Name: ph at key points in acid-base titration
Uploaded: 2020-09-24T15:06:51.000Z
Duration: 2 min 28 s
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Titration Calculations: Strong Acid - Strong Base

Lorsqu'un acide fort est titré avec une base forte ou réciproquement le pH tout au long du titrage peut être calculé en déterminant la concentration des ions hydronium ou hydroxyde restants. Par exemple, 50 millilitres d'acide chlorhydrique de 0, 10 molaire se dissocie en ions hydronium et chlorure de 0, 10 molaire avec un pH initial de un. Si 25 millilitres d'hydroxyde de sodium de 0, 10 molaire sont ajoutés, la nouvelle concentration d'ions hydronium peut être calculée en soustrayant les moles totales d'ions hydroxyde à partir des moles totales d'ions hydronium et en les divisant par le volume total 75 millilitres ou 0, 075 litres.50 millilitres d'acide chlorhydrique de 0, 10 molaire contiennent 0, 0050 mole d'hydronium, tandis que 25 millilitres de 0, 10 molaire l'hydroxyde de sodium contient 0, 0025 mole d'ions hydroxyde. En substituant ces valeurs dans l'équation, la concentration en ions hydronium est égale à 0, 033 molaire. Par conséquent, le pH de la solution est passé à 1, 48.Si l'ajout d'hydroxyde de sodium se poursuit jusqu'à 50 millilitres, tous les ions hydronium de l'acide chlorhydrique se neutralisent, et le point d'équivalence est atteint lorsque le pH monte à sept. Au-dessus du point d'équivalence, le pH de la solution est déterminé par les ions hydroxyde, car l'acide chlorhydrique a été complètement neutralisé. Si 70 millilitres de solution d'hydroxyde de sodium contenant 0, 0070 mole d'ions hydroxyde est ajoutée à la solution, la concentration finale d'ions hydroxyde peut être déterminée en soustrayant les moles initiales d'ions hydronium à partir du total des moles d'ions hydroxyde et en le divisant par le volume total de la solution.La concentration finale en ions hydroxyde étant de 0, 017 molaire, le pOH et le pH de la solution sont respectivement égaux à 1, 78 et 12, 22,

calculs de titrage : acide fort - base forte

Calcul du pH pour les solutions de titrage : acide fort/base forte 
 Un titrage de 25,00 ml de HCl 0,100 M (acide fort) avec une base forte NaOH de 0,100 M est effectué. Le pH aux différents volumes de solution de base ajoutée peut être calculé comme suit : 
 (A) Volume du titrant = 0 ml. Le pH de la solution est dû à l'ionisation de l’acide de HCl. Comme il s'agit d'un acide fort, l'ionisation est totale et la molarité de l'ion hydronium est de 0,100 M. le pH de la solution est alors : 
 <img alt="Eq1" src="/files/ftp_upload/11413/11413_Equation_1.png" style="text-align: center; height: 50px;" />
 (b) Volume du titrant = 12,50 mL. Comme l'échantillon d'acide et la base titrante sont monoprotiques et de concentrations égales, cette addition de titrant implique une quantité de base inférieure à une quantité stœchiométrique et il est donc complètement consommé par réaction avec l'excès d'acide dans l'échantillon. La concentration d'acide restant est calculée en soustrayant la quantité consommée de la quantité initiale, puis en divisant par le volume de solution : 
 <img alt="Eq2" src="/files/ftp_upload/11413/11413_Equation_2v2.png" style="text-align: center; height: 110px;" />
 (c) Volume du titrant = 25,00 mL. Cette addition de titrant implique une quantité stœchiométrique de base (le point d'équivalence), et donc seuls les produits de la réaction de neutralisation sont en solution (eau et NaCl). Ni le cation ni l'anion de ce sel ne subissent une ionisation acide-base ; le seul processus générant des ions hydronium est l'autoprolyse de l'eau. La solution est neutre, ayant un pH = 7,00. 
 (d) Volume du titrant = 37,50 mL. Cela implique l'ajout de titrant au-delà du point d'équivalence. Le pH de la solution est ensuite calculé à l'aide de la concentration d'ion hydroxyde : 
 <img alt="Eq3" src="/files/ftp_upload/11413/11413_Equation_3v2.png" style="text-align: center; height: 170px;" />
 Ce texte est adapté de<a href="https://openstax.org/books/chemistry-2e/pages/14-7-acid-base-titrations"> Openstax, Chimie 2e, Section 14.7 : Titrages acido-basiques. </a>

Calculs de titrage : acide fort - base forte

Calcul du pH pour les solutions de titrage : acide fort/base forte
Un titrage est effectué pour 25,00 mL de HCl 0,100 M (acide fort) avec 0,100 M d’un ...

