Name: weak acid equilibrium in water
Uploaded: 2020-09-24T15:06:51.000Z
Duration: 4 min 2 s
Channel: JoVE

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Weak Acid Solutions

A weak acid, like hydrocyanic acid, is a Br&#248;nsted acid as it donates a proton to the water molecule and produces the hydronium ion. A weak acid dissociates partially in water according to its acid dissociation constant, Ka, which is 4.9 &#215; 10&#8722;10 for hydrocyanic acid.
For hydrocyanic acid, the Ka is equal to the concentration of hydronium times the concentration of cyanide ions divided by the concentration of hydrocyanic acid.
The acid dissociation constant, Ka, can be used to determine the hydronium ion concentration in a weak acid solution and consequently, the pH of the solution.
The concentration of hydronium ions and the pH of a 0.15 molar solution of hydrocyanic acid can be calculated using its equilibrium expression and an ICE table.
The concentrations of hydrocyanic acid, hydronium, and cyanide initially and at equilibrium can be expressed in a table that shows the Initial, Change, and Equilibrium concentrations of each of the molecules.
To reach equilibrium, the initial concentration of the reactants decreases as the initial concentration of the products increases according to their molar ratios. This change in the concentration of the reactants and products is denoted by x.
Substituting equilibrium concentrations in the expression for the Ka yields x times x divided by 0.15 minus x. 
In many weak acids, x, the amount of dissociation, is likely to be very small compared to the initial concentration of 0.15 molar. 0.15 minus x can be assumed to be approximately 0.15.
When the equation is solved, x equals 8.6 &#215; 10&#8722;6 molar.
The approximation, 0.15 minus x equal to 0.15, is valid only if x is less than 5% of 0.15 molar. Here, x is 0.0057% of 0.15 molar and hence this approximation is valid.
Therefore, the concentration of hydronium is 8.6 &#215; 10&#8722;6 molar. To determine the pH, take the negative log of the hydronium ion concentration. Solving this shows the pH of the 0.15 M hydrocyanic acid solution is 5.07.
The pH of a solution can be used to determine the Ka of a weak acid.
For example, acetic acid dissociates partially into hydronium ions and acetate ions when dissolved in water. The Ka for acetic acid can be expressed as the hydronium ion concentration times the acetate ion concentration divided by the concentration of acetic acid.
If the pH of a 0.20 molar acetic acid solution is 2.72, its hydronium concentration can be calculated, which is 1.9 &#215; 10&#8722;3 molar.
The ICE table can be constructed from the initial and equilibrium concentrations of the acetic acid, hydronium ions, and acetate ions. 
Using significant figures, 0.20 minus 1.9 &#215; 10&#8722;3 is essentially equal to 0.20. By substituting the equilibrium values into the Ka expression, Ka equals 1.8 &#215; 10&#8722;5.

