Determine the minimum concentration of the precipitating agent on the right to cause precipitation of the cation from the solution on the left. 3.0*10^-2 M BaNO3;NaF
BaF2 ==> Ba^+ + 2F^-
Ksp = (Ba^+2)(F^-)^2
The problem tells you (Ba^+2) = 0.030M
Substitute into Ksp and solve for (F^-)
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To determine the minimum concentration of the precipitating agent needed to cause precipitation, we can use the concept of solubility products. The solubility product constant (Ksp) provides a measure of the solubility of a compound under specific conditions.
In this case, we need to find the minimum concentration of NaF needed to precipitate the cation (Ba2+) from the solution containing BaNO3. The balanced equation for the reaction is:
Ba(NO3)2 (aq) + 2 NaF (aq) → BaF2 (s) + 2 NaNO3 (aq)
The solubility product expression for BaF2 is:
Ksp = [Ba2+][F-]^2
Since the stoichiometric coefficient of NaF is 2 in the balanced equation, we need to consider the concentration of F- ions provided by NaF. Therefore, we need to determine the concentration of [F-] to find the minimum concentration of NaF required.
Given that the concentration of Ba2+ is 3.0 × 10^-2 M, we can assume that the concentration of F- is initially zero. If we want to determine the minimum concentration of NaF required for precipitation, it means we want to reach the point where the concentrations of [Ba2+] and [F-] will be equal to the Ksp of BaF2.
To find the minimum concentration of NaF required, we need to set up an equilibrium expression using the concentration of [Ba2+] and [F-] as:
Ksp = [Ba2+][F-]^2
Since the concentration of [Ba2+] is 3.0 × 10^-2 M, we can substitute this value into the equilibrium expression:
Ksp = (3.0 × 10^-2)[F-]^2
Now, solve for [F-]:
[F-]^2 = Ksp / (3.0 × 10^-2)
[F-] = √ (Ksp / (3.0 × 10^-2))
Finally, substitute the given Ksp value for BaF2 into the equation to get the minimum concentration of NaF required to cause precipitation.