Week 4. Titration

Titrations in Analytical Chemistry

Titrations in Analytical Chemistry

(Chapter13)

A standard solution is a reagent of known concentration. Standard solutions are used in titrations and in many other chemical analyses.

A standard solution (or a standard titrant) is a reagent of known concentration that is used to carry out a volumetric titration. The titration is performed by slowly adding a standard solution from a buret or other liquiddispensing device to a solution of the analyte until the reaction between the two is judged complete.

Buret standard solution (Standard titrant)

Erlenmeyer Flask Analyte

It is sometimes necessary to add an excess of the standard titrant and then determine the excess amount by backtitration with a second standard titrant.

solution

Con… For example, the amount of phosphate can be determined by adding a measured excess of standard silver nitrate, which leads to the formation of insoluble silver phosphate:

The excess silver nitrate is then back-titrated with a standard solution of potassium thiocyanate:

Amount of silver nitrate is chemically equivalent to the amount of phosphate ion plus the amount of thiocyanate used for the backtitration.

Primary Standards A primary standard is a highly purified compound that serves as a reference material in titrations and in other analytical methods. Important requirements for a primary standard: 1. High purity. (Established methods for confirming purity should be available) 2. Atmospheric stability. 3. Absence of hydrate water so that the composition of the solid does not change with variations in humidity. 4. Modest cost. 5. Reasonable solubility in the titration medium. 6. Reasonably large molar mass so that the relative error associated with weighing the standard is minimized.

Secondary standard A secondary standard is a compound whose purity has been determined by chemical analysis. The secondary standard serves as the working standard material for titrations and for many other analyses. The ideal standard solution for a titrimetric method will: 1. Be sufficiently stable so that it is necessary to determine its concentration only once. 2. React rapidly with the analyte so that the time required between additions of reagent is minimized. 3. React more or less completely with the analyte so that satisfactory end points are realized. 4. Undergo a selective reaction with the analyte that can be described by a balanced equation.

Equivalence Points and End Points • The EQUIVALENCE POINT (ep) is the point in a titration when the amount of added standard reagent is equivalent to the amount of analyte. For example, the equivalence point in the titration of NaCl with AgNO3 occurs after exactly 1 mole of silver ion has been added for 1 mole of chloride ion in the sample. 1AgNO3 + 1NaCl → 1AgCl + 1NaNO3

The equivalence point in the titration of H2SO4 with NaOH is reached after introducing 2 moles of base for 1 mole of acid. 1H2SO4 + 2NaOH → 1Na2SO4 + 2H2O The END POINT is the point in a titration when a physical change occurs that is associated with the condition of chemical equivalence.

Equivalence point, End point and Indicators • The equivalence point occurs when the volume of titrant added to the analyte is the exact stoichiometric amount the is needed to bring the reaction to completion. • The end point occurs when the indicator changes color. • When we want to measure the equivalence point actually measure the end point. We need to select an indicator that has the same end point as the equivalence point. • The indicator is added to the analyte. It is Not added to the titrant.

Con… • The difference in volume or mass between the equivalence point and the end point is the titration error. Et = Vep – Veq

Where: 1. Vep is the actual volume of reagent required to reach the END POINT (ep) 2. Veq is the theoretical volume necessary to reach the EQUIVALENCE POINT (eq).

Indicators Indicators are often added to the analyte solution to produce an observable physical change (signaling the end point) at or near the equivalence point. Large changes in the relative concentration of analyte or titrant occur in the equivalence-point region. These concentration changes cause the indicator to change in appearance. Typical indicator changes include: • Appearance or disappearance of a color • A change in color • Appearance or disappearance of turbidity

Indicators

standard solution (standard titrant)

Analyte

Con… For example: Indicator used in the neutralization titration of hydrochloric acid (HCl) with sodium hydroxide (NaOH) is phenolphthalein, which causes the solution to change from colorless to a pink color once excess sodium hydroxide has been added. During titration. The titrant is added to the flask with swirling until the color of the indicator persists.

The end point is achieved when the barely perceptible pink color of phenolphthalein persists.

Volumetric Calculations For the standard solutions used in most titrations, either molar concentration, c, or normal concentration, cN, is usually used. Molar concentration is the number of moles of reagent contained in one liter of solution, and normal concentration is the number of equivalents of reagent in the same volume.

Some Useful Relationships

(Where V is the volume of the solution)

Questions 1. 2.

3.

4.

Describe the preparation of 2.000 L of 0.0500 M AgNO3 (169.87 g/mol) from the primary-standardgrade solid. A standard 0.0100 M solution of Na+ is required to calibrate an ion-selective electrode method to determine sodium. (a) Describe how 500 mL of this solution can be prepared from primary standard Na2CO3 (105.99 g/mL). (b) How would you prepare 50.0 mL portions of standard solutions that are 0.00500 M, 0.00200 M, and 0.00100 M in Na+ from the solution. A 50.00 mL portion of an HCl solution required 29.71 mL of 0.01963 M Ba(OH)2 to reach an end point with bromocresol green indicator. Calculate the molar concentration of the HCl. Titration of 0.2121 g of pure Na2C2O4 (134.00 g/mol) required 43.31 mL of KMnO4. What is the molar concentration of the KMnO4 solution? The chemical reaction is:

5.

