For a reaction $X\left(g\right)+Y\left(g\right)\rightleftharpoons 2Z\left(g\right),1.0molofX,1.5$  mol of $Y$  and 0.5 mol of $Z$ were taken in a 1 L vessel and allowed to react. At equilibrium, the concentration of Z was $1.0mol{L}^{-1}$ . The equilibrium constant of the reaction is  $\frac{x}{15}$. The value of $x$  is__________. 

 $X+Y \underset{ }{\rightleftharpoons }2Z\ne$
 $t=0 1mol 1.5mol 0.5mol$

$t=t_{eq } 1-a1.5-a 0.5+2a$

$0.5+2a=1;a=0.25$
                  $\underset{0.75}{X} +\underset{1.25}{Y}\underset{ }{\rightleftharpoons }\underset{1}{2Z}$

$K_{eq}=\frac{{\left[Z\right]}^2}{\left[X\right]\left[Y\right]}=\frac{1}{0.75\times \left[1.25\right]}=\frac{x}{15}$

$\Rightarrow x=\frac{15}{(0.75\times 1.25)}=16$