This problem is asking for the dissolution reaction of barium fluoride, both the equilibrium and Ksp expressions in terms of concentrations and x and its molar solubility in water. Thus, answers shown below:
<h3>Solubility product</h3>
In chemistry, when a solid is dissolved in water, one must take into account the fact that not necessarily its 100 % will be able to break into ions and thus undergo dissolution.
In such a way, and specially for sparingly soluble solids, one ought to write the dissolution reaction at equilibrium as shown below for the given barium fluoride:

Next, we can write its equilibrium expression according to the law of mass action, which also demands us to omit any solid and refer it to the solubility product constant (Ksp):
![Ksp=[Ba^{2+}][F^-]^2](https://tex.z-dn.net/?f=Ksp%3D%5BBa%5E%7B2%2B%7D%5D%5BF%5E-%5D%5E2)
Afterwards, one can insert the reaction extent, x, as it stands for the molar solubility of this solid in water, taking into account the coefficients balancing the reaction:

Finally, we solve for the x as the molar solubility of barium fluoride as shown below:
![2.5x10^{-5}=(x)(2x)^2\\\\2.5x10^{-5}=4x^3\\\\x=\sqrt[3]{\frac{2.5x10^{-5}}{4} } \\\\x=0.0184M](https://tex.z-dn.net/?f=2.5x10%5E%7B-5%7D%3D%28x%29%282x%29%5E2%5C%5C%5C%5C2.5x10%5E%7B-5%7D%3D4x%5E3%5C%5C%5C%5Cx%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B2.5x10%5E%7B-5%7D%7D%7B4%7D%20%7D%20%5C%5C%5C%5Cx%3D0.0184M)
Learn more about chemical equilibrium: brainly.com/question/26453983