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.
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.