For a reaction $X+Y=2 Z, 1.0 \mathrm{~mol}$ of $X, 1.5 \mathrm{~mol}$ 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 $1.0 \mathrm{~mol} \mathrm{~L}^{-1}$. The equilibrium constant of the reaction is $\_\_\_\_$ $\frac{x}{15}$. The value of $x$ is $\_\_\_\_$ .