Now, the Henderson-Hasselbalch equation allows you to calculate the pH of a buffer without having to use an ICE chart. Here, we're going to say it only applies to buffers composed of a conjugate acid-base pair. We can look at the Henderson-Hasselbalch equation as two different formulas. The formula that you use is based on if they give you the Ka or Kb of your buffer solution. If they give you the Ka of your buffer solution, you can say that pH equals pKa plus logconjugate baseweak acid. Now, if they give you Kb, then you could use this formula: pH equals pKb plus logconjugate acidweak base. Now, when it comes to the sign, the brackets, we know that it tends to mean molarity or concentration. For the Henderson-Hasselbalch equations, it could also be used for moles. Okay. So, just remember that the units that can go within these brackets can be either molarity or moles. Remember that moles itself equals liters times molarity, so keep that in mind when you utilize the Henderson-Hasselbalch equations.
- 1. Matter and Measurements4h 29m
- What is Chemistry?5m
- The Scientific Method9m
- Classification of Matter16m
- States of Matter8m
- Physical & Chemical Changes19m
- Chemical Properties8m
- Physical Properties5m
- Intensive vs. Extensive Properties13m
- Temperature (Simplified)9m
- Scientific Notation13m
- SI Units (Simplified)5m
- Metric Prefixes24m
- Significant Figures (Simplified)11m
- Significant Figures: Precision in Measurements7m
- Significant Figures: In Calculations19m
- Conversion Factors (Simplified)15m
- Dimensional Analysis22m
- Density12m
- Specific Gravity9m
- Density of Geometric Objects19m
- Density of Non-Geometric Objects9m
- 2. Atoms and the Periodic Table5h 23m
- The Atom (Simplified)9m
- Subatomic Particles (Simplified)12m
- Isotopes17m
- Ions (Simplified)22m
- Atomic Mass (Simplified)17m
- Atomic Mass (Conceptual)12m
- Periodic Table: Element Symbols6m
- Periodic Table: Classifications11m
- Periodic Table: Group Names8m
- Periodic Table: Representative Elements & Transition Metals7m
- Periodic Table: Elemental Forms (Simplified)6m
- Periodic Table: Phases (Simplified)8m
- Law of Definite Proportions9m
- Atomic Theory9m
- Rutherford Gold Foil Experiment9m
- Wavelength and Frequency (Simplified)5m
- Electromagnetic Spectrum (Simplified)11m
- Bohr Model (Simplified)9m
- Emission Spectrum (Simplified)3m
- Electronic Structure4m
- Electronic Structure: Shells5m
- Electronic Structure: Subshells4m
- Electronic Structure: Orbitals11m
- Electronic Structure: Electron Spin3m
- Electronic Structure: Number of Electrons4m
- The Electron Configuration (Simplified)22m
- Electron Arrangements5m
- The Electron Configuration: Condensed4m
- The Electron Configuration: Exceptions (Simplified)12m
- Ions and the Octet Rule9m
- Ions and the Octet Rule (Simplified)8m
- Valence Electrons of Elements (Simplified)5m
- Lewis Dot Symbols (Simplified)7m
- Periodic Trend: Metallic Character4m
- Periodic Trend: Atomic Radius (Simplified)7m
- 3. Ionic Compounds2h 18m
- Periodic Table: Main Group Element Charges12m
- Periodic Table: Transition Metal Charges6m
- Periodic Trend: Ionic Radius (Simplified)5m
- Periodic Trend: Ranking Ionic Radii8m
- Periodic Trend: Ionization Energy (Simplified)9m
- Periodic Trend: Electron Affinity (Simplified)8m
- Ionic Bonding6m
- Naming Monoatomic Cations6m
- Naming Monoatomic Anions5m
- Polyatomic Ions25m
- Naming Ionic Compounds11m
- Writing Formula Units of Ionic Compounds7m
