16.15
Henderson-Hasselbalch Equation
The ionization-constant expression for a solution of a weak acid can be written as:
Rearranging to solve for [H3O+] yields:
Taking the negative logari…
The pH of a buffered solution containing a conjugate acid-base pair may be calculated using the Henderson-Hasselbalch equation as an alternative to an ICE table.
The Henderson-Hasselbalch equation is derived from the equilibrium constant expression for Ka.
This expression can be rearranged to determine the hydronium ion concentration. If the negative log of both sides is taken, the negative logarithm of the hydronium ion concentration and the negative logarithm of the acid dissociation constant can be replaced by the pH and the pKa, respectively.
This yields an equation where the pH of a buffer can be calculated by adding the pKa and the log of the equilibrium concentrations of a conjugate base over its weak acid.
These equilibrium values can be replaced by the initial concentrations if the change in the hydronium ion concentration, x, is less than the 5% of the initial concentrations of both the weak acid and the conjugate base.
The Henderson-Hasselbalch equation also shows the ratio of base to acid needed to prepare a buffer at a specific pH.
Similarly, the pH of a solution containing a weak base and its conjugate acid can be determined using this equation by calculating the pKa of the conjugate acid from the pKb using the formula: pKa plus pKb is equal to fourteen.
The pH of a buffer containing 0.15 molar formic acid and 0.18 molar sodium formate can be determined using either the Henderson-Hasselbalch equation or the Ka for formic acid and the ICE table. However, the Henderson-Hasselbalch equation is a quicker method to calculate the pH when a reaction involves a conjugate acid-base pair and the change in hydronium concentration is small.
The pKa is determined by taking the negative logarithm of the Ka for formic acid, which equals 3.75.
When the initial concentrations of formic acid and formate are plugged into the equation, the pH value for the solution equals 3.83.
This pH value can be used to determine the hydronium ion concentration, 1.5 × 10−4. As this value is less than 5% of 0.15 molar formic acid, the approximations needed to use the Henderson-Hasselbalch equation are valid.
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Q1: How is the Henderson-Hasselbalch equation derived from the Ka expression?
The Henderson-Hasselbalch equation is derived by rearranging the equilibrium constant expression for Ka to solve for hydronium ion concentration. Taking the negative logarithm of both sides converts the expression into pH and pKa terms. This yields the equation: pH = pKa + log([base]/[acid]), which relates pH to the ionization constant and concentrations of the conjugate acid-base pair in a buffered solution.
Q2: When is it valid to use initial concentrations instead of equilibrium concentrations in the Henderson-Hasselbalch equation?
Initial concentrations can replace equilibrium concentrations when the change in hydronium ion concentration, x, is less than 5% of the initial concentrations of both the weak acid and conjugate base. This approximation is valid because the change is negligible, making the initial and equilibrium concentrations essentially equivalent for practical pH calculations.
Q3: What is the advantage of using the Henderson-Hasselbalch equation over an ICE table?
The Henderson-Hasselbalch equation is a quicker method to calculate buffer pH when a reaction involves a conjugate acid-base pair and the change in hydronium concentration is small. Unlike ICE tables, which require multiple algebraic steps, the Henderson-Hasselbalch equation directly incorporates the pKa and concentration ratio, streamlining calculations for buffer solutions.
Q4: How can the Henderson-Hasselbalch equation be used to prepare a buffer at a specific pH?
The Henderson-Hasselbalch equation shows the ratio of base to acid needed to achieve a desired pH. By rearranging the equation to solve for the ratio [base]/[acid], you can determine the exact proportions of conjugate base and weak acid required. This allows chemists to design buffers with precise pH values for specific applications.
Q5: How do you calculate pH for a buffer containing a weak base and its conjugate acid?
For a weak base and its conjugate acid, first convert the pKb to pKa using the relationship: pKa + pKb = 14. Then apply the Henderson-Hasselbalch equation using the calculated pKa and the concentrations of the conjugate acid and base. This allows pH calculation for basic buffers using the same logarithmic framework.
Q6: What does pKa represent in the Henderson-Hasselbalch equation?
The pKa is the negative logarithm of the acid dissociation constant (Ka). It represents the strength of a weak acid; lower pKa values indicate stronger acids. In the Henderson-Hasselbalch equation, pKa is the reference point around which buffer pH is calculated, determining the optimal pH range for a given acid-base pair.
Q7: How do you verify that the Henderson-Hasselbalch approximation is valid for a specific buffer?
After calculating pH using the Henderson-Hasselbalch equation, convert the result back to hydronium ion concentration using [H3O+] = 10^(-pH). Then verify that this concentration is less than 5% of the initial weak acid concentration. If this condition is met, the approximation is valid and the calculated pH is reliable for the buffer solution.