Name: ph at key points in a weak acid titration
Uploaded: 2020-09-24T15:06:51.000Z
Duration: 3 min 55 s
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Titration Calculations: Weak Acid - Strong Base

The pH at different stages of a weak acid or base titration is calculated using different methods during various points of the titration.
If a weak acid or base is the main determinant of the pH, the Ka or Kb and an ICE table, or the Henderson-Hasselbalch equation are used. If strong acid or base is present after the neutralization reaction, the concentration of the remaining hydronium or hydroxide ions is used to calculate the pH.
The initial pH of 50 mL of a 0.10 M acetic acid solution is 2.87 and is calculated using the Ka and an ICE table, as acetic acid is the main contributor.
If this solution containing 0.0050 moles of acetate is titrated with 0.10 M sodium hydroxide, the hydroxide ions react with acetic acid to produce acetate, resulting in a buffer.
Therefore, when 10 mL of the sodium hydroxide containing 0.0010 moles of hydroxide ions is added, 0.0010 moles of acetate are formed, and 0.0040 moles of acetic acid remain. The pH of the buffer can be calculated by substituting these values into the Henderson-Hasselbalch equation and equals 4.14.
When 25 mL of the sodium hydroxide is added, half of the initial moles of acetic acid are converted into acetate. At this point, the pH equals the pKa, as the amount of acetic acid and acetate ion are equal.
The further addition of sodium hydroxide up to 50 mL converts all of the acetic acid molecules into acetate, and the equivalence point is reached. As acetate ions are basic, the equivalence point lies in the basic region.
The concentration of the acetate ion is calculated by dividing the number of moles by the total volume of the solution. 
The pH is determined using the Kb for acetate ions and an ICE table, as the acetate ion is the main contributor to the pH at the equivalence point.
The Kb for acetate is calculated using the formula, Kw = Ka &#215; Kb, and equals 5.6 &#215; 10&#8722;10.
Substituting equilibrium concentrations in the expression for Kb gives the hydroxide concentration, 5.3 &#215; 10&#8722;6 M. The pOH and pH of the solution are 5.28 and 8.72, respectively. 
Further addition of sodium hydroxide in the solution results in a mixture of acetate ions and sodium hydroxide. However, the final concentration of sodium hydroxide determines the pH of the solution, as it is a stronger base than acetate.
Therefore, if 70 mL of sodium hydroxide is added into the solution, the final concentration of the hydroxide ions can be calculated by subtracting the total moles of acetic acid, 0.0050 moles, from the total moles of hydroxide ions added, 0.0070 moles, and dividing it by the total volume of the solution, 120 mL or 0.12 L. 
As the hydroxide ion concentration is 0.017 M, the pOH and pH of the solution are calculated to be 1.78 and 12.22, respectively.

