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8.9 Henderson-Hasselbalch Equation

2 min readjanuary 9, 2023

Dylan Black

Dylan Black

Jillian Holbrook

Jillian Holbrook

Dylan Black

Dylan Black

Jillian Holbrook

Jillian Holbrook

Introduction to the Henderson-Hasselbalch Equation

This section focuses intimately on one equation: the . The is useful because it helps us find the of a . Thinking back to 8.8, a is a solution that resists changes to its and is composed of a and its or a and its .

Let's take a look at the Henderson-Hasselbalch equation and get ourselves situated with it:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-QYCkvrO1Jd1Z.png?alt=media&token=f4e695d5-4ee9-4fa6-b8e9-df6cd074cd5a

Breaking Down The Equation

Breaking the equation down, is the -log([H+]) and is oftentimes the unknown when we apply the . is -log(Ka) is a to describe the of an acid (lower = more acidic). Finally, we get to the new bit, the log base 10 of the ratio of the concentrations of an ion, A-, and an acid HA. We can start by realizing that there is a unique relationship between [A-] and [HA]. They constitute a -base pair! HA is a , and A- is its !

This is where the ties into buffers because you will always have a concentration of and a concentration of . It also shows why the strongest is when these concentrations are equal because then log([A-]/[HA]) = 0.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-6aMV6h7tLPi2.png?alt=media&token=fab16aa2-ce8f-4ef7-8e48-b6366be71e64

Two Forms of the Henderson-Hasselbalch Equation. Image from MicrobeNotes

Example Problems

Example Problem #1: Directly Stated Buffer

Find the of a with 0.5M CH3COOH mixed with 0.25M CH3COONa (Ka = 1.8 * 10^-5).

For this, we can plug directly into the Henderson-Hasselbalch:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-deeFWkgO5HjT.png?alt=media&token=2c6d3ea5-33a4-4ee6-ad8f-87d388642899

Example Problem #2: Using the Hasselbalch During A Titration

Calculate the in the of 25.0 mL of 0.100M acetic acid with 0.100M NaOH after adding 15.0 mL of 0.100M NaOH.

Start by writing out our net ionic equation for this reaction:

CH3COOH + NaOH <=> CH3COONa + H2O

CH3COOH + OH- <=> CH3COO- + H2O

Next, we can use to find how many mmol of each compound we have after the reaction goes forward:

CH3COOH + OH- <=> CH3COO- + H2O

Start: 2.5mmol CH3COOH, 1.5mmol OH-, 0mmol CH3COO-, 0mmol H2O

End: 2mmol CH3COOH, 0mmol OH-, 1.5mmol CH3COO-, 1.5mmol H2O

Because we have concentrations of both an acid and its , we can find the of this by finding the of that using the Henderson-Hasselbalch. Note that because we are dividing by the same volume to find concentration, they cancel out and we can just divide the mmols:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-UEwkOZmgoCEX.png?alt=media&token=e9b6d663-6969-4482-aca1-2e5fe0f435ea

Key Terms to Review (14)

Acid Concentration

: Acid concentration refers to the amount of acid present in a solution, usually measured in moles per liter (Molarity).

Acidity

: Acidity refers to how much acid is present in a substance, or its ability to donate protons (H+ ions).

Buffer

: A buffer is a solution that resists changes in pH when small amounts of an acid or a base are added to it.

Conjugate Acid

: A conjugate acid is a species formed by the reception of a proton (H+) by a base—in other words, it is the base with a hydrogen ion added to it.

Conjugate Base

: The conjugate base is what remains of an acid after it has donated its proton during an acid-base reaction.

Henderson-Hasselbalch Equation

: The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a solution given the pKa (acid dissociation constant) and the ratio of the concentrations of the acid and its conjugate base.

Ion Concentration

: Ion concentration refers to the amount of ions in a given volume or mass of solution or substance.

Logarithmic Scale

: A logarithmic scale is a nonlinear scale used when there is a large range of quantities. In this scale, each increment on the axis increases by a factor of a fixed value, rather than by equal increments.

pH

: pH is a measure of the acidity or alkalinity of a solution. It's calculated as the negative logarithm (base 10) of the concentration of hydrogen ions in a solution.

pKa

: The pKa value is used to express the strength of acids. It's defined as -log10 Ka where Ka is the acid dissociation constant.

Stoichiometry

: Stoichiometry involves calculations based on balanced chemical equations regarding quantities involved in chemical reactions - both reactants and products.

Titration

: Titration is an analytical method used in chemistry to determine the concentration of an unknown solution using a known concentration of another solution.

Weak Acid

: A weak acid is one that does not completely dissociate into its ions in water, meaning only some of its molecules donate protons when placed in water.

Weak Base

: A weak base is one that does not completely dissociate into its ions in water.

