 2000}}{T}} \right)$

$C \rightarrow  D;\ \ \  K_2 = 10^{14}\  exp. \ \left( {\frac{{ - 1000}}{T}} \right)$

The temperature at which $K_1 = K_2$ is ........... $K$ ($exp. = e$)