weak acid solutions

Few compounds act as strong acids. A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majority of dissolved molecules in their original form and generating a relatively small amount of hydronium ions. Weak acids are commonly encountered in nature, being the substances partly responsible for the tangy taste of citrus fruits, the stinging sensation of insect bites, and the unpleasant smells associated with body odor. A familiar example of a weak acid is acetic acid, the main ingredient in vinegar:
<img alt="Protein purification using chromatography; diagram of column setup and separation process." src="/files/ftp_upload/11400/11400_Equation_1.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
The use of a double-arrow in the equation above denotes the partial reaction aspect of this process. When dissolved in water under typical conditions, only about 1% of acetic acid molecules are present in the ionized form, CH3COO&#8722;.
Calculating Hydronium Ion Concentrations and the pH of a Weak Acid Solution
Formic acid, HCO2H, is one irritant that causes the body&#8217;s reaction to some ant bites and stings. What is the concentration of hydronium ion and the pH of a 0.534-M solution of formic acid?
<img alt="Nonlinear optics diagram showing second-harmonic generation; laser beam interaction, frequency doubling." src="/files/ftp_upload/11400/11400_Equation_2.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq2" />
The ICE table for this system is
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td style="color: black; border: 1px solid black; text-align: center;"> HCO2H (aq) </td>
			<td style="color: black; border: 1px solid black; text-align: center;">H3O+ (aq)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">HCO2&#8722; (aq)</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Initial Concentration (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.534</td>
			<td style="color: black; border: 1px solid black; text-align: center;">~0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Change (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">&#8722;x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+x</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Equilibrium Concentration (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.534 &#8722; x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">x</td>
		</tr>
	</tbody>
</table>
Substituting the equilibrium concentration terms into the Ka expression gives
<img alt="DNA transcription diagram with RNA polymerase, DNA&#8594;RNA. Gene expression process illustration." src="/files/ftp_upload/11400/11400_Equation_3.png" style="height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq3" />
The relatively large initial concentration and small equilibrium constant permits the simplifying assumption that x will be much lesser than 0.534, and so the equation becomes
<img alt="Static equilibrium, &#931;Fx=0 equation, mathematical concept diagram, forces vector breakdown." src="/files/ftp_upload/11400/11400_Equation_4.png" style="height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq4" />
Solving the equation for x yields
<img alt="DNA transcription process, DNA&#8594;RNA, molecular biology flowchart diagram." src="/files/ftp_upload/11400/11400_Equation_5.png" style="height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq5" />
To check the assumption that x is small compared to 0.534, its relative magnitude can be estimated:
<img alt="DNA replication diagram showing the semiconservative process and helicase enzyme action." src="/files/ftp_upload/11400/11400_Equation_6.png" style="height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq6" />
Because x is less than 5% of the initial concentration, the assumption is valid. As defined in the ICE table, x is equal to the equilibrium concentration of hydronium ion:
<img alt="Chemical equilibrium formula, aA+bB&#8652;cC+dD, balanced reaction diagram, illustrating stoichiometry." src="/files/ftp_upload/11400/11400_Equation_7.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq7" />
Finally, the pH is calculated to be
<img alt="Hydrolysis reaction of a lactose molecule, structural formula diagram, glucose galactose formation." src="/files/ftp_upload/11400/11400_Equation_8.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq8" />
Determination of Ka from pH
The pH of a 0.0516 M solution of nitrous acid, HNO2, is 2.34. What is its Ka?
<img alt="Electron shell diagram of carbon, showing 6 electrons, atomic model of element carbon, chemistry." src="/files/ftp_upload/11400/11400_Equation_9.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq9" />
The nitrous acid concentration provided is a formal concentration, one that does not account for any chemical equilibria that may be established in solution. Such concentrations are treated as &#8220;initial&#8221; values for equilibrium calculations using the ICE table approach. Notice the initial value of hydronium ion is listed as approximately zero because a small concentration of H3O+ is present (1 &#215; 10&#8722;7 M) due to the autoionization of water. In many cases, this concentration is much less than that generated by ionization of the acid (or base) in question and may be neglected.
The pH provided is a logarithmic measure of the hydronium ion concentration resulting from the acid ionization of the nitrous acid, and so it represents an &#8220;equilibrium&#8221; value for the ICE table:
<img alt="Gene editing CRISPR mechanism diagram with Cas9 targeting DNA sequences for genetic modification." src="/files/ftp_upload/11400/11400_Equation_10.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
The ICE table for this system is then
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td style="color: black; border: 1px solid black; text-align: center;"> HNO2 (aq) </td>
			<td style="color: black; border: 1px solid black; text-align: center;">H3O+ (aq)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">NO2&#8722; (aq)</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Initial Concentration (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.0516</td>
			<td style="color: black; border: 1px solid black; text-align: center;">~0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Change (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">&#8722;0.0046</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+0.0046</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+0.0046</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Equilibrium Concentration (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.0470</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.0046</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.0046</td>
		</tr>
	</tbody>
</table>
Finally, calculate the value of the equilibrium constant using the data in the table:
<img alt="Chemical equilibrium equations diagram; depicts lithium oxide formation, heat absorption, solid phase." src="/files/ftp_upload/11400/11400_Equation_11.png" style="height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq11" />
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/4-2-classifying-chemical-reactions">Openstax, Chemistry 2e, Section 4.2: Classifying Chemical Reactions</a> and <a href="https://openstax.org/books/chemistry-2e/pages/14-3-relative-strengths-of-acids-and-bases">Openstax, Chemistry 2e,14.3 Relative Strengths of Acids and Bases.</a>

Few compounds act as strong acids. A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majority of ...

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Acids and Bases

KEY TERMS AND CONCEPTS

weak acid equilibrium in water

Weak acid equilibrium in water explains why many acids only partially react when dissolved. Most weak acid molecules stay in their original form, and only a small amount of hydronium ions forms. Weak acids are common in nature. They help create the tangy taste of citrus fruits, the stinging sensation from insect bites, and the smells linked to body odor.

Acetic acid is a familiar weak acid. It is the main ingredient in vinegar. Its equation uses a double arrow to show that the reaction with water is only partial. Under typical conditions, only about 1% of acetic acid molecules are present as the ionized form, CH3COO−.