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Acid-base and Solubility Equilibria

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KEY TERMS AND CONCEPTS

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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 mL of titrant, the base added is less than the stoichiometric amount needed to neutralize the acid. Since the acid sample and the base titrant are both monoprotic and equally concentrated, the added base is fully consumed by the excess acid. The remaining acid concentration is found by subtracting the amount reacted and dividing by the total solution volume.

At 25.00 mL of titrant, the equivalence point is reached. This means a stoichiometric amount of base has been added, so only the neutralization products remain in solution. Those products are water and NaCl, and neither ion from this salt undergoes acid-base ionization. The only source of hydronium ions is the autoprotolysis of water, so the solution is neutral with a pH of 7.00.

At 37.50 mL of titrant, the base is in excess beyond the equivalence point. In this region, the pH is calculated from the hydroxide ion concentration. This example shows how pH calculations shift from excess acid, to equivalence, to excess base during a strong acid-strong base titration.

pH at Key Points in Acid-Base Titration

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+...

buffers

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...

calculating ph changes in a buffer solution

calculating-ph-changes-in-a-buffer-solution

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...

buffer effectiveness

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

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...

titration calculations: weak acid - strong base

titration-calculations-weak-acid-strong-base

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...

indicators

Acid-Base Color Changes

Acid-base indicators show color changes that help identify the pH of a solution. These are often weak organic acids or weak organic bases, and they respond to changes in hydronium ion concentration in dilute aqueous solution. Phenolphthalein is one example. It is colorless when the hydronium ion concentration is greater than 5.0 × 10^-9 M, which means the pH is below 8.3. In more basic solutions, where the hydronium ion concentration is lower, it turns red or pink. Methyl orange shows how an...

titration of a polyprotic acid

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...

solubility equilibria

Predicting Precipitation with Ksp

Solubility equilibria explain how a dissolved ionic compound and its solid form can exist in balance. In a saturated solution, the solute dissolves and the ions precipitate at equal rates. These ideas matter in real settings such as tooth decay and water purification, where compound solubility affects the outcome. A substance with finite solubility can form a saturated solution when more solute is added than the solvent can dissolve. The result is a heterogeneous mixture of the saturated...

factors affecting solubility

Common Ion Effects on Solubility

The common ion effect lowers the solubility of an ionic compound in water when the solution already contains one of the ions made by that compound. It follows the law of mass action and can be explained with Le Châtelier’s principle. When a common ion is added, the dissolution equilibrium shifts toward the solid, so less of the salt stays dissolved. Silver iodide shows this effect clearly. If silver ions or iodide ions are added to a solution of AgI, the equilibrium shifts left and more AgI...

formation of complex ions

Ligands and Complex Ion Stability

Complex ions form when a central atom, often a transition metal cation, binds to ligands. Ligands are ions or molecules around the metal ion. They can be neutral molecules such as H2O or NH3, or ions such as CN− or OH−. In many cases, the ligands act as Lewis bases by donating a pair of electrons to the central atom. These reactions are part of coordination chemistry, which studies coordination complexes. When a metal ion reacts with one or more ligands to form a complex, the equilibrium...

precipitation of ions

Solubility Limits and Selective Precipitation

Solubility limits and selective precipitation explain when ions form a solid in water. The key idea is the balance between an insoluble compound and its dissolved ions. In aqueous solutions that contain calcium ions and carbonate ions, this equilibrium can exist even if the solution was not made by saturating water with calcium carbonate. When two soluble salts are mixed, such as sodium carbonate and calcium nitrate, the ion concentrations determine whether a precipitate forms. If the reaction...

qualitative analysis

Cation Identification by Precipitation Tests

Cation identification by precipitation tests uses selective reactions to find metal ions in a mixture. In qualitative analysis, different reagents are added step by step. Each reaction can produce a characteristic precipitate for a specific group of cations. Other steps, such as changing pH, heating the mixture to dissolve a precipitate again, or adding reagents that form complex ions, help separate ions within the same group. Group IV cations such as Ba2+, Ca2+, and Mg2+ are identified...

henderson-hasselbalch equation

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,...

acid-base titration curves

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 pH changes in a strong acid-strong base titration using HCl and NaOH. Learn how to calculate pH before, at, and after the equivalence point.

pH at Key Points in Acid-Base Titration | JoVE K12

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Chemical Equations

Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are ...

Reaction Stoichiometry

A balanced chemical equation provides a great deal of information in a very succinct format. Chemical formulas provide the identities of the reactants and ...

Limiting Reactant

The relative amounts of reactants and products represented in a balanced chemical equation are often referred to as stoichiometric amounts. However, in ...

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Chemical Reactions in Aqueous Solutions

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Precipitation Reactions

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Oxidation&ndash;Reduction Reactions

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Oxidation Numbers

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Acids, Bases and Neutralization Reactions

An acid-base reaction is one in which a hydrogen ion, H+, is transferred from one chemical species to another. Such reactions are of central importance to ...

