Name: weak base ph and kb calculations
Uploaded: 2020-09-24T15:06:51.000Z
Duration: 3 min 21 s
Channel: JoVE

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Weak Base Solutions

A weak base, like ammonia, is a Br&#248;nsted base that accepts a proton from water to produce the hydroxide ion. Weak bases react partially with water according to their base dissociation constant, Kb, which is 1.76 &#215; 10&#8722;5 for ammonia.
The Kb for ammonia can be expressed as the ammonium ion concentration times the hydroxide ion concentration divided by the concentration of ammonia at equilibrium.
Kb can be used to determine the hydroxide ion concentration in a weak base solution and consequently, the pOH and pH of the solution.
The hydroxide ion concentration and pH of 0.23 M of ammonia solution can be determined using its base dissociation constant and by preparing an ICE table containing the initial and equilibrium values of the ammonia, ammonium ions, and hydroxide ions.
Substituting equilibrium concentrations in the Kb expression, Kb equals x times x divided by 0.23 minus x. As weak bases show partial dissociation, 0.23 minus x can be considered to be approximately 0.23.
When the equation is solved, x equals 2 &#215; 10&#8722;3 M.
The approximation 0.23 minus x is equal to 0.23 is valid here as the hydroxide ion concentration is only 0.86% of 0.23 molar.
To calculate the pH of this solution, first determine the pOH by taking the negative log of the hydroxide ion concentration, which equals 2.70. The pH can be determined using the formula: pH plus pOH is equal to 14 and calculated to be 11.30.
The Kb for a weak base solution can be calculated if the pH of the weak base solution is known.
Methylamine is a weak base that partially dissociates in water into methylammonium ions and hydroxide ions.
The Kb for methylamine can be expressed as the methylammonium ion concentration times the hydroxide ion concentration divided by the concentration of methylamine at equilibrium.
To calculate the Kb of a 0.040 M methylamine solution with pH 11.6, first the pOH needs to be calculated followed by its hydroxide ion concentration. As the pH is 11.60, the pOH is 2.40, and its hydroxide ion concentration is 4.0 &#215; 10&#8722;3. 
The ICE table can be constructed from the initial and the equilibrium concentrations of methylamine, methylammonium, and hydroxide.
Substituting equilibrium concentrations in the expression for the Kb yields value for Kb, which is 4.4 &#215; 10&#8722;4.

