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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 }(which is equal to 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/pK_{a}:
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 in concentrations is negligible in order for the system to reach equilibrium, the HendersonHasselbalch equation will be:
pH = 9.095
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Key Term Reference
 acid
 Appears in these related concepts: The Halogens (Group 17), Basic and Amphoteric Hydroxides, and Calculating Percent Dissociation
 acid dissociation constant
 Appears in these 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 these related concepts: MoletoMole Conversions, Effect of a Common Ion on Solubility, and Reaction Stoichiometry
 base
 Appears in these related concepts: Changing Logarithmic Bases, Logarithms of Powers, and Rational Exponents
 buffer
 Appears in these related concepts: Weak AcidStrong Base Titrations, Chemical Buffer Systems, and pH, Buffers, Acids, and Bases
 buffers
 Appears in these related concepts: Other Rechargeable Batteries, The Common Ion Effect, and Buffers Containing a Base and Conjugate Acid
 concentration
 Appears in these related concepts: Calculating Equilibrium Concentrations , Molarity, and Diffusion
 conjugate base
 Appears in these related concepts: Relative Amounts of Acid and Base, Brønsted Acids and Bases, and The BrønstedLowry Definition of Acids and Bases
 dissociation
 Appears in these related concepts: pOH and Other p Scales, Water’s Solvent Properties, and Hypnosis
 equilibrium
 Appears in these related concepts: Free Energy Changes for Nonstandard States, Second Condition, and The Equilibrium Interest Rate
 logarithm
 Appears in these related concepts: Solving Problems with Logarithmic Graphs, Graphs of Logarithmic Functions, and The Number e
 pH
 Appears in these related concepts: AcidBase Indicators, Financial Applications of Quadratic Functions, and The Acid Dissociation Constant
 ratio
 Appears in these related concepts: The Importance of Productivity, Basic Descriptive Statistics, and Schedules of Reinforcement
 solution
 Appears in these related concepts: Electrolyte and Nonelectrolyte Solutions, Turning Your Claim Into a Thesis Statement, and What is an Equation?
 system
 Appears in these related concepts: Definition of Management, Comparison of Enthalpy to Internal Energy, and Local, regional, national, international, and global marketers
 weak acid
 Appears in these related concepts: Overview of the AcidBase Properties of Salt, Weak Acids, and Irreversible Addition Reactions
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Cite This Source
Source: Boundless. “The HendersonHasselbalch Equation.” Boundless Chemistry. Boundless, 26 May. 2016. Retrieved 29 Jul. 2016 from https://www.boundless.com/chemistry/textbooks/boundlesschemistrytextbook/acidbaseequilibria16/buffersolutions117/thehendersonhasselbalchequation4763652/