For the following reaction  $2x+y\stackrel{K}{\to }P$
The rate of reaction is $\frac{d\left[P\right]}{dt}=K\left[x\right]$  . 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 rate constant K is  $13.86\times {10}^{-x}$ , x is __________.
 

$\begin{array}{l} 2x +y \stackrel{k}{\to }P\\ att=0\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}2mol1mol 0\\ att=50\sec \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \left(2-2\times 0.5\right)0.5mol0.5mol\\ 1mol0.5mol0.5mol\\ k=\frac{2.303}{t}\log \left[\frac{R_0}{R}\right]\\ k=\frac{2.303}{50}\log \frac{2}{1}\\ k=\frac{2.303}{50}\times 0.3010\\ =\frac{0.693}{50}\\ =0.01380s^{-1}=13.86\times {10}^{-3}\end{array}$