PH And PKa: Definition, Relationship & Equation | StudySmarter

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pH and pKa

pH and pKa

If you have ever tried lemon juice, then you and I can agree that lemon juice has a very acidic taste. Lemon juice is a type of weak acid, and to learn about the pH and pKa of weak acids, we need to dive into the world of Ka, ICE tables and even percent ionization!

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Bronsted-Lowry acids are proton (H+) _____.

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Bronsted-Lowry bases are proton (H+) _____ .

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_____ is a measurement of the [H+] ion concentration in a solution.

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Ka is known as the ________.

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True or false: to calculate pH and pKa of weak acids, we need to know Ka.

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The higher the Ka of an acid, the _____ the acid will be.

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True or false: pKa is referred to as the positive log of Ka.

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The higher the pKa , the ______ the acid.

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Acids have a _____ pH value.

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Bases have a ______ pH value.

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Substances with a low pKa value are considered _______ acids.

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Bronsted-Lowry acids are proton (H+) _____.

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Bronsted-Lowry bases are proton (H+) _____ .

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_____ is a measurement of the [H+] ion concentration in a solution.

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Ka is known as the ________.

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True or false: to calculate pH and pKa of weak acids, we need to know Ka.

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The higher the Ka of an acid, the _____ the acid will be.

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True or false: pKa is referred to as the positive log of Ka.

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The higher the pKa , the ______ the acid.

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Acids have a _____ pH value.

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Bases have a ______ pH value.

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Substances with a low pKa value are considered _______ acids.

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Last Updated: 14.02.2023
Published at: 23.05.2022
12 min reading time

Chemical Analysis
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Types of Mixtures
VSEPR Theory
Valence Electrons
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Vapor Pressure
Water in Chemical Reactions
Wave Mechanical Model
Weak Acid and Base Equilibria
Weak Acids and Bases
Writing Chemical Formulae
pH
pH Change
pH Curves and Titrations
pH Scale
pH and Solubility
pH and pKa
pH and pOH

The Earths Atmosphere

Contents

Chemical Analysis
Chemical Reactions
Chemistry Branches
Inorganic Chemistry
Ionic and Molecular Compounds
Kinetics
Making Measurements
Nuclear Chemistry
Organic Chemistry
Physical Chemistry