- Naming Ionic Hydrates6m
- Naming Acids18m
- 4. Molecular Compounds2h 18m
- Covalent Bonds6m
- Naming Binary Molecular Compounds6m
- Molecular Models4m
- Bonding Preferences6m
- Lewis Dot Structures: Neutral Compounds (Simplified)8m
- Multiple Bonds4m
- Multiple Bonds (Simplified)6m
- Lewis Dot Structures: Multiple Bonds10m
- Lewis Dot Structures: Ions (Simplified)8m
- Lewis Dot Structures: Exceptions (Simplified)12m
- Resonance Structures (Simplified)5m
- Valence Shell Electron Pair Repulsion Theory (Simplified)4m
- Electron Geometry (Simplified)8m
- Molecular Geometry (Simplified)11m
- Bond Angles (Simplified)11m
- Dipole Moment (Simplified)15m
- Molecular Polarity (Simplified)7m
- 5. Classification & Balancing of Chemical Reactions3h 17m
- Chemical Reaction: Chemical Change5m
- Law of Conservation of Mass5m
- Balancing Chemical Equations (Simplified)13m
- Solubility Rules16m
- Molecular Equations18m
- Types of Chemical Reactions12m
- Complete Ionic Equations18m
- Calculate Oxidation Numbers15m
- Redox Reactions17m
- Spontaneous Redox Reactions8m
- Balancing Redox Reactions: Acidic Solutions17m
- Balancing Redox Reactions: Basic Solutions17m
- Balancing Redox Reactions (Simplified)13m
- Galvanic Cell (Simplified)16m
- 6. Chemical Reactions & Quantities2h 35m
- 7. Energy, Rate and Equilibrium3h 46m
- Nature of Energy6m
- First Law of Thermodynamics7m
- Endothermic & Exothermic Reactions7m
- Bond Energy14m
- Thermochemical Equations12m
- Heat Capacity19m
- Thermal Equilibrium (Simplified)8m
- Hess's Law23m
- Rate of Reaction11m
- Energy Diagrams12m
- Chemical Equilibrium7m
- The Equilibrium Constant14m
- Le Chatelier's Principle23m
- Solubility Product Constant (Ksp)17m
- Spontaneous Reaction10m
- Entropy (Simplified)9m
- Gibbs Free Energy (Simplified)18m
- 8. Gases, Liquids and Solids3h 25m
- Pressure Units6m
- Kinetic Molecular Theory14m
- The Ideal Gas Law18m
- The Ideal Gas Law Derivations13m
- The Ideal Gas Law Applications6m
- Chemistry Gas Laws16m
- Chemistry Gas Laws: Combined Gas Law12m
- Standard Temperature and Pressure14m
- Dalton's Law: Partial Pressure (Simplified)13m
- Gas Stoichiometry18m
- Intermolecular Forces (Simplified)19m
- Intermolecular Forces and Physical Properties11m
- Atomic, Ionic and Molecular Solids10m
- Heating and Cooling Curves30m
- 9. Solutions4h 10m
- Solutions6m
- Solubility and Intermolecular Forces18m
- Solutions: Mass Percent6m
- Percent Concentrations10m
- Molarity18m
- Osmolarity15m
- Parts per Million (ppm)13m
- Solubility: Temperature Effect8m
- Intro to Henry's Law4m
- Henry's Law Calculations12m
- Dilutions12m
- Solution Stoichiometry14m
- Electrolytes (Simplified)13m
- Equivalents11m
- Molality15m
- The Colligative Properties15m
- Boiling Point Elevation16m
- Freezing Point Depression9m
- Osmosis16m
- Osmotic Pressure9m
- 10. Acids and Bases3h 29m
- Acid-Base Introduction11m
- Arrhenius Acid and Base6m
- Bronsted Lowry Acid and Base18m
- Acid and Base Strength17m
- Ka and Kb12m
- The pH Scale19m
- Auto-Ionization9m
- pH of Strong Acids and Bases9m
- Acid-Base Equivalents14m
- Acid-Base Reactions7m
- Gas Evolution Equations (Simplified)6m
- Ionic Salts (Simplified)23m
- Buffers25m
- Henderson-Hasselbalch Equation16m
- Strong Acid Strong Base Titrations (Simplified)10m
- 11. Nuclear Chemistry56m
- BONUS: Lab Techniques and Procedures1h 38m
- BONUS: Mathematical Operations and Functions47m
- 12. Introduction to Organic Chemistry1h 34m
