Question

You are asked to determine the pH of a very dilute solution of a strong base (e.g., 1.1 × 10−8 M KOH). You know you will need to use the ion-product of water equation: [H+][OH−] = Kw; the charge-balance equation: Σ pos. charges = Σ neg. charges; and the quadratic equation: ax2 + bx + c = 0. What would the constant “a” in the generalized quadratic equation represent in the above scenario? Assume you are solving for [H+] directly and not [OH−]. Select all that apply.

a = 1

a = −[K+]

a = −1

a = [K+]

a = [H+]

a = −[H+]

a = Kw

a = [H+]2

a = −Kw

Answer 1

Note that HCl is a stong acid

HCl will dissociate 100% to form H+ and Cl-

and H2O <->H+ + OH- equilibirum must be considered since:

H+ concentration is too small

[H₃O⁺] = [OH⁻] + [Cl⁻]

note that [C-] = 1.1*10^-8

[H₃O⁺] = [OH⁻] + 1.1*10^-8

Recall Equilibrium of water:

Kw = 10^-14

Kw = [H₃O⁺][OH⁻]

substitute known values

Kw = ([OH⁻] + 1.1*10^-8) * [OH⁻]

10^-14 = [OH⁻]^2 + (1.1*10^-8)*[OH⁻]

which is similar to a quadratic eqution

let x = [OH-] so

x^2 + (1.1*10^-8)x - 10^-14 = 0

note that

ax^2 + bx + c = 0; in this case:

a = 1; b = 1.1*10^-8; c = -10^-14

choose then

a = 1