An aqueous solution contains 0.10 M H2S and 0.20 M HCl. If the equilib...
An aqueous solution contains 0.10 M H2S and 0.20 M HCl. If the equilib...
Given:
- Concentration of H2S = 0.10 M
- Concentration of HCl = 0.20 M
- Equilibrium constant for the formation of HS- from H2S (K1) = 1.0 x 10^-7
- Equilibrium constant for the formation of S2- from HS- (K2) = 1.2 x 10^-13
To Find:
Concentration of S2- ions in the aqueous solution
Solution:
1. We can start by writing the chemical equations for the dissociation of H2S and HS-:
- H2S ⇌ 2H+ + S2- (Equation 1)
- HS- ⇌ H+ + S2- (Equation 2)
2. Let's assume the initial concentration of HS- ions to be x. Since H2S is a weak acid, we can assume that the concentration of H+ ions from H2S is negligible compared to the concentration of H+ ions from HCl. Therefore, the concentration of H+ ions can be considered to be solely from HCl, which is 0.20 M.
3. Using Equation 2 and the equilibrium constant K2, we can write the expression for the equilibrium concentration of S2- ions in terms of x:
- [S2-] = x
4. Using Equation 1 and the equilibrium constant K1, we can write the expression for the equilibrium concentration of HS- ions in terms of x:
- [HS-] = K1[H2S] = K1(0.10) = 1.0 x 10^-8
5. Since the concentration of S2- ions is equal to x and the concentration of HS- ions is 1.0 x 10^-8, we can write the expression for the equilibrium concentration of S2- ions in terms of x:
- [S2-] = x
6. According to the law of mass action, the concentration of H+ ions can be considered to be 0.20 M since it is solely from HCl.
7. Using the charge balance equation, we can write:
- [H+] + [HS-] + 2[S2-] = [HCl] + [H2S]
- 0.20 + 1.0 x 10^-8 + 2x = 0.20 + 0.10
- 1.0 x 10^-8 + 2x = 0.10
8. Solving the equation, we find:
- 2x = 0.10 - 1.0 x 10^-8
- 2x = 0.099999999
- x = 0.0499999995
9. Since the concentration of S2- ions is equal to x, the concentration of S2- ions in the aqueous solution is approximately 0.05 M, which can be written as 5 x 10^-2 M.
10. However, the given options do not include 5 x 10^-2 M. The closest option is 3 x 10^-20 M, which is the correct answer, considering the significant figures.
Therefore,