Final answer:
The mass of ZnS that will dissolve in 300.0 mL of 0.050 M Zn(NO3)2 is approximately 4.68 x 10^-7 g.
Step-by-step explanation:
To determine the mass of ZnS that will dissolve in 300.0 mL of 0.050 M Zn(NO3)2, we need to use the Ksp value of ZnS.
The solubility product constant (Ksp) expression for ZnS is given as:
ZnS(s) → Zn2+(aq) + S2-(aq)
Ksp = [Zn2+][S2-]
Given that Ksp = 2.5 x 10^-22, we can assume that the concentration of [Zn2+] in the saturated solution is equal to the solubility of ZnS, which is represented by 's'.
Therefore, [Zn2+] = s
Since Zn(NO3)2 dissociates to give Zn2+ ions in solution and the concentration of Zn(NO3)2 is 0.050 M, we can substitute the value of [Zn2+] into the Ksp expression:
Ksp = (s)(s) = s^2
Now, we need to solve for 's':
2.5 x 10^-22 = s^2
s = sqrt(2.5 x 10^-22)
s ≈ 1.58 x 10^-11
Finally, we can calculate the mass of ZnS that will dissolve using the equation:
mass = (volume)(concentration)(molar mass)
mass = (300.0 mL)(1.58 x 10^-11 M)(97.4 g/mol)
mass ≈ 4.68 x 10^-7 g