Absolute Entropy And Entropy Change
Acid Dissociation Constant
Acid-Base Indicators
Acid-Base Reactions and Buffers
Acids and Bases
Alkali Metals
Allotropes of Carbon
Amorphous Polymer
Amount of Substance
Application of Le Chatelier's Principle
Arrhenius Equation
Arrhenius Theory
Atom Economy
Atomic Structure
Autoionization of Water
Avogadro Constant
Avogadro's Number and the Mole
Beer-Lambert Law
Bond Enthalpy
Bonding
Born Haber Cycles
Born-Haber Cycles Calculations
Boyle's Law
Brønsted-Lowry Acids and Bases
Buffer Capacity
Buffer Solutions
Buffers
Buffers Preparation
Calculating Enthalpy Change
Calculating Equilibrium Constant
Calorimetry
Carbon Structures
Cell Potential
Cell Potential and Free Energy
Chalcogens
Chemical Calculations
Chemical Equations
Chemical Equilibrium
Chemical Thermodynamics
Closed Systems
Colligative Properties
Collision Theory
Common-Ion Effect
Composite Materials
Composition of Mixture
Constant Pressure Calorimetry
Constant Volume Calorimetry
Coordination Compounds
Coupling Reactions
Covalent Bond
Covalent Network Solid
Crystalline Polymer
De Broglie Wavelength
Determining Rate Constant
Deviation From Ideal Gas Law
Diagonal Relationship
Diamond
Dilution
Dipole Chemistry
Dipole Moment
Dissociation Constant
Distillation
Dynamic Equilibrium
Electric Fields Chemistry
Electrochemical Cell
Electrochemical Series
Electrochemistry
Electrode Potential
Electrolysis
Electrolytes
Electromagnetic Spectrum
Electron Affinity
Electron Configuration
Electron Shells
Electronegativity
Electronic Transitions
Elemental Analysis
Elemental Composition of Pure Substances
Empirical and Molecular Formula
Endothermic and Exothermic Processes
Energetics
Energy Diagrams
Enthalpy Changes
Enthalpy For Phase Changes
Enthalpy of Formation
Enthalpy of Reaction
Enthalpy of Solution and Hydration
Entropy
Entropy Change
Equilibrium Concentrations
Equilibrium Constant Kp
Equilibrium Constants
Examples of Covalent Bonding
Factors Affecting Reaction Rates
Finding Ka
Free Energy
Free Energy Of Dissolution
Free Energy and Equilibrium
Free Energy of Formation
Fullerenes
Fundamental Particles
Galvanic and Electrolytic Cells
Gas Constant
Gas Solubility
Gay Lussacs Law
Giant Covalent Structures
Graham's Law
Graphite
Ground State
Group 3A
Group 4A
Group 5A
Half Equations
Heating Curve for Water
Heisenberg Uncertainty Principle
Henderson-Hasselbalch Equation
Hess' Law
Hybrid Orbitals
Hydrogen Bonds
Ideal Gas Law
Ideal and Real Gases
Intermolecular Forces
Introduction to Acids and Bases
Ion And Atom Photoelectron Spectroscopy
Ion dipole Forces
Ionic Bonding
Ionic Product of Water
Ionic Solids
Ionisation Energy
Ions: Anions and Cations
Isotopes
Kinetic Molecular Theory
Lattice Structures
Law of Definite Proportions
Le Chatelier's Principle
Lewis Acid and Bases
London Dispersion Forces
Magnitude Of Equilibrium Constant
Mass Spectrometry
Mass Spectrometry of Elements
Maxwell-Boltzmann Distribution
Measuring EMF
Mechanisms of Chemical Bonding
Melting and Boiling Point
Metallic Bonding
Metallic Solids
Metals Non-Metals and Metalloids
Mixtures and Solutions
Molar Mass Calculations
Molarity
Molecular Orbital Theory
Molecular Solid
Molecular Structures of Acids and Bases
Moles and Molar Mass
Nanoparticles
Neutralisation Reaction
Oxidation Number
Partial Pressure
Particulate Model
Partition Coefficient
Percentage Yield
Periodic Table Organization
Phase Changes
Phase Diagram of Water
Photoelectric Effect
Photoelectron Spectroscopy
Physical Properties
Polarity
Polyatomic Ions
Polyprotic Acid Titration
Prediction of Element Properties Based on Periodic Trends
Pressure and Density
Properties Of Equilibrium Constant
Properties of Buffers
Properties of Solids
Properties of Water
Quantitative Electrolysis
Quantum Energy
Quantum Numbers
RICE Tables
Rate Equations
Rate of Reaction and Temperature
Reacting Masses
Reaction Quotient
Reaction Quotient And Le Chateliers Principle
Real Gas
Redox
Relative Atomic Mass
Representations of Equilibrium
Reversible Reaction
SI units chemistry
Saturated Unsaturated and Supersaturated
Shapes of Molecules
Shielding Effect
Simple Molecules
Solids Liquids and Gases
Solubility
Solubility Curve
Solubility Equilibria
Solubility Product
Solubility Product Calculations
Solutes Solvents and Solutions
Solution Representations
Solutions and Mixtures
Specific Heat
Spectroscopy
Standard Potential
States of Matter
Stoichiometry In Reactions
Strength of Intermolecular Forces
The Laws of Thermodynamics
The Molar Volume of a Gas
Thermodynamically Favored
Trends in Ionic Charge
Trends in Ionisation Energy
Types of Mixtures
VSEPR Theory
Valence Electrons
Van der Waals Forces
Vapor Pressure
Water in Chemical Reactions
Wave Mechanical Model
Weak Acid and Base Equilibria
Weak Acids and Bases
Writing Chemical Formulae
pH
pH Change
pH Curves and Titrations
pH Scale
pH and Solubility
pH and pKa
pH and pOH

The Earths Atmosphere

Contents

Fact Checked Content
Last Updated: 14.02.2023
12 min reading time

Content creation process designed by Lily Hulatt
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Jump to a key chapter

This article is about pH and PKa.
First, we will talk about definitions of pH and pKa
Then, we will look at calculations involving pH and pKa
Lastly, we will learn about percent ionization.