titration calculations: weak acid - strong base

Calculating pH for Titration Solutions: Weak Acid/Strong Base
For the titration of 25.00 mL of 0.100 M CH3CO2H with 0.100 M NaOH, the reaction can be represented as:
<img alt="Chromatography diagram with solvent flow direction showing components' separation process." src="/files/ftp_upload/11414/11414_Equation_1.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Quantum harmonic oscillator energy level diagram with wave function symbols, illustrating quantization." />
The pH of the titration solution after the addition of the different volumes of NaOH titrant can be calculated as follows:
(a) The initial pH is computed for the acetic acid solution in the usual ICE approach:
<img alt="Static equilibrium; &#931;Fx=0, &#931;Fy=0 equations; vector diagram; physics principles; balance analysis." src="/files/ftp_upload/11414/11414_Equation_2.png" style="text-align: center; height: 155px;" data-altupdatedat="1754904545000" data-alt="Mohr's circle diagram for stress analysis, illustrating principal stresses and shear plane orientation." />
(b) The acid and titrant are both monoprotic and the sample and titrant solutions are equally concentrated; thus, this volume of titrant represents the equivalence point. Unlike the strong-acid example, the reaction mixture in this case contains a weak conjugate base (acetate ion). The solution pH is computed considering the base ionization of acetate, which is present at a concentration of
<img alt="chemical reaction mechanism diagram showing transformation of reactants to products via intermediates" src="/files/ftp_upload/11414/11414_Equation_3.png" style="text-align: center; height: 72px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium, &#931;Fx=0, force vector diagram, illustrating balance and tension in physics." />
Base ionization of acetate is represented by the equation
<img alt="Static equilibrium; equations, &#931;Fx=0, &#931;Fy=0; free-body diagram; force vector analysis." src="/files/ftp_upload/11414/11414_Equation_4.png" style="text-align: center; height: 115px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram; sum of forces &#931;Fx=0 formula; mechanical system with forces and moments." />
Assuming x &#60;&#60; 0.0500, the pH may be calculated via the usual ICE approach:
<img alt="Ligand exchange process formulas; chemical reaction diagram." src="/files/ftp_upload/11414/11414_Equation_5.png" style="text-align: center; height: 150px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram with &#931;Fx=0 and MA=0 equations; truss with nodes and force vectors." />
Note that the pH at the equivalence point of this titration is significantly greater than 7, as expected when titrating a weak acid with a strong base.
(c) Titrant volume = 12.50 mL. This volume represents one-half of the stoichiometric amount of titrant, and so one-half of the acetic acid has been neutralized to yield an equivalent amount of acetate ion. The concentrations of these conjugate acid-base partners, therefore, are equal. A convenient approach to computing the pH is use of the Henderson-Hasselbalch equation:
<img alt="Peptide bond formation diagram showing amino acids linked by covalent bonds, illustrating protein synthesis." src="/files/ftp_upload/11414/11414_Equation_6.png" style="text-align: center; height: 115px;" data-altupdatedat="1754904545000" data-alt="DNA replication process diagram; visualization of DNA synthesis method; educational genetics diagram." />
(pH = pKa at the half-equivalence point in a titration of a weak acid)
(d) Titrant volume = 37.50 mL. This volume represents a stoichiometric excess of titrant, and a reaction solution containing both the titration product, acetate ion, and the excess strong titrant. In such solutions, the solution pH is determined primarily by the amount of excess strong base:
<img alt="NMR spectroscopy graph; chemical shifts vs. intensity; aromatic compound analysis results." src="/files/ftp_upload/11414/11414_Equation_7.png" style="text-align: center; height: 155px;" data-altupdatedat="1754904545000" data-alt="Chromatography equipment diagram for separating solution mixtures, with labeled components." />
This text is adapted from<a href="https://openstax.org/books/chemistry-2e/pages/14-7-acid-base-titrations"> Openstax, Chemistry 2e, Section 14.7: Acid-base Titrations.</a>

Calculating pH for Titration Solutions: Weak Acid/Strong Base
For the titration of 25.00 mL of 0.100 M CH3CO2H with 0.100 M NaOH, the reaction can be ...

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ph at key points in a weak acid titration

pH at key points in a weak acid titration can be calculated for an acetic acid solution as sodium hydroxide is added. The example uses 25.00 mL of 0.100 M CH3CO2H titrated with 0.100 M NaOH. The reaction is shown as the weak acid reacts with the strong base.

The initial pH is found from the acetic acid solution using the usual ICE approach. ICE means initial, change, and equilibrium, and it is a common way to set up equilibrium problems. The solution pH is calculated before any titrant is added.

When 25.00 mL of NaOH has been added, the titration reaches the equivalence point. The acid and titrant are both monoprotic, and the sample and titrant have the same concentration. At this point, the mixture contains acetate ion, which is the weak conjugate base of acetic acid.

Because acetate ion is present, the pH at the equivalence point is found from its base ionization. The acetate concentration is used in an ICE setup, and x is assumed to be much less than 0.0500. The pH at this point is significantly greater than 7, which is expected for a weak acid titrated with a strong base.

At 12.50 mL of NaOH, the titration is at the half-equivalence point. This is one-half of the stoichiometric amount of titrant, so one-half of the acetic acid has been neutralized. Equal amounts of acetic acid and acetate are present, and the Henderson-Hasselbalch equation is a convenient way to find the pH. At the half-equivalence point, pH equals pKa.

At 37.50 mL of NaOH, there is a stoichiometric excess of titrant. The reaction mixture contains acetate ion from the titration product and extra strong base. In this case, the pH is determined mainly by the amount of excess base.

pH at Key Points in a Weak Acid Titration

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common ion effect

Common Ion Effect on Solubility

The common ion effect reduces the solubility of an ionic compound in a solution that already contains one of its ions. In aqueous solutions, this means less of the solid dissolves than it would in pure water. The effect follows the law of mass action and can be explained with Le Châtelier’s principle. Silver iodide shows this equilibrium clearly. When silver(I) ions or iodide ions are added, the dissolution equilibrium shifts left. More AgI precipitates, and the concentrations of dissolved Ag+...

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Buffer Solutions and pH Stability

Buffer solutions are mixtures that help keep pH steady. A buffer contains an appreciable amount of a weak conjugate acid-base pair. It resists a change in pH when small amounts of a strong acid or a strong base are added. One common buffer uses a weak acid and its salt. Acetic acid and sodium acetate form this type of system, written as CH3COOH(aq) + CH3COONa(aq). Another buffer uses a weak base and its salt. A solution of ammonia and ammonium chloride, NH3(aq) + NH4Cl(aq), is an example. The...

