What is the value of [H₃O⁺] in a solution with pH = 10.82? A)6.6 × 10^-4 M B)1.5 × 10^-11 M C)1.03 M D)10.82 M E)3.18 M

Question

Quizplus · Accepted Answer

The given expression represents a weak acid (HS1U1B) and its conjugate base (S1U1B0O) in equilibrium with their corresponding protonated forms (H+ and HS1U1B13S1U1P1). The equilibrium expression for this reaction can be written as:
Ka = ([HS1U1B13S1U1P1][S1U1B0O])/([HS1U1B][H+])
At pH = 10.82, [H+] = 10^(-10.82) M
We can assume that [HS1U1B] ≈ [HS1U1B13S1U1P1] (since the value of Ka is small) and [S1U1B0O] ≈ [HS1U1B13S1U1P1] + [OH-]
Hence, we can rewrite the equilibrium expression as:
Ka = ([HS1U1B13S1U1P1]^2)/([HS1U1B13S1U1P1] + [OH-])
Solving for [HS1U1B13S1U1P1], we get:
[HS1U1B13S1U1P1] = (-Ka ± sqrt(Ka^2+4Ka[OH-]))/2
Substituting the given values, we get:
[HS1U1B13S1U1P1] = 1.5 × 10^(-11) M
Therefore, the value of [HS1U1B13S1U1B0OS1U1P1+S1S1P0] = [HS1U1B13S1U1P1] + [S1U1B0O] = [HS1U1B13S1U1P1] + [OH-] = 1.5 × 10^(-11) + 3.18 × 10^(-11) = 4.68 × 10^(-11) M
Hence, the correct answer is B.

What Is the Value of [H3O+] in a Solution with PH

What Is the Value of [H₃O⁺] in a Solution with PH