What is the pH at the equivalence point for the titration of 0.20 M nitrous acid by 0.20 M sodium hydroxide? [Ka for nitrous acid is 4.5 × 10^-4] A) 5.83 B) 7.00 C) 8.17 D) 9.00 E) 10.67

Question

Quizplus · Accepted Answer

At the equivalence point, the moles of nitrous acid will be equal to the moles of sodium hydroxide, resulting in a solution containing only the conjugate base of nitrous acid (NO2-) and sodium ions. Since NO2- is a weak base, it will hydrolyze water to a small extent, generating OH- ions and increasing the pH of the solution. The pH can be calculated using the expression for the base dissociation constant (Kb) of NO2-:

Kb = Kw/Ka = (1.0 x 10^-14)/(4.5 x 10^-4) = 2.22 x 10^-11

At the equivalence point, [NO2-] = [OH-] = 0.1 M (assuming equal volumes of titrant added), so we can use the Kb expression to calculate the concentration of OH- ions produced by the hydrolysis of NO2-:

Kb = [OH-]^2/[NO2-] = (x^2)/(0.1 - x)

where x is the concentration of OH- ions formed. Since x will be small compared to 0.1, we can simplify the expression to:

Kb = x^2/0.1

0.1x 2.22 x 10^-11 = x^2

x = sqrt(2.22 x 10^-10) = 1.49 x 10^-5 M

Thus, the pOH at the equivalence point is:

pOH = -log(1.49 x 10^-5) = 4.83

And the pH at the equivalence point is:

pH = 14.00 - pOH = 9.17

Therefore, the best choice is C, 8.17 (which is the closest answer choice to the calculated pH of 9.17).

What Is the PH at the Equivalence Point for the Titration