- 13. Alkenes, Alkynes, and Aromatic Compounds2h 12m
- 14. Compounds with Oxygen or Sulfur1h 6m
- 15. Aldehydes and Ketones1h 1m
- 16. Carboxylic Acids and Their Derivatives1h 11m
- 17. Amines38m
- 18. Amino Acids and Proteins1h 51m
- 19. Enzymes1h 37m
- 20. Carbohydrates1h 46m
- Intro to Carbohydrates4m
- Classification of Carbohydrates4m
- Fischer Projections4m
- Enantiomers vs Diastereomers8m
- D vs L Enantiomers8m
- Cyclic Hemiacetals8m
- Intro to Haworth Projections4m
- Cyclic Structures of Monosaccharides11m
- Mutarotation4m
- Reduction of Monosaccharides10m
- Oxidation of Monosaccharides7m
- Glycosidic Linkage14m
- Disaccharides7m
- Polysaccharides7m
- 21. The Generation of Biochemical Energy2h 8m
- 22. Carbohydrate Metabolism2h 22m
- 23. Lipids2h 26m
- Intro to Lipids6m
- Fatty Acids25m
- Physical Properties of Fatty Acids6m
- Waxes4m
- Triacylglycerols12m
- Triacylglycerol Reactions: Hydrogenation8m
- Triacylglycerol Reactions: Hydrolysis13m
- Triacylglycerol Reactions: Oxidation7m
- Glycerophospholipids15m
- Sphingomyelins13m
- Steroids15m
- Cell Membranes7m
- Membrane Transport10m
- 24. Lipid Metabolism1h 45m
- 25. Protein and Amino Acid Metabolism1h 37m
- 26. Nucleic Acids and Protein Synthesis2h 54m
- Intro to Nucleic Acids4m
- Nitrogenous Bases16m
- Nucleoside and Nucleotide Formation9m
- Naming Nucleosides and Nucleotides13m
- Phosphodiester Bond Formation7m
- Primary Structure of Nucleic Acids11m
- Base Pairing10m
- DNA Double Helix6m
- Intro to DNA Replication20m
- Steps of DNA Replication11m
- Types of RNA10m
- Overview of Protein Synthesis4m
- Transcription: mRNA Synthesis9m
- Processing of pre-mRNA5m
- The Genetic Code6m
- Introduction to Translation7m
- Translation: Protein Synthesis18m
Henderson-Hasselbalch Equation - Online Tutor, Practice Problems & Exam Prep
The Henderson-Hasselbalch equation is essential for calculating the pH of buffer solutions, particularly those composed of a conjugate acid-base pair. When given the acid dissociation constant (K_{a}), the equation is pH = pK_{a} + log([conjugate base]/[weak acid]). Conversely, if provided with the base dissociation constant (K_{b}), use pH = pK_{b} + log([conjugate acid]/[weak base]). Buffers are most effective within a pH range of pK_{a} ± 1, ideally when the concentrations of the weak acid and conjugate base are equal.
Henderson-Hasselbalch Equation
Video transcript
Henderson-Hasselbalch Equation Example
Video transcript
Calculate the pH of a solution containing 2.0 molar of nitrous acid and 1.48 molar of lithium nitrate. Here we're told that the K_{a} of our weak acid is 4.6 × 10 - 4 . Now here because the K_{a} value is less than 1, we know that nitrous acid is a weak acid. Lithium nitrate looks similar to nitrous acid, except it has one less H^{+} ion. Because of this, this has to be the conjugate base. So, we have a weak acid, and we have a conjugate base. This is the pairing that helps to make a buffer. So we're going to use the Henderson-Hasselbalch equation to calculate the pH of this buffer. We're going to say pH equals now because they give us K_{a}, we can say pH equals pK_{a} plus log of conjugate base over weak acid. Here pK_{a}, remember, is just negative log of K_{a}. So, negative log of 4.6 × 10 - 4 , plus log of conjugate base amount, which is going to be 1.48 molar, divided by weak acid amount which is 2.0 molar. When we plug this in, we get 3.21 as the pH for this buffer solution.
