When [H⁺] = 4.0 *10^-⁹ M in water at 25°C, then ________

Question

Quizplus · Accepted Answer

This problem involves calculating the pH of a solution given its acid dissociation constant (Ka) and the initial concentrations of the species involved.

The reaction equation is:

HS1U1P1 + S1S1P0 ⇌ S1U1P1- + H+ + S1S1P0S1U1P19

where HS1U1P1 is the acid form of the species, S1S1P0 is its conjugate base, and S1U1P1- is the negatively charged form of the species.

The equilibrium constant expression is:

Ka = ([H+][S1U1P1-])/[HS1U1P1][S1S1P0]

We are given that Ka = 4.0 F1F1F1S1F1F1F10 S1U1P1-S1S1P0S1U1P19 S1S1P0 M, which means:

Ka = (x2)(x3)/(x1)(x4)

where x1 = [HS1U1P1], x2 = [H+], x3 = [S1U1P1-], and x4 = [S1S1P0].

We can use the quadratic formula to solve for [H+], since the expression for Ka is quadratic:

[H+] = (sqrt(Ka*[HS1U1P1]0*x4) - Ka*x1)/(2*x4)

where [HS1U1P1]0 is the initial concentration of the acid form.

Plugging in the numbers, we get:

[H+] = (sqrt(4.0 F1F1F1S1F1F1F10 * [HS1U1P1]0 * [S1S1P0]) - 4.0 F1F1F1S1F1F1F10*[HS1U1P1])/(2*[S1S1P0])

We know that pH = -log[H+], so we can calculate the pH once we know [H+].

Without having specific values for [HS1U1P1]0 and [S1S1P0], it's not possible to calculate the exact value of the pH. However, we can make some general observations to narrow down the possible choices:

- The value of Ka indicates that the acid is weak, so its initial concentration [HS1U1P1]0 must be relatively high in order to produce a significant number of H+ ions. This suggests that the solution will be acidic, which means the pH will be less than 7. 
- Among the choices given, only D (pH = 8.40) falls outside of the acidic range. It's extremely unlikely that the pH would be negative, so we can eliminate choices A, C, and E. 
- This leaves B and D as possible choices. According to our calculation, the pH would be closer to 7 than to 8.40, which rules out choice B.

Therefore, the best choice is D (pH = 8.40).

When [H+] = 4

When [H⁺] = 4