8.9 Henderson-Hasselbalch Equation

2 min readjanuary 9, 2023

Dylan Black

Dylan Black

Jillian Holbrook

Jillian Holbrook

Dylan Black

Dylan Black

Jillian Holbrook

Jillian Holbrook

Introduction to the Henderson-Hasselbalch Equation

This section focuses intimately on one equation: the . The is useful because it helps us find the of a . Thinking back to 8.8, a is a solution that resists changes to its and is composed of a and its or a and its .

Let's take a look at the Henderson-Hasselbalch equation and get ourselves situated with it:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-QYCkvrO1Jd1Z.png?alt=media&token=f4e695d5-4ee9-4fa6-b8e9-df6cd074cd5a

Breaking Down The Equation

Breaking the equation down, is the -log([H+]) and is oftentimes the unknown when we apply the . is -log(Ka) is a to describe the of an acid (lower = more acidic). Finally, we get to the new bit, the log base 10 of the ratio of the concentrations of an ion, A-, and an acid HA. We can start by realizing that there is a unique relationship between [A-] and [HA]. They constitute a -base pair! HA is a , and A- is its !

This is where the ties into buffers because you will always have a concentration of and a concentration of . It also shows why the strongest is when these concentrations are equal because then log([A-]/[HA]) = 0.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-6aMV6h7tLPi2.png?alt=media&token=fab16aa2-ce8f-4ef7-8e48-b6366be71e64

Two Forms of the Henderson-Hasselbalch Equation. Image from MicrobeNotes

Example Problems

Example Problem #1: Directly Stated Buffer

Find the of a with 0.5M CH3COOH mixed with 0.25M CH3COONa (Ka = 1.8 * 10^-5).

For this, we can plug directly into the Henderson-Hasselbalch:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-deeFWkgO5HjT.png?alt=media&token=2c6d3ea5-33a4-4ee6-ad8f-87d388642899

Example Problem #2: Using the Hasselbalch During A Titration

Calculate the in the of 25.0 mL of 0.100M acetic acid with 0.100M NaOH after adding 15.0 mL of 0.100M NaOH.

Start by writing out our net ionic equation for this reaction:

CH3COOH + NaOH <=> CH3COONa + H2O

CH3COOH + OH- <=> CH3COO- + H2O

Next, we can use to find how many mmol of each compound we have after the reaction goes forward:

CH3COOH + OH- <=> CH3COO- + H2O

Start: 2.5mmol CH3COOH, 1.5mmol OH-, 0mmol CH3COO-, 0mmol H2O

End: 2mmol CH3COOH, 0mmol OH-, 1.5mmol CH3COO-, 1.5mmol H2O

Because we have concentrations of both an acid and its , we can find the of this by finding the of that using the Henderson-Hasselbalch. Note that because we are dividing by the same volume to find concentration, they cancel out and we can just divide the mmols:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-UEwkOZmgoCEX.png?alt=media&token=e9b6d663-6969-4482-aca1-2e5fe0f435ea

Key Terms to Review (14)

Acid Concentration

: Acid concentration refers to the amount of acid present in a solution, usually measured in moles per liter (Molarity).

Acidity

: Acidity refers to how much acid is present in a substance, or its ability to donate protons (H+ ions).

Buffer

: A buffer is a solution that resists changes in pH when small amounts of an acid or a base are added to it.

Conjugate Acid

: A conjugate acid is a species formed by the reception of a proton (H+) by a base—in other words, it is the base with a hydrogen ion added to it.

Conjugate Base

: The conjugate base is what remains of an acid after it has donated its proton during an acid-base reaction.

Henderson-Hasselbalch Equation

: The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a solution given the pKa (acid dissociation constant) and the ratio of the concentrations of the acid and its conjugate base.

Ion Concentration

: Ion concentration refers to the amount of ions in a given volume or mass of solution or substance.

Logarithmic Scale

: A logarithmic scale is a nonlinear scale used when there is a large range of quantities. In this scale, each increment on the axis increases by a factor of a fixed value, rather than by equal increments.

pH

: pH is a measure of the acidity or alkalinity of a solution. It's calculated as the negative logarithm (base 10) of the concentration of hydrogen ions in a solution.

pKa

: The pKa value is used to express the strength of acids. It's defined as -log10 Ka where Ka is the acid dissociation constant.

Stoichiometry

: Stoichiometry involves calculations based on balanced chemical equations regarding quantities involved in chemical reactions - both reactants and products.

Titration

: Titration is an analytical method used in chemistry to determine the concentration of an unknown solution using a known concentration of another solution.

Weak Acid

: A weak acid is one that does not completely dissociate into its ions in water, meaning only some of its molecules donate protons when placed in water.

Weak Base

: A weak base is one that does not completely dissociate into its ions in water.


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© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.