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Buffer pH After Acid or Base Addition

A buffer solution can resist sudden pH changes when a strong acid or strong base is added. It does not stop the pH from changing completely. The shift is usually small, as long as the addition stays within the buffer’s capacity. To find the new pH, first determine how the added acid or base changes the amounts of the buffer components. A buffer contains a weak acid and its conjugate base, or the reverse pair. These amounts are found with stoichiometric calculations, which track how much of...

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Buffer Capacity and pH Stability

Buffer solutions help keep pH fairly constant, but they do not work forever. Their resistance to pH change depends on having enough of a weak acid and its conjugate base, or a weak base and its conjugate acid, in the mixture. When too much strong acid or strong base is added, one part of the buffer pair is used up and the buffer action becomes weaker. Buffer capacity describes how much acid or base can be added to a fixed volume of buffer before the pH changes noticeably, usually by about one...

titration calculations: strong acid - strong base

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pH at Key Points in Acid-Base Titration

pH at key points in a strong acid and strong base titration can be calculated from the amounts of acid and base present. The example uses 25.00 mL of 0.100 M HCl, a strong acid, and 0.100 M NaOH, a strong base. The pH changes as base is added, and each stage follows a different calculation. At 0 mL of titrant, the pH comes from the ionization of HCl. Because HCl is a strong acid, its ionization is complete. The hydronium ion molarity is 0.100 M, and the pH is found from that value. At 12.50...

pH at key points in a weak acid titration can be calculated for an acetic acid solution as sodium hydroxide is added. The example uses 25.00 mL of 0.100 M CH3CO2H titrated with 0.100 M NaOH. The reaction is shown as the weak acid reacts with the strong base. The initial pH is found from the acetic acid solution using the usual ICE approach. ICE means initial, change, and equilibrium, and it is a common way to set up equilibrium problems. The solution pH is calculated before any titrant is...

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Polyprotic Acid Equivalence Points

Polyprotic acids have more than one ionizable hydrogen, so they lose protons in steps during titration. When the acid dissociation constants for those protons are far enough apart, the titration curve shows a separate equivalence point for each hydrogen that can ionize. Diprotic acids have two ionizable hydrogens and produce two equivalence points. Triprotic acids have three ionizable hydrogens and produce three equivalence points. Carbonic acid, H2CO3, is a weak diprotic acid. Carbonic acid...

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Common Ion Effects on Solubility

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Solubility Limits and Selective Precipitation

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Cation Identification by Precipitation Tests

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Buffer pH with the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation helps relate buffer pH to the weak acid in the solution. It comes from the ionization-constant expression for a weak acid. By rearranging that expression to solve for hydronium ion concentration, [H3O+], and then taking the negative logarithm of both sides, the equation can be written in terms of pH. In this form, pKa is defined as the negative logarithm of the weak acid ionization constant, or pKa = −log Ka. The equation shows the connection between pH, pKa,...

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Tracking pH During Acid-Base Titration

Acid-base titration uses pH changes to track how a solution responds as titrant is added. A titration curve is a graph of a solution property versus the amount of added titrant. In acid-base titrations, pH is the main property to follow because it changes in a predictable way with the solution makeup and helps show the endpoint. This pattern can be seen with a strong acid and strong base, a strong acid and weak base, or a strong base and weak acid. For example, 25.00 mL of 0.100 M HCl titrated...

key terms and concepts

Follow how pH changes during a weak acid titration with strong base, including the initial solution, half-equivalence point, equivalence point, and excess base.