Relationship between pH and pKa

Before diving into pH and pKa, let's recall the definition of Bronsted-Lowry acids and bases, and also the meaning of conjugate acids and bases.

Bronsted-Lowry acids are proton (H+) donors, whereas Bronsted-Lowry bases are proton (H+) acceptors. Let's look at the reaction between ammonia and water.

pH and pKa Chemistry equation of the reaction between ammonia and water StudySmarter Fig. 1: The reaction between ammonia and water, Isadora Santos - StudySmarter Originals.

Conjugate acids are bases that gained a proton H+. On the other hand, Conjugate bases are acids that lost a proton H+. For example, when HCl is added to H2O, it dissociates to form H3O+ and Cl-. Water will gain a proton, and HCl will lose a proton.

pH and pKa Conjugate pairs in a reaction between HCl and water StudySmarter Fig. 2: Conjugate pairs in a reaction between HCl and Water, Isadora Santos - StudySmarter Originals.

Some chemistry books use H+ instead of H3O+ to refer to hydrogen ions. However, these two terms can be used interchangeably.

Now that those definitions are fresh in our minds, let's look at how pH and pKa are related. The first thing you need to know is that we can use pH and pKa to describe the relationship between weak acids in an aqueous solution.

pH is a measurement of the [H+] ion concentration in a solution.

You can learn more about pH by reading "pH Scale"!

The definition of pKa can sound confusing, especially if you are not familiar with the acid dissociation constant, also known as Ka. So, let's talk about that!

When it comes to weak acids and pH calculation, we need an extra piece of information, the acid dissociation constant (Ka). Kais used to determine the strength of an acid and its ability to stabilize its conjugate base. It measures how fully an acid is able to dissociate in water. In general, the higher the Ka of an acid, the stronger the acid will be.

Ka can also be called acid ionization constant, or acidity constant.

The general formula for a monobasic acid can be written as:HA (aq) ⇌ H+ (aq) A- (aq), where:

HA is the weak acid.
H+ is the hydrogen ions.
A- is the conjugate base.

We can use the following formula for Ka:

$$K_{a}=\frac{[products]}{[reactants]}=\frac{[H^{+}]\cdot [A^{-}]}{HA}=\frac{[H^{+}]^{2}}{HA}c$$

Keep in mind that solids (s) and pure liquids(l) like H2O (l) should not be included when calculating Ka because they have constant concentrations. Let's look at an example!

What would be the equilibrium expression for the following equation?

$$CH_{3}COOH^{(aq)}\rightleftharpoons H^{+}_{(aq)}+CH_{3}COO^{-}_{(aq)}$$

Using the formula for Ka, the equilibrium expression would be:

$$K_{a}=\frac{[products]}{[reactants]}=\frac{[H^{+}\cdot [CH_{3}COO^{-}]]}{[CH_{3}CCOH]}$$

For extra practice, try writing the equilibrium expression of: $$NH_{4\ (aq)}^{+}\rightleftharpoons H^{+}_{(aq)}+NH_{3\ (aq)}$$ !

Now that we know what Ka means, we can define pKa. Don't worry about pKa calculations right now - we will deal with it in a little bit!

pKa is referred to as the negative log of Ka.

pKa can be calculated using the equation: pKa = - log10 (Ka)

Buffers are solutions that contain either a weak acid + its conjugate base or a weak base + its conjugate acid, and have the ability to resist changes in pH.

