Published by Team Giralda Center

A 0.20 mol/L solution of propionic acid has a pH of 2.79. What is the pKa of propionic acid?


Step 1: Understand the Dissociation of Propionic Acid

CHCHCOOH, is a weak acid that partially dissociates in water according to the following reaction:

⇒ CHCHCOOH(aq) + HO(l) ⇌ CHCHCOO⁻(aq) + HO⁺(aq)

Step 2: Understanding the Equilibrium Constant, Ka

The equilibrium constant for this reaction, Ka, is given by:


Step 3: Understand the Concept of pH

The pH is a measure of the hydronium ion concentration, [HO⁺], and is given by:

⇒ pH = –log[HO⁺]

Step 4: Find [H₃O⁺]

Given that the pH of the propionic acid solution is 2.79, we can find the [HO⁺] by taking the antilog of -pH:

⇒ [HO⁺] = 10-pH = 102.79 = 1.62 × 10⁻³ M

Step 5: Calculation of Ka

In a 0.20 mol/L solution of propionic acid, the concentration of propionic acid [CHCHCOOH] is approximately 0.20 M (since it’s a weak acid and doesn’t fully ionize). The concentration of the propionate ion [CHCHCOO⁻] is equal to the [HO⁺] at equilibrium, so we can substitute these values into the Ka expression:


⇒ Ka = (1.62 × 10⁻³ M) * (1.62 × 10⁻³ M) / 0.20 M

∴ Ka = 1.32 × 10⁻⁵

Step 6: Calculation of pKa

The pKa is the negative logarithm (base 10) of Ka:

⇒ pKa = -log(Ka)

⇒ pKa = -log(1.32 × 10⁻⁵)

∴ pKa = 4.88

Therefore, the pKa of propionic acid is 4.88.

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