p -Block elements - ll — Chemistry STD 12 Science — Question

$Ni ( s )+2 Ag ^{+}(0.001 M ) \rightarrow Ni ^{2+}(0.001 M )+2 Ag ( s )$

$($ Given that $E _{\text {cell }}^{\circ}=10.5 \,V , \frac{2.303 RT }{ F }=0.059$ at $298\, K )$

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

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

$\mathop {Pt\,|\,C{l_2}\left( g \right)}\limits_{\left( {0.4\,bar} \right)} \,|\,\mathop {C{l^ - }\left( {aq.} \right)}\limits_{0.1\,M} \,||\,\,\mathop {C{l^ - }\left( {aq.} \right)}\limits_{0.01} \,|\,\mathop {C{l_2}\left( g \right)\,|\,Pt}\limits_{0.2\,bar} $

the measured potential at $298\, K$ is .............. $\mathrm{V}$

$\left([ P ]_0\right.$ is the initial concentration of $P$ )