The K_{b} of C_{6}H_{5}NH_{2} (aniline) is 3.9 × 10^{−10}. Determine pH of a buffer solution made up of 500 mL of 1.4 M C_{6}H_{5}NH_{2} and 230 mL of 2.3 M C_{6}H_{5}NH_{3}^{+}.
4.81
9.62
4.38
9.29
Determine the buffer component concentration ratio (CB/WA) for a buffer with a pH of 4.7. K_{a} of boric acid (H3BO3) is 5.4 × 10^{−10}.
4.568 : 1
2.706 × 10^{−5} : 1
1 : 4.568
1 : 2.706 × 10^{−5}
Calculate mass of NaN_{3} that needs be added to 1.8 L of 0.35 M HN_{3} in order to make a buffer with a pH of 6.5. K_{a} of hydrazoic acid is 1.9 × 10^{−5}.
1.4 g NaN_{3}
1.0 × 10^{−2} g NaN_{3}
2.5 × 10^{3} g NaN^{3}
3.55 g NaN^{3}
Calculating Buffer Range
Video transcript
Now, when it comes to calculating buffer range, first, it's important to remember that buffers are effective at a specific pH range. To figure that out, we say that pH=pKa±1. That's the range, the pH range, in which a buffer will act most effectively in resisting a sharp change in pH.
Now recall that a buffer is ideal when the concentration of weak acid is equal to the concentration of conjugate base, or you could say when the concentration of weak base is equal to the concentration of conjugate acid, same thing. This is because the pH of the buffer will be equal to the pKa of the weak acid, and this will resist a pH change the best.
Now here, if we had an example, we have pH=pKa+log(conjugatebaseweakacid). Remember, when it comes to the Henderson-Hasselbalch equation we can observe it in 2 different ways. If they're giving you Ka, you can use the top version where pH=pKa+log(conjugatebase/weakacid). The bottom one you use if they give you Kb. Here pH=pKb+log(conjugateacid/weakbase). Well, going back to this, we can see that both the conjugate base and weak acid amounts are equal to one another. So 0.40 divided by 0.40 is just equal to 1. And remember, if we're dealing with log of 1, which this is, you punch that into your calculator, log of 1 gives you 0. So the equation simplifies to pH=pKa+0. And if you drop off the 0, then pH=pKa. So when the amount of conjugate base and weak acid are equal to each other, or when the amount of conjugate acid is equal to weak base, we have an ideal buffer. And then the Henderson-Hasselbalch equations simplify down to pH=pKa or pH=pKb, depending on which one you're using.
Alright? So keep that in mind. The effectiveness of a buffer happens best within a pH range of pH=pKa±1, and it's most ideal when the concentrations of the species are equal to one another.
Henderson-Hasselbalch Equation Example
Video transcript
Here in this example it says, determine the buffering range of a solution containing lactic acid, which has a Ka1.4 times 10-4, and sodium lactate, its conjugate base. Now here, we're looking for a buffering range. Remember that when it comes to your buffer range, the pH range, so the range in which the buffer works most effectively, is pH=pKa±1. Remember that pKa=-logKa. So just take the negative log of this Ka value. When we do that, we have 3.85. So, that means our buffering range or pH range for the effectiveness of a buffer is equal to 3.85±1. That would mean our range is 3.85-1to3.85+1, which will translate to a range of 2.85pHto4.85pH. Okay. This would be our buffering range in which this particular buffer will be most effective.