Weak acid problems often use an ICE table to find hydronium ion concentration and pH. Formic acid, HCO2H, is one example because it can cause the irritation from some ant bites and stings. For a 0.534-M formic acid solution, the ICE table starts with formic acid, H3O+, and HCO2−, then tracks the change as x forms and the equilibrium amounts are written in terms of x. The Ka expression is set up from those equilibrium concentrations.

Because the initial formic acid concentration is much larger than the amount that reacts, x is assumed to be much less than 0.534. That lets the expression simplify and makes the calculation easier. After solving for x, the result is checked against the 5% rule. Since x is less than 5% of the initial concentration, the assumption is valid. The value of x equals the equilibrium hydronium ion concentration, and the pH is then calculated from that concentration.

The same ICE table method can also be used in reverse to find Ka from pH. For nitrous acid, HNO2, the given pH is 2.34 for a 0.0516-M solution. That concentration is a formal concentration, which means it does not include any equilibrium changes. In these setups, the initial hydronium ion is shown as approximately zero because water already contains a very small amount, about 1 × 10−7 M, from autoionization. In many cases, that amount is much smaller than the acid-produced hydronium ion and can be ignored.

The pH gives the equilibrium hydronium ion concentration for the nitrous acid solution. The ICE table then shows HNO2, H3O+, and NO2− changing to equilibrium values. Using those values in the equilibrium expression gives the Ka of the acid. This approach shows how pH and Ka connect to the behavior of weak acids in water.

Weak Acid Equilibrium in Water

bronsted-lowry acids and bases

Proton Transfer in Acids and Bases

Acids and bases can be understood through proton transfer. Early scientists described acids by their sour taste, their effect on dyes, and their reaction with limestone, which releases carbon dioxide. Robert Boyle also noted that acid solutions can lose these properties after contact with alkali, or base, solutions. The modern view developed step by step. Humphry Davy showed that hydrogen is the essential part of acids. Joseph Louis Gay-Lussac then described acids as substances that neutralize...

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Water can act as both a Brønsted-Lowry acid and a Brønsted-Lowry base. When hydrogen fluoride dissolves in water, it donates protons to water. This is acid ionization. The products are hydronium ions and fluoride ions. Water can also accept protons from another substance. When pyridine dissolves in water, it accepts a proton from water molecules. This is base ionization. The products are hydroxide ions and pyridinium ions. These reactions show that water can play either role. A substance that...

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pH and pOH in Water

pH and pOH show how hydronium and hydroxide ions behave in water and other aqueous solutions. These ion concentrations are linked by the ion product of water, K w , so when one goes up, the other goes down. Because ion concentrations can differ by huge amounts, a logarithmic scale is used to describe them. pH is defined from the hydronium ion concentration, [H3O+], and pOH is the matching p-function for hydroxide ion concentration. These two values are also connected through the K w...

relative strengths of conjugate acid-base pairs

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How Ka and Kb Show Acid-Base Strength

Brønsted-Lowry acid-base chemistry is based on proton transfer. That idea helps show how the strength of an acid is linked to the strength of its conjugate base, and vice versa. Acid and base strength is measured with ionization constants, Ka and Kb, which tell how far an ionization reaction goes. For the conjugate pair HA and A−, the acid ionizes in water and the base reaction can be written for the partner species. When the two reactions are added, they give the autoionization of water. The...

strong acid and base solutions

Strong Acids, Strong Bases, and pH

Strong acids and strong bases change the pH of a solution by dissociating completely in water. A strong acid produces hydronium ions, which are H3O+ ions, and a strong base produces hydroxide ions, OH-. Because the dissociation is complete, the ion concentration can be found from the starting concentration and the molar ratio. For example, 0.20 M hydrobromic acid dissociates fully in water. It produces 0.20 M hydronium ions and 0.20 M bromide ions. A 0.015 M KOH solution also dissociates...

Weak acid equilibrium in water explains why many acids only partially react when dissolved. Most weak acid molecules stay in their original form, and only a small amount of hydronium ions forms. Weak acids are common in nature. They help create the tangy taste of citrus fruits, the stinging sensation from insect bites, and the smells linked to body odor. Acetic acid is a familiar weak acid. It is the main ingredient in vinegar. Its equation uses a double arrow to show that the reaction with...

weak base solutions

Weak Base pH and Kb Calculations

Weak base pH and Kb calculations show how partially reacting bases change water chemistry. Weak bases produce hydroxide ions when they dissolve by reacting with water molecules. Because the reaction only happens partly, these compounds are classified as weak bases. Weak bases are common in nature and in technology. Ammonia is one major example. Global production of ammonia is typically well over 100 metric tons each year. It is used as an agricultural fertilizer, a starting material for...

