What is the solubility of MnS, in grams per liter, in a buffer solution that is 0.120 M HC2H3O2 - 0.490 M NaC2H3O2? For MnS, Kspa=3x10^7.
First determine the pH of the buffer solution.
pH = pKa + log(base)/(acid) and convert pH to H^+.
You then have
Ksp = (Mn^2+)(S^2-)
You have k1 and k2 for H2S as
(H^+)(HS^-)/(H2S) = k1
(H^+)(S^2-)/(HS^-) = k2
and (Mn^2+) = (S^2-) + (HS^-) + (H2S)
This is four unknowns and four equations but it isn't that bad. You can solve these four without assumptions. Most quant books show how to do this.
To determine the solubility of MnS in the given buffer solution, you need to consider the common ion effect and the Ksp expression.
Given:
- MnS with Ksp = 3x10^7
- Buffer solution with a concentration of 0.120 M HC2H3O2 and 0.490 M NaC2H3O2
1. Initialize the variables:
- Let 'x' be the solubility of MnS in grams per liter.
- Let 's' be the concentration of S^2- ions in moles per liter, which is equal to the solubility of MnS.
2. Write the balanced equation for the dissociation of MnS:
MnS(s) ⇌ Mn2+(aq) + S^2-(aq).
3. Write the Ksp expression for MnS:
Ksp = [Mn2+][S^2-]
4. Determine the value of [Mn2+]:
Since MnS dissociates in a 1:1 ratio, the concentration of Mn2+ ions is equal to the concentration of S^2-, which is 's'.
5. Determine the value of [S^2-]:
Since MnS dissociates completely, the concentration of S^2- ions is also equal to 's'.
6. Write the expression for [Mn2+] and [S^2-]:
[Mn2+] = [S^2-] = s
7. Calculate the concentrations of HC2H3O2 and NaC2H3O2:
[HAc] = [HC2H3O2] = 0.120 M
[Ac-] = [NaC2H3O2] = 0.490 M
8. Apply the common ion effect by adjusting the concentrations of Mn2+ and S^2-:
[Mn2+] = [S^2-] = s - [Ac-]
9. Substitute the values into the Ksp expression:
Ksp = (s - [Ac-])(s)
10. Solve for 's':
3x10^7 = (s - [Ac-])(s)
11. Solve the quadratic equation:
Expand the brackets and rearrange the equation:
3x10^7 = s^2 - [Ac-]s
Substitute the values for [Ac-]:
3x10^7 = s^2 - (0.490 M)s
Rearrange the equation to the standard quadratic form:
s^2 - (0.490 M)s - 3x10^7 = 0
12. Use the quadratic formula to solve for 's':
s = (-b ± √(b^2 - 4ac)) / (2a)
Substitute the values:
s = (0.490 M ± √((0.490 M)^2 - 4(1)(-3x10^7))) / (2(1))
Calculate the value inside the square root:
√((0.490 M)^2 - 4(1)(-3x10^7)) ≈ 1.348 M
Substitute the value into the equation:
s ≈ (0.490 M ± 1.348 M) / 2
13. Calculate the possible values of 's':
s ≈ (0.490 M + 1.348 M) / 2 ≈ 0.919 M
s ≈ (0.490 M - 1.348 M) / 2 ≈ -0.429 M
Since concentration cannot be negative, the solubility of MnS (S^2-) is approximately 0.919 M in the given buffer solution.