Calculate the pH of a buffer which contains 0.0500 M pyruvic acid and 0.0450 M sodium pyruvate. (The Ka of pyruvic acid is 4.1 × 10–3)
Use the Henderson-Hasselbalch equation. You will need to convert Ka to pKa. pyruvic is the acid, of course, and the sodium salt is the base.
Answer is 2.72
To calculate the pH of a buffer, we can use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is given by:
pH = pKa + log ([A-] / [HA])
where pH is the desired pH, pKa is the negative logarithm (base 10) of the acid dissociation constant (Ka), [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.
In this case, the weak acid is pyruvic acid (C3H4O3) and its conjugate base is sodium pyruvate (C3H3O3-). The pKa of pyruvic acid is 4.1 × 10^-3.
Given:
[HA] = 0.0500 M (concentration of pyruvic acid)
[A-] = 0.0450 M (concentration of sodium pyruvate)
pKa = 4.1 × 10^-3
Substituting the given values into the Henderson-Hasselbalch equation:
pH = 4.1 × 10^-3 + log (0.0450 / 0.0500)
Next, calculate the ratio of [A-] / [HA]:
[A-] / [HA] = 0.0450 / 0.0500
[A-] / [HA] = 0.90
Taking the logarithm:
log (0.90) ≈ -0.046
Now, substitute this value back into the Henderson-Hasselbalch equation:
pH = 4.1 × 10^-3 - 0.046
pH ≈ 4.1 × 10^-3 - 0.046
pH ≈ 3.98
Therefore, the pH of the buffer containing 0.0500 M pyruvic acid and 0.0450 M sodium pyruvate is approximately 3.98.
To calculate the pH of a buffer solution, we use the Henderson-Hasselbalch equation, which is given by:
pH = pKa + log ([A-] / [HA])
In this case, pyruvic acid (HA) is a weak acid, and sodium pyruvate (A-) is its conjugate base.
Given:
[HA] = 0.0500 M (concentration of pyruvic acid)
[A-] = 0.0450 M (concentration of sodium pyruvate)
Ka (acid dissociation constant) of pyruvic acid = 4.1 × 10–3
First, we need to calculate the pKa of pyruvic acid using the Ka value:
pKa = -log10(Ka)
pKa = -log10(4.1 × 10–3)
Now, let's calculate the pKa:
pKa = -log10(4.1 × 10–3)
pKa ≈ -(-2.39)
pKa ≈ 2.39
Next, we substitute the values into the Henderson-Hasselbalch equation to calculate the pH:
pH = pKa + log ([A-] / [HA])
pH = 2.39 + log (0.0450 / 0.0500)
Now, let's calculate the pH:
pH = 2.39 + log (0.0450 / 0.0500)
pH ≈ 2.39 + (-0.022)
pH ≈ 2.37
Therefore, the pH of the buffer solution containing 0.0500 M pyruvic acid and 0.0450 M sodium pyruvate is approximately 2.37.