The rate constant for the reaction $H_2 + I_2 \to 2HI$ is $k_1 = 49$. What is the rate constant for the reverse reaction $2HI \to H_2 + I_2$?

For the following reaction
$2X + Y \xrightarrow{i} P$
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 $100 \ s$,$-\frac{d[Y]}{dt} = 3.46 \times 10^{-3} \ mol \ L^{-1} \ s^{-1}$.

Which of the following statements is correct?

Select the incorrect statement.

The consecutive reaction $X$ $\longrightarrow Y$ $\longrightarrow Z$ takes place in a closed container. Initially,the container has $A_{0}$ moles of $X$ (and no $Y$ and $Z$). The plot of total moles of the constituents in the container as a function of time will be:

The rate constant for the first order decomposition of $H_{2}O_{2}$ is given by the following equation:
$\log k = 14.34 - 1.25 \times 10^{4} \, K / T$
Calculate $E_{a}$ for this reaction and at what temperature will its half-period be $256 \, min$?