Final answer:
To calculate the volume of water needed to solubilize 0.05 g of cadmium hydroxide, we can use the solubility product constant (Ksp) for cadmium hydroxide. The Ksp value is given as 5.27x10⁻15. Using the Ksp expression and the equation for the dissociation of cadmium hydroxide, we can find the concentration of Cd(OH)2 in the solution, and then calculate the volume of water needed.
Step-by-step explanation:
To calculate the volume of water needed to solubilize 0.05 g of cadmium hydroxide, we need to use the solubility product constant (Ksp) for cadmium hydroxide. The Ksp value is given as 5.27x10⁻15. From the equation for the dissociation of cadmium hydroxide (Cd(OH)2), we can see that each mole of Cd(OH)2 dissociates into one mole of Cd²⁺ and two moles of OH⁻.
Using the equation:
Ksp = [Cd²⁺][OH⁻]²
Let's assume that the concentration of Cd(OH)2 in the solution is x M.
Then, [Cd²⁺] = x M and [OH⁻] = 2x M.
Substituting these values into the Ksp expression:
5.27x10⁻15 = x * (2x)² = 4x⁶
Simplifying the equation:
x³ = 1.3175x10⁻15
Taking the cube root of both sides:
x = 1.48x10⁻⁵ M
The concentration of Cd(OH)2 in the solution is 1.48x10⁻⁵ M.
To calculate the volume of water needed, we can use the equation:
Volume of water = mass of solute / molar mass of solute / concentration of solute
Volume of water = 0.05 g / (112.41 g/mol) / (1.48x10⁻⁵ mol/L) = 2.06x10³ L
Therefore, the volume of water needed to solubilize 0.05 g of cadmium hydroxide is 2.06x10³ L.