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The HendersonHasselbalch Equation
The Henderson–Hasselbalch equation connects the measurable value of the pH of a solution with the theoretical value pKa.
Learning Objective

Calculate the pH of a buffer system using the HendersonHasselbalch equation.
Key Points

The HendersonHasselbalch equation is useful for estimating the pH of a buffer solution and finding the equilibrium pH in an acidbase reaction.

The formula for the Henderson–Hasselbalch equation is:
$pH=p{ K }_{ a }+log(\frac { { [A }^{  }] }{ [HA] } )$ , where pH is the concentration of [H+], pK_{a} is the acid dissociation constant, and [A] and [HA] are concentrations of the conjugate base and starting acid. 
The equation can be used to determine the amount of acid and conjugate base needed to make a buffer solution of a certain pH.
Term

pKa
A quantitative measure of the strength of an acid in solution; a weak acid has a pKa value in the approximate range 2 to 12 in water and a strong acid has a pKa value of less than about 2.
Full Text
The Henderson–Hasselbalch equation mathematically connects the measurable pH of a solution with the pK_{a }(log K_{a}) of the acid. The equation is also useful for estimating the pH of a buffer solution and finding the equilibrium pH in an acidbase reaction. The equation can be derived from the formula of pK_{a} for a weak acid or buffer. The balanced equation for an acid dissociation is:
The acid dissociation constant is:
After taking the log of the entire equation and rearranging it, the result is:
This equation can be rewritten as:
Distributing the negative sign gives the final version of the HendersonHasselbalch equation:
In an alternate application, the equation can be used to determine the amount of acid and conjugate base needed to make a buffer of a certain pH. With a given pH and known pK_{a}, the solution of the HendersonHasselbalch equation gives the logarithm of a ratio which can be solved by performing the antilogarithm of pH/pKa:
An example of how to use the HendersonHasselbalch equation to solve for the pH of a buffer solution is as follows:
What is the pH of a buffer solution consisting of 0.0350 M NH_{3} and 0.0500 M NH_{4}^{+ }(K_{a} for NH_{4}^{+} is 5.6 x 10^{10})? The equation for the reaction is:
Assuming that the change (x) is negligible, the HendersonHasselbalch equation will be:
pH = 9.41
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Key Term Reference
 acid
 Appears in this related concepts: The Halogens (Group 17), Basic and Amphoteric Hydroxides, and Calculating Percent Dissociation
 acid dissociation constant
 Appears in this related concepts: Calculating Changes in a Buffer Solution, Absolute Concentrations of the Acid and Conjugate Base, and Acid Dissociation Constant (Ka)
 balanced equation
 Appears in this related concepts: MoletoMole Conversions, Effect of a Common Ion on Solubility, and Reaction Stoichiometry
 base
 Appears in this related concepts: Overview of the AcidBase Properties of Salt, Balancing Redox Equations, and AcidBase Balance by the Kidneys
 buffer
 Appears in this related concepts: The Common Ion Effect, Weak AcidStrong Base Titrations, and pH, Buffers, Acids, and Bases
 buffers
 Appears in this related concepts: Other Rechargeable Batteries, Buffers Containing a Base and Conjugate Acid, and Reactions of Amino Acids
 concentration
 Appears in this related concepts: Calculating Equilibrium Concentrations , Factors that Affect Reaction Rate, and Diffusion
 conjugate base
 Appears in this related concepts: Weak Acids, Brønsted Acids and Bases, and The BrønstedLowry Definition of Acids and Bases
 dissociation
 Appears in this related concepts: pOH and Other p Scales, Specialized Equilibrium Constants, and Water’s Solvent Properties
 equilibrium
 Appears in this related concepts: How Supply and Demand Affect Businesses, Ecology of Ecosystems, and Equilibrium
 logarithm
 Appears in this related concepts: Derivatives of Logarithmic Functions, Converting between Exponential and Logarithmic Equations, and Special Logarithms
 pH
 Appears in this related concepts: AcidBase Titrations, Chemical Buffer Systems, and Applications
 ratio
 Appears in this related concepts: Classification, Equity Theory, and The Importance of Productivity
 solution
 Appears in this related concepts: Electrolyte and Nonelectrolyte Solutions, Using Molarity in Calculations of Solutions, and Solubility
 weak acid
 Appears in this related concepts: Binary Acids, AcidBase Reactions, and Nucleophilic Addition Reactions & Reduction
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Source: Boundless. “The HendersonHasselbalch Equation.” Boundless Chemistry. Boundless, 14 Apr. 2015. Retrieved 14 Apr. 2015 from https://www.boundless.com/chemistry/textbooks/boundlesschemistrytextbook/acidbaseequilibria16/buffersolutions117/thehendersonhasselbalchequation4763652/