pH at Key Points in a Weak Acid Titration | JoVE K12

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Chemical reactions
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Content elaboration: In the Physical Science course, coefficients were used to balance simple equations. Other representations, including Lewis structures and three-dimensional models, were also used and manipulated to demonstrate the conservation of matter in chemical reactions. In this course, more complex reactions will be studied, classified and represented with balanced chemical equations and three-dimensional models. Classifying reactions into types can be a helpful organizational tool for recognizing patterns of what may happen when two substances are mixed. Teachers should be aware that the common reaction classifications that are often used in high school chemistry courses may lead to misconceptions because they are not based on the actual chemistry, but on surface features that can be similar from one system to another (e.g., exchanging partners), even though the underlying chemistry is not the same. However, these classifications may be useful in making predictions about what happens when two substances are mixed. Some general types of chemical reactions are oxidation/reduction, synthesis, decomposition, single replacement, double replacement (including precipitation reactions and some acid-base neutralizations) and combustion reactions. Some reactions can fit into more than one category. For example, a single replacement reaction can also be classified as an oxidation/reduction reaction. Identification of reactions involving oxidation and reduction as well as indicating what substance is being oxidized and what is being reduced are appropriate in this course. However, balancing complex oxidation/reduction reactions is reserved for more advanced study. Organic molecules release energy when undergoing combustion reactions and are used to meet the energy needs of society (e.g., oil, gasoline, natural gas) and to provide the energy needs of biological organisms (e.g., cellular respiration). When a reaction between two ionic compounds in aqueous solution results in the formation of a precipitate or molecular compound, the reaction often occurs because the new ionic or covalent bonds are stronger than the original ion-dipole interactions of the ions in solution. Laboratory experiences (3-D or virtual) with different types of chemical reactions should be provided. Reactions occur when reacting particles collide in an appropriate orientation and with sufficient energy. The rate of a chemical reaction is the change in the amount of the reactants or products in a specific period of time. Increasing the probability or effectiveness of the collisions between the particles increases the rate of the reaction. Therefore, changing the concentration of the reactants, changing the temperature or the pressure of gaseous reactants, or using a catalyst, can change the reaction rate. Likewise, the collision theory can be applied to dissolving solids in a liquid solvent and can be used to explain why reactions are more likely to occur between reactants in the aqueous or gaseous state than between solids. The rate at which a substance dissolves should not be confused with the amount of solute that can dissolve in a given amount of solvent (solubility). Mathematical treatment of reaction rates is reserved for more advanced study. Computer simulations can help visualize reactions from the perspective of the kinetic-molecular theory. In middle school, the differences between potential and kinetic energy and the particle nature of thermal energy were introduced. For chemical systems, potential energy is in the form of chemical energy and kinetic energy is in the form of thermal energy. The total amount of chemical energy and/or thermal energy in a system is impossible to measure. However, the energy change of a system can be calculated from measurements (mass and change in temperature) from calorimetry experiments in the laboratory. Conservation of energy is an important component of calorimetry equations. Thermal energy is the energy of a system due to the movement of its particles. The thermal energy of an object depends upon the temperature and chemical composition. Some materials require little energy to change their temperature and other materials require a great deal to change their temperature by the same amount. Specific heat is a measure of how much energy is needed to change the temperature of a specific mass of material a specific amount. Specific heat values can be used to calculate the thermal energy change, the temperature (initial, final or change in) or mass of a material in calorimetry. Water has a particularly high specific heat capacity, which is important in regulating Earth's temperature. As studied in middle school, chemical energy is the potential energy associated with chemical systems. Chemical reactions involve valence electrons forming bonds to yield more stable products with lower energies. Energy is required to break interactions and bonds between the reactant atoms and energy is released when an interaction or bond is formed between the atoms in the products. Molecules with weak bonds (e.g., ATP) are less stable and tend to react to produce more stable products, releasing energy in the process. Generally, energy is transferred out of the system (exothermic) when the products have stronger bonds than the reactants and is transferred into the system (endothermic) when the reactants have stronger bonds than the products. Predictions of the energy requirements (endothermic or exothermic) of a reaction can be made given a table of bond energies. Graphic representations can be drawn and interpreted to represent the energy changes during a reaction. The role of energy in determining the spontaneity of chemical reactions is dealt with conceptually in this course. Entropy and its influence on the spontaneity of reactions are reserved for more advanced study. All reactions are reversible to a degree and many reactions do not proceed completely toward products but appear to stop progressing before the reactants are all used up. At this point, the amounts of the reactants and the products appear to be constant and the reaction can be said to have reached dynamic equilibrium. Dynamic equilibrium means the rate of the reverse reaction is equal to the rate of the forward reaction so there is no apparent change in the reaction. If a chemical system at equilibrium is disturbed by a change in the conditions of the system (e.g., increase or decrease in the temperature, pressure on gaseous equilibrium systems, concentration of a reactant or product), then the equilibrium system will respond by shifting to a new equilibrium state, reducing the effect of the change (Le Chatelier's Principle). If products are removed as they are formed during a reaction, then the equilibrium position of the system is forced to shift to favor the products. In this way, an otherwise unfavorable reaction can be made to occur. Mathematical treatment of equilibrium reactions is reserved for advanced study. Computer simulations can help visualize the progression of a reaction to dynamic equilibrium and the continuation of both the forward and reverse reactions after equilibrium has been attained. Properties of acids and bases and the ranges of the pH scale were introduced in Physical Science. In this course, the structural features of molecules are explored to further understand acids and bases. Acids often result when hydrogen is covalently bonded to an electronegative element and is easily dissociated from the rest of the molecule to bind with water to form a hydronium ion (H3O+). The acidity of an aqueous solution can be expressed as pH, where pH can be calculated from the concentration of the hydronium ion. Bases are likely to dissociate in water to form a hydroxide ion. Acids can react with bases to form a salt and water. Such neutralization reactions can be studied quantitatively by performing titration experiments.

pH at Key Points in a Weak Acid Titration

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