When dealing with buffers, pH and pKa are related through the Henderson-Hasselbalch equation, which has the following formula:

$$pH=pK_{a}+log\frac{[A^{-}]}{[HA]}$$

Difference between pKa and pH

The main difference between pH and pKa is that pKa is used to show the strength of an acid. On the other hand, pH is a measure of the acidity or alkalinity of an aqueous solution. Let's make a table comparing pH and pKa.

pH	pKa
pH = -log10 [H+]	pKa= -log10 [Ka]
↑ pH = basic↓ pH = acidic	↑ pKa = weak acid↓ pKa = strong acid
depends on [H+] concentration	depends on [HA], [H+] and A-

pH and pKa Equation

When we have a strong acid, such as HCl, it will completely dissociate into H+ and Cl- ions. So, we can assume that the concentration of [H+] ions will be equal to the concentration of HCl.

$$HCl\rightarrow H^{+}+Cl^{-}$$

However, calculating the pH of weak acids is not as simple as with strong acids. To calculate the pH of weak acids, we need to use ICE charts to determine how many H+ ions we will have at equilibrium, and also use equilibrium expressions (Ka).

$$HA_{(aq)}\rightleftharpoons H^{+}_{(aq)}+A^{-}_{(aq)}$$

Weak acidsare those that partially ionize in solution.

ICE Charts

The easiest way to learn about ICE tables is by looking at an example. So, let's use an ICE chart to find the pH of a 0.1 M solution of acetic acid (The Ka value for acetic acid is 1.76 x 10-5).

Step 1: First, write down the generic equation for weak acids:

$$HA_{(aq)}\rightleftharpoons H^{+}_{(aq)}+A^{-}_{(aq)}$$

Step 2: Then, create an ICE chart. "I" stands for initial, "C" stands for change, and "E" stands for equilibrium. From the problem, we know that the initial concentration of acetic acid is equal to 0.1 M. So, we need to write that number on the ICE chart. Where? On the "I" row, under HA. Before dissociation, we don't have H+ or A- ions. So, write a value of 0 under those ions.

pH and pKa How to fill the I row on ICE charts StudySmarter Fig. 3: How to fill the "I" row on the ICE chart, Isadora Santos - StudySmarter Originals

Actually, pure water does have a little bit of H+ ions (1 x 10-7 M). But, we can ignore it for now since the amount of H+ ions that will be produced by the reaction will be way more significant.

Step 3: Now, we need to fill out the "C" (change) row. When dissociation occurs, change goes to the right. So, the change in HA will be -x, whereas the change in the ions will be +x.

pH and pKa How to fill the C row on ICE charts StudySmarter Fig. 4: Filling out the "C" row on the ICE Chart. Isadora Santos - StudySmarter Originals.

Step 4: The equilibrium row shows the concentration at equilibrium. "E" can be filled by using the values of "I" and "C". So, HA will have a concentration of 0.1 - x at equilibrium and the ions will have a concentration of x at equilibrium.

pH and pKa How to fill the E row on ICE charts StudySmarter Fig. 5: Filling the "E" row on the ICE chart, Isadora Santos - StudySmarter Originals.

Step 5: Now, we have to create an equilibrium expression using the values in the equilibrium row, which will then be used to solve for x.

x is equal to the [H+] ion concentration. So, by finding x, we will be able to know [H+] and then calculate pH.

$$K_{a}=\frac{[H^{+}]\cdot [A^{-}]}{HA}=\frac{x^{2}}{0.1-x}$$

Step 6: Plugin all the known values to the Ka expression and solve for x. Since x will usually be a small number, we can ignore the x that's being subtracted from 0.1.

$$K_{a}=\frac{x^{2}}{0.1-x}\cdot 1.76\cdot 10^{-5}=\frac{x^{2}}{0.1}x=\sqrt{(1.76\cdot 10^{-5})}\cdot 0.1=0.0013M=[H^{+}]$$

If after doing this step it turns out that x is bigger than 0.05 then you will have to do the whole quadratic equation. After some algebra in this case you would get x^2 +Ka*x - 0.1*Ka = 0. You can just use the normal quadratic formula now to solve for x.

