Calculate the pH of a 1.0 M solution of sodium acetate (CH₃CO₂Na) considering that the K_a of acetic acid (CH₃CO₂H is 1.7 x 10^-5.

CH₃CO₂Na is a salt of a strong base NaOH and a weak acid CH₃CO₂H therefore, the solution will be basic.

 

Dissociate the salt and write the reaction of its weak component with water.

 

CH₃CO₂Na → Na⁺ + CH₃CO₂^–

CH₃CO₂^–(aq) + H₂O(l) → CH₃CO₂H(aq) + OH^–(aq)  (basic)

 

Next, determine the K_b from the K_a:

 

K_a · K_b = K_w = 10^-14

 

Rearranging this, we get an expression for K_a:

 

\[{K_{{\rm{b}}}}\; = \,\frac{{{K_{\rm{w}}}}}{{{K_{\rm{a}}}}}\; = \;\frac{{{\rm{1}}{{\rm{0}}^{{\rm{ – 14}}}}}}{{{\rm{1}}{\rm{.7}}\; \times \;{\rm{1}}{{\rm{0}}^{{\rm{ – 5}}}}}}\; = \;{\rm{5}}{\rm{.9 }} \times {\rm{ 1}}{{\rm{0}}^{{\rm{ – 10}}}}\]

 

Set up an ICE table for K_b assigning x mol/l for the ionization.

CH₃CO₂^–(aq) + H₂O(l) → CH₃CO₂H(aq) + OH^–(aq)

	[CH3CO2–]	[CH3CO2H]	[OH–]
Initial	1.0	0	0
Change	-x	+x	+x
Equil	1.0 – x	x	x

 

Write the expression for K_b using the equilibrium concentrations in the ICE table in order to determine [OH^–].

 

\[{K_{{\rm{b}}}}\; = \,\frac{{{\rm{[C}}{{\rm{H}}_{\rm{3}}}{\rm{C}}{{\rm{O}}_{\rm{2}}}{\rm{H][O}}{{\rm{H}}^{\rm{ – }}}{\rm{]}}}}{{{\rm{[C}}{{\rm{H}}_{\rm{3}}}{\rm{C}}{{\rm{O}}_{\rm{2}}}^{\rm{ – }}{\rm{]}}}}\;{\rm{ = }}\;\frac{{{{\rm{x}}^{\rm{2}}}}}{{{\rm{1}}{\rm{.0}}\;{\rm{ – }}\;{\rm{x}}}}\; \approx \;\frac{{{{\rm{x}}^{\rm{2}}}}}{{{\rm{1}}{\rm{.0}}}}{\rm{ = }}\;{\rm{5}}{\rm{.9}}\;{\rm{ \times }}\,{\rm{1}}{{\rm{0}}^{{\rm{ – 10}}}}\]

 

We find that x = 2.4 x 10^-5 mol/l.

Check if the approximation was valid:

 

\[\% \, = \;\frac{{2.4\, \times \;{{10}^{ – 5}}}}{{1.0}}\; \times \;100\% \; = \;0.0024\% \]

 

The approximation is valid, so the concentration of OH^– ions at equilibrium is 3.0 x 10^-6 M.

We can now calculate the pOH, and then pH using the pH + pH = 14 relationship:

 

pOH = -log 2.4 x 10^-5 = 4.6, and therefore, the pH is:

pH = 14 – pOH = 14 – 4.6 = 9.4

 

And this answer is also reasonable because we predicted to have a basic solution.

 

Check Also

• Definitions of Acids and Bases
• Acid-Base Reactions
• Acid-Base Titrations
• Conjugate Acid and Conjugate Base
• Autoionization of Water and K_w
• The pH and Acidity
• Acid Strength, K_a, and pK_a
• Base Strength, K_b, and pK_b
• Ka, pKa, Kb, and pK_b Relationship
• The pH of a Strong Acid and Base
• pH + pOH = 14
• The pH of a Weak Acid
• The pH of a Weak Base
• The pH of Polyprotic Acids
• The acidity of a Salt Solution
• The pH of a Salt Solution
• The pH of Salts With Acidic Cations and Basic Anions
• pH Practice Problems
• Acids and Bases Practice Problems
  Acids and Bases Quiz