Which of the following weak acid-conjugate base combinations would result in an ideal buffer solution with a pH of 9.4?
a) formic acid (HCHO_{2}) and sodium formate (K_{a} = 1.8 x 10^{-4})
b) benzoic acid (HC_{7}H_{5}O_{2}) and potassium benzoate (K_{a} = 6.5 x 10^{-5})
c) hydrocyanic acid (HCN) and lithium cyanide (K_{a} = 4.9 x 10^{-10})
d) iodic acid (HIO_{3}) and sodium iodate (K_{a} = 1.7 x 10^{-1})
formic acid (HCHO_{2}) and sodium formate (K_{a} = 1.8 x 10^{-4})
benzoic acid (HC_{7}H_{5}O_{2}) and potassium benzoate (K_{a} = 6.5 x 10^{-5})
hydrocyanic acid (HCN) and lithium cyanide (K_{a} = 4.9 x 10^{-10})
iodic acid (HIO_{3}) and sodium iodate (K_{a} = 1.7 x 10^{-4})
Do you want more practice?
Here’s what students ask on this topic:
What is the Henderson-Hasselbalch equation and how is it used?
The Henderson-Hasselbalch equation is used to calculate the pH of buffer solutions, particularly those composed of a conjugate acid-base pair. The equation is:
$\mathrm{pH}=\mathrm{pK}{a}_{}+log\left(\frac{\mathrm{[conjugate\; base]}}{\mathrm{[weak\; acid]}}\right)$
Alternatively, if given the base dissociation constant (K_{b}), the equation is:
$\mathrm{pH}=\mathrm{pK}{b}_{}+log\left(\frac{\mathrm{[conjugate\; acid]}}{\mathrm{[weak\; base]}}\right)$
This equation helps in determining the pH without using an ICE chart, making it a valuable tool in chemistry.
How do you calculate the pH of a buffer solution using the Henderson-Hasselbalch equation?
To calculate the pH of a buffer solution using the Henderson-Hasselbalch equation, follow these steps:
1. Identify whether you have the acid dissociation constant (K_{a}) or the base dissociation constant (K_{b}).
2. Use the appropriate equation:
If given K_{a}: $\mathrm{pH}=\mathrm{pK}{a}_{}+log\left(\frac{\mathrm{[conjugate\; base]}}{\mathrm{[weak\; acid]}}\right)$
If given K_{b}: $\mathrm{pH}=\mathrm{pK}{b}_{}+log\left(\frac{\mathrm{[conjugate\; acid]}}{\mathrm{[weak\; base]}}\right)$
3. Plug in the concentrations (or moles) of the conjugate base and weak acid (or conjugate acid and weak base).
4. Calculate the pH.
What is the effective pH range of a buffer according to the Henderson-Hasselbalch equation?
The effective pH range of a buffer according to the Henderson-Hasselbalch equation is pK_{a} ± 1. This means that the buffer will effectively resist changes in pH within one pH unit above and below the pK_{a} of the weak acid. For example, if the pK_{a} is 4.75, the buffer will be effective in the pH range of 3.75 to 5.75. This range ensures that the buffer can neutralize added acids or bases, maintaining a relatively stable pH.
Why is a buffer most effective when the concentrations of the weak acid and conjugate base are equal?
A buffer is most effective when the concentrations of the weak acid and conjugate base are equal because, at this point, the pH of the buffer is equal to the pK_{a} of the weak acid. This is derived from the Henderson-Hasselbalch equation:
$\mathrm{pH}=\mathrm{pK}{a}_{}+log\left(\frac{\mathrm{[conjugate\; base]}}{\mathrm{[weak\; acid]}}\right)$
When [conjugate base] = [weak acid], the log term becomes log(1), which is 0. Thus, pH = pK_{a}. At this point, the buffer has the maximum capacity to neutralize added acids or bases, making it most effective in resisting pH changes.
Can the Henderson-Hasselbalch equation be used with moles instead of molarity?
Yes, the Henderson-Hasselbalch equation can be used with moles instead of molarity. The equation:
$\mathrm{pH}=\mathrm{pK}{a}_{}+log\left(\frac{\mathrm{[conjugate\; base]}}{\mathrm{[weak\; acid]}}\right)$
or
$\mathrm{pH}=\mathrm{pK}{b}_{}+log\left(\frac{\mathrm{[conjugate\; acid]}}{\mathrm{[weak\; base]}}\right)$
can be applied using the concentrations in moles, as long as the volumes of the solutions are the same. This is because the ratio of moles will be the same as the ratio of molarities, simplifying the calculation process.