Synthesis and Decomposition Reactions

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Reaction Rate

The rate of reaction is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time ...

Measuring Reaction Rates

Polarimetry finds application in chemical kinetics to measure the concentration and reaction kinetics of optically active substances during a chemical ...

Concentration and Rate Law

The rate of a reaction is affected by the concentrations of reactants. Rate laws (differential rate laws) or rate equations are mathematical expressions ...

Determining Order of Reaction

Rate laws describe the relationship between the rate of a chemical reaction and the concentration of its reactants. In a rate law, the rate constant k and ...

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The Integrated Rate Law: The Dependence of Concentration on Time

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Half-life of a Reaction

The half-life of a reaction (t1/2) is the time required for one-half of a given amount of reactant to be consumed. In each succeeding half-life, half of ...

Temperature Dependence on Reaction Rate

The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. ...

Arrhenius Plots

The Arrhenius equation relates the activation energy and the rate constant, k, for chemical reactions. In the Arrhenius equation, k = Ae&#8722;Ea/RT, R is ...

Reaction Mechanisms

Chemical reactions often occur in a stepwise fashion, involving two or more distinct reactions taking place in a sequence. A balanced equation indicates ...

Thermochemical Equations

For a chemical reaction (the system) carried out at constant pressure &ndash; with the only work done caused by expansion or contraction &ndash; the ...

Rate-Determining Steps

Relating Reaction Mechanisms
In a multistep reaction mechanism, one of the elementary steps progresses significantly slower than the others. This slowest ...

Constant Pressure Calorimetry

Calorimetry is a technique used to measure the amount of heat involved in a chemical or physical process or to measure the heat transferred to or from a ...

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The presence of a catalyst affects the rate of a chemical reaction. A catalyst is a substance that can increase the reaction rate without being consumed ...

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Chemical reactions, such as those that occur when you light a match, involve changes in energy as well as matter.

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First Law of Thermodynamics

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Internal Energy

The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with ...

Dynamic Equilibrium

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Quantifying Heat

Thermal Energy&#160;

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The Equilibrium Constant

Consider the oxidation of sulfur dioxide:

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Homogeneous Equilibria for Gaseous Reactions

Homogeneous Equilibria for Gaseous Reactions
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Enthalpy

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Calculating the Equilibrium Constant

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Reaction Quotient

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Relative Strengths of Conjugate Acid-Base Pairs

Br&#248;nsted-Lowry acid-base chemistry is the transfer of protons; thus, logic suggests a relation between the relative strengths of conjugate acid-base ...

Calculating Equilibrium Concentrations

Being able to calculate equilibrium concentrations is essential to many areas of science and technology&#8212;for example, in the formulation and dosing ...

Strong Acid and Base Solutions

A strong acid is a compound that dissociates completely in an aqueous solution and produces a concentration of hydronium ions equal to the initial ...

The Small x Assumption

If a reaction has a small equilibrium constant, the equilibrium position favors the reactants. In such reactions, a negligible change in concentration may ...

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 ...

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Le Chatelier's Principle: Changing Concentration

A system at equilibrium is in a state of dynamic balance, with forward and reverse reactions taking place at equal rates. If an equilibrium system is ...

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 ...

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Le Chatelier's Principle: Changing Volume (Pressure)

For gas-phase equilibria, changes in the concentrations of reactants and products can occur with altered volume and pressure. The partial pressure, P, of ...

Mixtures of Acids

The pH of a solution containing an acid can be determined using its acid dissociation constant and its initial concentration. If a solution contains two ...

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Le Chatelier's Principle: Changing Temperature

Consistent with the law of mass action, an equilibrium stressed by a change in concentration will shift to re-establish equilibrium without any change in ...

Ions as Acids and Bases

Salts with Acidic Ions
Salts are ionic compounds composed of cations and anions, either of which may be capable of undergoing an acid or base ionization ...

Bronsted-Lowry Acids and Bases

The acid-base reaction class has been studied for quite some time. In 1680, Robert Boyle reported traits of acid solutions that included their ability to ...

Determining the pH of Salt Solutions

The pH of a salt solution is determined by its component anions and cations. Salts that contain pH-neutral anions and the hydronium ion-producing cations ...

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Acid/Base Strengths and Dissociation Constants

The relative strength of an acid or base is the extent to which it ionizes when dissolved in water. If the ionization reaction is essentially complete, ...

Polyprotic Acids

Acids are classified by the number of protons per molecule that they can give up in a reaction. Acids such as HCl, HNO3, and HCN that contain one ...

Water: A Bronsted-Lowry Acid and Base

The reaction between a Br&#248;nsted-Lowry acid and water is called acid ionization. For example, when hydrogen fluoride dissolves in water and ionizes, ...

Chemical reactions
• Types of reactions
• Kinetics
• Energy
• Equilibrium
• Acids/bases

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 Acid-Base Titration

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