A solution is found to have a pH of 10.45. What is [H₃O⁺]?

Question

Quizplus · Accepted Answer

To find the concentration of the hydrogen sulfide ion [HS-], we need to use the pH and the dissociation constant (pKa) of hydrogen sulfide. 
pH = pKa + log([HS-]/[H2S]) 
10.45 = 7.0 + log([HS-]/[H2S]) 
log([HS-]/[H2S]) = 3.45 
[HS-]/[H2S] = 3.5 x 10^-4

Since the solution is basic, we can assume that [OH-] is significantly greater than [H+], therefore:
[H2S] ≈ [HS-] + [S2-]

We don't have information to calculate the concentration of sulfide ion [S2-]. However, we can assume that it is negligible compared to [HS-] and [H2S], so:
[H2S] ≈ [HS-]

[HS-] + [H2S] = 1 M 
Substituting [HS-]/[H2S] = 3.5 x 10^-4, we get:

[HS-] + 3.5 x 10^-4 [HS-] = 1 M 
[HS-] (1 + 3.5 x 10^-4) = 1 M 
[HS-] = 1 / (1 + 3.5 x 10^-4) = 2.8 x 10^-4 M

Finally, since we are not given any other species besides HS-, the answer is [HS-] = 2.8 x 10^-4 M.

A Solution Is Found to Have a PH of 10