Step 7: Use the [H+] value to calculate pH.

$$=-log_{10}[H^{+}]pH=-log_{10}[0.0013]pH=2.9$$

Normally, when finding the pH of a weak acid, you will be asked to construct an ICE table. However, for your AP exam (and also to reduce time), there is a little shortcut that you can take to find the [H+] ion concentration of a weak acid that is needed to find its pH.

So, to calculate the [H+] all you need to know is the value for the concentration of the weak acid and the Ka value, and plug those values into the following equation:

$$[H^{+}]=\sqrt{K_{a}\cdot initial\ concentration\ of\ HA}$$

Then, you can use the [H+] value to calculate pH. Note that this equation will not be given to you in the AP exam, so you should try to memorize it!

pH and pKa Formulas

To calculate pH and pKa, you should be familiar with the following formulas:

pH and pKa Formulas relating pH and pKa ICE charts StudySmarter Fig. 6: Formulas relating pH and pKa, Isadora Santos - StudySmarter Originals.

Let's look at a problem!

Find the pH of a solution containing 1.3·10-5 M [H+] ion concentration.

All we have to do is use the first formula above to calculate pH.

$$pH=-log_{10}[H^{+}]pH=-log_{10}[1.3\cdot 10^{-5}M]pH=4.9$$

That was pretty straightforward, right? But, let's amp up the difficulty a bit more!

Find the pH of 0.200 M of benzoic acid. The Ka value for C6H5COOH is 6.3 x 10-5 mol dm-3.

$$C_{6}H_{5}COOH\rightarrow H^{+}C_{6}H_{5}COO^{-}$$

Although we can make an ICE table to find the [H+] ion concentration of benzoic, let's use the shortcut formula:

$$[H^{+}]=\sqrt{K_{a}\cdot initial\ concentration\ of\ HA}$$

So, the value for the hydrogen ion concentration of H+ will be:

$$[H^{+}]=\sqrt{(6.3\cdot 10^{-5})\cdot (0.200)}=0.00355$$

Now, we can use the calculated [H+] value to find pH:

$$pH=-log_{10}[H^{+}]pH=-log_{10}[0.00355]pH=2.450$$

Now, what if you were asked to calculate pKa from Ka? All you need to do is use the pKa formula if you know the value for Ka.

For example, if you know that the Ka value for benzoic acid is 6.5x10-5 mol dm-3, you can use it to calculate pKa:

$$pK_{a}=-log_{10}(K_{a})pK_{a}=-log_{10}(6.3\cdot 10^{-5})pKa=4.2$$

Calculating pKa from pH and Concentration

We can use the pH and concentration of a weak acid to calculate the pKa of the solution. Let's look at an example!

Calculate the pKa of a 0.010 M solution of a weak acid containing a pH value of 5.3.

Step 1: Use the pH value to find [H+] ion concentration by rearranging the pH formula. By knowing the concentration of [H+], we can also apply it to the concentration of A- since the reaction of weak acids is at equilibrium.

$$H^{+}=10^{-pH}[H^{+}]=10^{-5.3}=5.0\cdot 10^{-6}$$

Step 2: Make an ICE chart. Remember that "X" is the same as the [H+] ion concentration.

pH and pKa ICE Chart Calculating pKa from pH and Concentration StudySmarter Fig. 8: ICE chart for a 0.010 M solution of a weak acid, Isadora Santos - StudySmarter Originals.

Step 3: Write the equilibrium expression using the values in the equilibrium row (E), and then solve for Ka.

