Henderson-Hasselbalch Equation: Videos & Practice Problems

The Henderson-Hasselbalch equation is a valuable tool for calculating the pH of a buffer solution, specifically those composed of a conjugate acid-base pair, without the need for an ICE chart. This equation can be expressed in two forms, depending on whether the acid dissociation constant (K_a) or the base dissociation constant (K_b) is provided.

When given K_a, the equation is:

pH = pK_a + log₁₀ \(\frac{[A^-]}{[HA]}\)

In this formula, [A^-] represents the concentration of the conjugate base, and [HA] represents the concentration of the weak acid. The pK_a is the negative logarithm of K_a, which helps in simplifying the calculation of pH.

Conversely, if K_b is provided, the equation is:

pH = pK_b + log₁₀ \(\frac{[HA]}{[B^-]}\)

Here, [HA] is the concentration of the conjugate acid, and [B^-] is the concentration of the weak base. The pK_b is similarly defined as the negative logarithm of K_b.

It is important to note that the brackets in these equations indicate concentration, which can be expressed in either molarity (moles per liter) or moles. Remember that moles can be calculated using the formula:

moles = liters × molarity

This understanding is crucial when applying the Henderson-Hasselbalch equations to ensure accurate calculations of pH in buffer solutions.

To calculate the pH of a buffer solution containing 2.0 M nitrous acid (HNO₂) and 1.48 M lithium nitrite (LiNO₂), we can utilize the Henderson-Hasselbalch equation, which is particularly useful for buffer solutions. The equation is expressed as:

pH = pKa + log₁₀([A^-]/[HA])

In this case, HNO₂ is the weak acid (HA), and LiNO₂ provides the conjugate base (A^-), which is nitrite ion (NO₂^-). Given that the acid dissociation constant (K_a) for nitrous acid is 4.6 × 10^-4, we first need to calculate the pK_a:

pK_a = -log₁₀(K_a) = -log₁₀(4.6 × 10^-4)

Calculating this gives us:

pK_a ≈ 3.34

Next, we substitute the values into the Henderson-Hasselbalch equation:

pH = 3.34 + log₁₀(1.48/2.0)

Calculating the log term:

log₁₀(1.48/2.0) ≈ log₁₀(0.74) ≈ -0.128

Now, substituting this back into the pH equation gives:

pH ≈ 3.34 - 0.128 ≈ 3.21

Thus, the pH of the buffer solution is approximately 3.21. This calculation demonstrates the effectiveness of the Henderson-Hasselbalch equation in determining the pH of a buffer system composed of a weak acid and its conjugate base.

Buffers play a crucial role in maintaining pH stability in various chemical and biological systems. Their effectiveness is confined to a specific pH range, which can be determined using the relationship:

pH = pK_a ± 1

This equation indicates that a buffer is most effective at resisting pH changes within one unit above or below the pK_a of the weak acid or base involved. An ideal buffer occurs when the concentrations of the weak acid and its conjugate base are equal, or conversely, when the concentrations of the weak base and its conjugate acid are equal. In such cases, the pH of the buffer equals the pK_a of the weak acid, providing optimal resistance to pH fluctuations.

To calculate the pH of a buffer solution, the Henderson-Hasselbalch equation is utilized:

pH = pK_a + log₁₀([Conjugate Base]/[Weak Acid])

Alternatively, if the base dissociation constant (K_B) is provided, the equation can be expressed as:

pH = pK_B + log₁₀([Conjugate Acid]/[Weak Base])

For example, if the concentrations of the conjugate base and weak acid are both 0.40 M, the ratio becomes:

log₁₀(0.40/0.40) = log₁₀(1) = 0

This simplifies the Henderson-Hasselbalch equation to:

pH = pK_a + 0

Thus, when the concentrations of the buffer components are equal, the pH directly corresponds to the pK_a or pK_B, depending on the context. Therefore, the effectiveness of a buffer is maximized within the pH range of pK_a ± 1, and it is most ideal when the concentrations of the acid and base components are equal.

To determine the buffering range of a solution containing lactic acid and its conjugate base, sodium lactate, we first need to calculate the pKa of lactic acid. The acid dissociation constant (Ka) for lactic acid is given as \(1.4 \times 10^{-4}\). The pKa can be calculated using the formula:

\(pK_a = -\log(K_a)\)

Substituting the value of Ka, we find:

\(pK_a = -\log(1.4 \times 10^{-4}) \approx 3.85\)

The buffering range, which indicates the pH range in which the buffer is most effective, is determined by the equation:

\(pH = pK_a \pm 1\)

Applying this to our calculated pKa, we have:

\(pH = 3.85 \pm 1\)

This results in a buffering range of:

Lower limit: \(3.85 - 1 = 2.85\)

Upper limit: \(3.85 + 1 = 4.85\)

Therefore, the effective buffering range for this solution is between a pH of 2.85 and 4.85. This range indicates where the buffer will maintain a relatively stable pH when small amounts of acids or bases are added.