mixtures of acids

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The pH of acid mixtures depends on the acids present, their dissociation constants, and their starting concentrations. When a solution contains two different acids, the pH can be found by choosing the method that fits their relative strengths. This makes acid mixtures a useful case for applying acid-base rules in chemistry. In a mixture of a strong acid and a weak acid, the strong acid dissociates completely and supplies almost all of the hydronium ions in the solution. The weak acid...

ions as acids and bases

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determining the ph of salt solutions

Salt Hydrolysis and pH in Solutions

Salt hydrolysis and pH in solutions depend on the ions released when a salt dissolves. Some ions react with water, while others do not. The balance between the cation and anion helps show whether the solution becomes acidic, basic, or neutral. Salts with pH-neutral anions and cations that produce hydronium ions give acidic solutions with pH below 7. Ammonium nitrate is one example. In NH4NO3, NO3− does not react with water, but NH4+ forms hydronium ions, so the solution is acidic. Other salts...

acid/base strengths and dissociation constants

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Acid and Base Strength in Water

Acid and base strength in water depends on how much a substance ionizes after it dissolves. If ionization is nearly complete, the substance is called strong. If only a small amount ionizes, it is called weak. Weak acids and weak bases are much more common than strong ones. The most common strong acids are HClO4, HCl, HBr, HI, HNO3, and H2SO4. The most common strong bases are LiOH, NaOH, KOH, Ca(OH)2, Sr(OH)2, and Ba(OH)2. These strong acids and bases ionize essentially completely in water. <br...

polyprotic acids

Stepwise Ionization of Polyprotic Acids

Polyprotic acids lose hydrogen ions in steps. The number of ionizable protons in a molecule determines whether an acid is monoprotic, diprotic, or triprotic. This video also shows that polyprotic bases can accept more than one proton. Monoprotic acids have one ionizable hydrogen atom per molecule. Examples include HCl, HNO3, and HCN. Their reactions with water form hydronium ions and the matching anion. Acetic acid, CH3CO2H, is also monoprotic because only the hydrogen in the carboxyl group...

acid strength and molecular structure

How Bonding Affects Acid Strength

Acid strength depends on bonding, electronegativity, and oxidation number. These factors help explain why some hydrogen compounds act as strong acids, while others behave as weak acids or bases. For binary acids, which are hydrogen compounds with one other nonmetal, acidity increases as the H-A bond gets weaker down a group. That is why the order for group 17 is HF &lt; HCl &lt; HBr &lt; HI, and for group 16 it is H2O &lt; H2S &lt; H2Se &lt; H2Te. Across a period, acid strength increases as...

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Electron-Pair Reactions in Acid-Base Chemistry

Electron-pair reactions explain Lewis acid-base chemistry. In 1923, G. N. Lewis described acids and bases by how they accept or donate a pair of electrons. When that electron pair forms a coordinate covalent bond, one atom supplies both bonding electrons. This bond is also called a dative bond. A simple example is the reaction of water with a hydrogen ion to make a hydronium ion. Ammonia can also combine with a hydrogen ion to form an ammonium ion. In both cases, the reaction creates a Lewis...

key terms and concepts

Explore how weak acids partially ionize in water, use ICE tables to find hydronium ion concentration and pH, and calculate Ka from pH.

Weak Acid Equilibrium in Water | JoVE K12

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In some cases, there are seemingly more than one valid Lewis structures for molecules and polyatomic ions. The concept of formal charges can be used to ...

Exceptions to the Octet Rule

Many covalent molecules have central atoms that do not have eight electrons in their Lewis structures. These molecules fall into three categories:


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Bond Energies and Bond Lengths

Stable molecules exist because covalent bonds hold the atoms together. The strength of a covalent bond is measured by the energy required to break it, ...

Analyze and interpret data to explain the mechanisms and properties of the two main types of intramolecular (ionic and covalent) bonds.

PS.Chm.3.1

molecular-comparison-of-gases-liquids-and-solids

Molecular Comparison of Gases, Liquids, and Solids

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no ...

Intermolecular vs Intramolecular Forces

Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular ...

Intermolecular Forces

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions ...

comparing-intermolecular-forces-melting-point-boiling-point

Comparing Intermolecular Forces: Melting Point, Boiling Point, and Miscibility

Intermolecular forces are attractive forces that exist between molecules. They dictate several bulk properties, such as melting points, boiling points, ...

surface-tension-capillary-action-and-viscosity

Surface Tension, Capillary Action, and Viscosity

Surface Tension
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded ...

Construct an explanation to summarize the influences intermolecular forces have on the properties of chemical compounds.

PS.Chm.3.2

Analyze the structure of atoms and isotopes.

Weak Acid Equilibrium in Water

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