Ka = [products][reactants]= [H+][A-]HA = X20.010 - XKa = (5.0×10-6)(5.0×10-6)0.010 - 5.0×10-6 = 2.5×10-9 mol dm-3

Step 4: Use the calculated Ka to find pKa.

$$K_{a}=\frac{[products]}{[reactants]}=\frac{[H^{+}]\cdot[A^{-}]}{HA}=\frac{x^{2}}{0.010-x}K_{a}=\frac{(5.0\cdot 10^{-6})(5.0\cdot 10^{-6})}{0.010-5.0\cdot 10^{-6}}=2.5\cdot 10^{-9}mol\cdot dm^{-3}$$

Finding Percent Ionization given pH and pKa

Another way of measuring the strength of acids is through percent ionization. The formula to calculate percent ionization is given as:

$$%\ ionization=\frac{concentration\ of\ H^{+}\ ions\ in\ equilibrium}{initial\ concentration\ of\ the\ weak\ acid}=\frac{x}{[HA]}\cdot 100$$

Remember: the stronger the acid, the greater the % ionization. Let's go ahead and apply this formula to an example!

Find the Ka value and the percent ionization of a 0.1 M solution of a weak acid containing a pH of 3.

1. Use the pH to find [H+].

$$[H^{+}]=10^{-pH}\cdot [H^{+}]=10^{-3}$$

2. Make an ICE table to find the concentrations of HA, H+, and A- in equilibrium.

pH and pKa ICE Chart Calculating percent ionization pH and pKa StudySmarter Fig. 9: ICE table of a 0.1 M solution of a weak acid, Isadora Santos - StudySmarter Originals.

3. Calculate percent ionization using the value for x ([H+]) and for HA from the ICE table.

$$%\ ionization= \frac{[H^{+}]}{[HA]}\cdot 100%\ ionization=\frac{[10^{-3}M]}{0.1M-10^{-3}M}\cdot 100=1%$$

Now, you should have what it takes to find the pH and pKa of weak acids!

pH and pKa - Key takeaways

pH is a measurement of the [H+] ion concentration in a solution.
pKa is referred to as the negative log of Ka.
To calculate the pH and pKa of weak acids, we need to use ICE charts to determine how many H+ ions we will have at equilibrium, and also Ka.
If we know the concentration of H+ ions in equilibrium, and the initial concentration of the weak acid, we can calculate percent ionization.

References:

Brown, T. L., Nelson, J. H., Stoltzfus, M., Kemp, K. C., Lufaso, M., & Brown, T. L. (2016). Chemistry: The central science. Harlow, Essex: Pearson Education Limited.

Malone, L. J., & Dolter, T. (2013). Basic concepts of of Chemistry. Hoboken, NJ: John Wiley.

Ryan, L., & Norris, R. (2015). Cambridge International as and A level chemistry. Cambridge: Cambridge University Press.

Salazar, E., Sulzer, C., Yap, S., Hana, N., Batul, K., Chen, A., . . . Pasho, M. (n.d.). Chad's general chemistry Master course. Retrieved May 4, 2022, from https://courses.chadsprep.com/courses/general-chemistry-1-and-2

Flashcards in pH and pKa

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Bronsted-Lowry acids are proton (H+) _____.

donors

Bronsted-Lowry bases are proton (H+) _____ .

acceptors

_____ is a measurement of the [H+] ion concentration in a solution.

Ka is known as the ________.

Acid dissociation constant

True or false: to calculate pH and pKa of weak acids, we need to know Ka.

True

The higher the Ka of an acid, the _____ the acid will be.

stronger

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Frequently Asked Questions about pH and pKa

How to calculate pH from pKa and concentration

To calculate the pH and pKa of weak acids, we need to use an equilibrium expression and an ICE chart.

Are pH and pKa the same?

No, they are not the same. pH is a measurement of the [H+] ion concentration in a solution. On ther other hand, pKa is used to show whether an acid is strong or weak.

How are pH and pKa related?

In buffers, pH and pKa are related through the Henderson-Hasselbalch equation.

What is pKa and pH?

pH is the negative log (base 10) of [H+]. pKa is the negative log (base) of Ka.

Save Article Test your knowledge with multiple choice flashcards

Bronsted-Lowry acids are proton (H+) _____.

A. donors B. acceptors

Bronsted-Lowry bases are proton (H+) _____ .

A. donors B. acceptors

_____ is a measurement of the [H+] ion concentration in a solution.

A. pKa B. Ka C. pH

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Tag » How To Find Pka From Ph

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Flashcards in pH and pKa

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