weak base solutions

Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other compounds, and an active ingredient in household cleaners. When dissolved in water, ammonia reacts partially to yield hydroxide ions, as shown here:
<img alt="Mass spectrometry process; diagram illustrating fragmentation pathways with labeled ions for analysis." src="/files/ftp_upload/11401/11401_Equation_1.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
This is, by definition, an acid-base reaction, in this case involving the transfer of H+ ions from water molecules to ammonia molecules. Under typical conditions, only about 1% of the dissolved ammonia is present as NH4+ ions.
Calculating Hydroxide Ion Concentrations and pOH in a Weak Base Solution
Find the concentration of hydroxide ion, the pOH, and the pH of a 0.25 M solution of trimethylamine, a weak base:
<img alt="Levers in static equilibrium diagram; &#931;F=0, &#931;M=0, force balance analysis; mechanical advantage." src="/files/ftp_upload/11401/11401_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;">(CH3)3N (aq)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">(CH3)3NH+ (aq) </td>
			<td style="color: black; border: 1px solid black; text-align: center;">OH&#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;">0.25</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;">0.25 &#8722; x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0 + x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">~0 + x</td>
		</tr>
	</tbody>
</table>
Substituting the equilibrium concentration terms into the Kb expression gives
<img alt="Chromatography system diagram for compound separation; gas flow path and detector labels." src="/files/ftp_upload/11401/11401_Equation_3.png" style="height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq3" />
Assuming x &#60;&#60; 0.25 and solving for x yields
<img alt="Static equilibrium equations, &#931;Fx=0, &#931;Fy=0, demonstrating force balance in a diagram." src="/files/ftp_upload/11401/11401_Equation_4.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq4" />
This value is less than 5% of the initial concentration (0.25), so the assumption is justified.
As defined in the ICE table, x is equal to the equilibrium concentration of hydroxide ion:
<img alt="Static equilibrium diagram; &#931;Fx=0; &#931;Fy=0; &#931;MA=0; force balance and moments analysis; educational use." src="/files/ftp_upload/11401/11401_Equation_5.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq5" />
The pOH is calculated to be
<img alt=':&#60;br&#62;
"Damped harmonic oscillator equation, F=ma-mc, motion dynamics diagram, physics concept"' src="/files/ftp_upload/11401/11401_Equation_6.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq6" />
Using the relation;
<img alt="Chromatography diagram showing column elution process with stationary and mobile phases labeled." src="/files/ftp_upload/11401/11401_Equation_7.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq7" />
permits the computation of pH:
<img alt="Quantum harmonic oscillator wave functions diagram; &#968;0 to &#968;3; energy states; physics education." src="/files/ftp_upload/11401/11401_Equation_8.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq8" />
Determination of Kb from pH
If the pH of 0.28 M solution of ethylamine (C2H5NH2) is 12.10, what is its Kb?
<img alt="Static equilibrium diagram with forces labeled &#931;Fx=0, diagram for mechanical analysis and physics study." src="/files/ftp_upload/11401/11401_Equation_9.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq9" />
To calculate the Kb of ethylamine, first the pOH and the hydroxide ion concentration need to be determined. As the pH is 12.10, the pOH can be calculated as follows:
<img alt="Chemical reaction mechanism diagram showing electrophilic aromatic substitution of benzene." src="/files/ftp_upload/11401/11401_Equation_10.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq10" />
As the pOH is 1.90, the hydroxide ion concentration of the solution can be calculated using the formula
<img alt="Static equilibrium, &#931;Fx=0 equation, vector forces diagram, mechanical physics, balance analysis." src="/files/ftp_upload/11401/11401_Equation_11.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq11" />
The ICE table can be constructed for this system as follows
<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;">C2H5NH2 (aq)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">C2H5NH3+ (aq)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">OH&#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;">0.28</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;0.0126</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+0.0126</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+0.0126</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;">0.28 &#8722; 0.0126</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.0126</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0.0126</td>
		</tr>
	</tbody>
</table>
As the 0.0126 M is 4.5% of 0.28 M, 0.28 &#8722; 0.0126 can be considered as almost equal to 0.28 M by the 5% rule.
After substituting the above values in the expression for the Kb of ethylamine,
<img alt="Mass-spring-damper model equations, includes F=ma, mx&#34; + cx' + kx=0; mechanics diagram." src="/files/ftp_upload/11401/11401_Equation_12.png" style="height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq12" />
This text is adapted from Openstax, Chemistry 2e <a href="https://openstax.org/books/chemistry-2e/pages/4-2-classifying-chemical-reactions">Section 4.2: </a><a href="https://openstax.org/books/chemistry-2e/pages/4-2-classifying-chemical-reactions">Classifying Chemical Reactions</a> and <a href="https://openstax.org/books/chemistry-2e/pages/14-3-relative-strengths-of-acids-and-bases">14.3 Relative Strengths of Acids and Bases.</a>

Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and ...

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Acids and Bases

KEY TERMS AND CONCEPTS

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 chemical synthesis, and an ingredient in household cleaners.

When ammonia dissolves in water, it reacts only partially to form hydroxide ions. This is an acid-base reaction because H+ ions move from water molecules to ammonia molecules. Under typical conditions, only about 1% of the dissolved ammonia is present as NH4+ ions.

The video also shows how to calculate hydroxide ion concentration, pOH, and pH for a weak base solution. For a 0.25 M trimethylamine solution, an ICE table is used to track initial, change, and equilibrium concentrations. The Kb expression is then written with the equilibrium terms, and the x &lt;&lt; 0.25 assumption is checked with the 5% rule before solving for x as the hydroxide ion concentration. From there, pOH is found and pH is calculated.

A second example shows how to determine Kb from pH. For a 0.28 M ethylamine solution with a pH of 12.10, the pOH is first found, then the hydroxide ion concentration is calculated. An ICE table is built for ethylamine, ethylammonium ion, and hydroxide ion. After applying the 5% rule, the values are substituted into the Kb expression to find the base dissociation constant.

Weak Base pH and Kb Calculations

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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...

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key terms and concepts

Learn how weak bases form hydroxide ions, then use ICE tables to find pOH, pH, and Kb for trimethylamine and ethylamine examples.

Weak Base pH and Kb Calculations | JoVE K12

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Structure and Nomenclature of Ethers

Structure and Bonding
Ethers are organic compounds with an ether functional group which is characterized by an oxygen atom connected to two &#8212; ...

IUPAC Nomenclature of Aldehydes

Aldehydes are named based on the systematic nomenclature rules set by the IUPAC. For acyclic aldehydes, the longest carbon chain containing the aldehydic ...

IUPAC Nomenclature of Ketones

Like aldehydes, ketones are named using IUPAC rules; in this case, by replacing &#8220;e&#8221; in the name of the longest hydrocarbon chain with ...

IUPAC Nomenclature of Carboxylic Acids

IUPAC names of carboxylic acids are systematically derived following a few rules discussed below.
For acyclic saturated monocarboxylic acids, the longest ...

Use models to apply International Union of Pure and Applied Chemistry (IUPAC) conventions to name and write formulas for simple compounds.

PS.PSc.2.2

Understand types, properties, and structure of matter.

Weak Base pH and Kb Calculations

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