The solubility product of a sparingly soluble salt $\mathrm{A}_2 \mathrm{X}_3$ is $1.1 \times 10^{-23}$. If specific conductance of the solution is $3 \times 10^{-5} \mathrm{~S} \mathrm{~m}^{-1}$, the limiting molar conductivity of the solution is $x \times 10^{-3} \mathrm{~s} \mathrm{~m}^2 \mathrm{~mol}^{-1}$. The value of x is _______.