A 0.8040-g sample of an iron ore is dissolved in acid. The iron is then reduced to Fe 21 and titrated with 47.22 mL of 0.02242 M KMnO4 solution. Calculate the results of this analysis in terms of (a) % Fe (55.847 g/mol) and (b) % Fe3O4 (231.54 g/mol).

6.

A 100.0 mL sample of brackish water was made ammoniacal, and the sulphide it contained was titrated with 16.47 mL of 0.02310 M AgNO3. The analytical reaction is: Calculate the concentration of H2S in the water in parts per million, cppm.

Con… 8. The phosphorus in a 4.258 g sample of a plant food was converted to PO43- and precipitated as Ag3PO4 by adding 50.00 mL of 0.0820 M AgNO3. The excess AgNO3 was back-titrated with 4.06 mL of 0.0625 M KSCN. Express the results of this analysis in terms of % P2O5.

9. The CO in a 20.3 L sample of gas was converted to CO2 by passing the sample over iodine pentoxide heated to 150°C. The iodine was distilled at this temperature and was collected in an absorber containing 8.25 mL of 0.01101 M Na2S2O3. The excess Na2S2O3 was back-titrated with 2.16 mL of 0.00947 M, I2 solution. Calculate the concentration of CO (28.01 g/mol) in mg per liter of sample. .

Gravimetric Titrations Mass (weight) or gravimetric titrations differ from their volumetric counterparts in that the mass of titrant is measured rather than the volume. Therefore, in a mass titration, a balance and a weighable solution dispenser are substituted for a buret and its markings. With the advent of reliable burets, however, mass titrations were largely supplanted by volumetric methods because the former required relatively elaborate equipment and were tedious and time consuming. The availability of sensitive, low-cost, top-loading digital analytical balances and convenient plastic solution dispensers has changed this situation completely, and mass titrations can now be performed as easily and rapidly as volumetric titrations.

Calculations Associated with Mass Titrations The most common way to express concentration for mass titrations is the weight concentration, cw, in weight molar concentration units, Mw, which is the number of moles of a reagent in one kilogram of solution or the number of millimoles in one gram of solution. Mw

Titration Curves An End point is signaled by an observable physical change near the equivalence point of a titration.

The two most widely used signals involve 1. Changes in color due to the reagent (titrant), the analyte, or an indicator 2. A change in potential of an electrode that responds to the titrant concentration or the analyte concentration. 3. A titration curve is a plot of some function of the analyte or titrant concentration on the y axis versus titrant volume on the x axis.

Types of Titration Curves Two general types of titration curves (and thus two general types of end points) occur in titrimetric methods. • In the first type, called a sigmoidal curve, important observations are confined to a small region (typically 60.1 to 60.5 mL) surrounding the equivalence point. A sigmoidal curve in which the p-function of analyte (or sometimes the titrant) is plotted as a function of titrant volume. • In the second type of curve, called a linear segment curve, measurements are made on both sides of, but well away from, the equivalence point. Measurements near equivalence are avoided. Sigmoidal curve

Linear segment curve

Concentration Changes During Titrations The equivalence point in a titration is characterized by major changes in the relative concentrations of reagent and analyte.

The data in the second column of the table show the changes in the hydronium ion concentration as a 50.00 mL aliquot of a 0.1000 M solution of hydrochloric acid is titrated with 0.1000 M sodium hydroxide.

Calculating the NaOH Volumes Shown in the First Column of Table.

Principles of Neutralization Titrations (Chapter 14) Solutions and indicators for acid/base titrations Like all titrations, neutralization titrations depend on a chemical reaction of the analyte with a standard reagent. There are several different types of acid/base titrations. One of the most common is the titration of a strong acid, such as hydrochloric or sulfuric acid, with a strong base, such as sodium hydroxide. Another common type is the titration of a weak acid, such as acetic or lactic acid, with a strong base. Weak bases, such as sodium cyanide or sodium salicylate, can also be titrated with strong acids.

Standard Solutions The standard reagents used in acid/base titrations are always strong acids or strong bases, most commonly HCl, HClO4, H2SO4, NaOH, Ba(OH)2 and KOH. Weak acids and bases are never used as standard reagents because they react incompletely with analytes. Nitric acid is seldom used because its oxidizing properties offer the potential for undesirable side reactions. Hot concentrated perchloric and sulfuric acids are potent oxidizing agents and are very hazardous.

Acid/Base Indicators Many naturally occurring and synthetic compounds exhibit colors that depend on the pH of the solutions in which they are dissolved. An acid/base indicator is a weak organic acid or a weak organic base whose undissociated form differs in color from its conjugate base or its conjugate acid form. The behaviour of an acid-type indicator, HIn, is described by the equilibrium

Acid/Base Indicators The equilibrium for a base-type indicator, In, is

The equilibrium-constant expression for the dissociation of an acid-type indicator takes the form

Acidic form after hydrolysis of the lactone form

Basic form

Color change and molecular modes for phenolphthalein. The human eye is not very sensitive to color differences in a solution containing a mixture of HIn and In-, particularly when the ratio [HIn]/[In-] is greater than about 10 or smaller than about 0.1. At greater or smaller ratios, the color appears essentially constant to the eye and is independent of the ratio. As a result, we can write that the average indicator, HIn, exhibits its pure acid color when: and its base color when:

The Common Acid/Base Indicators

Indicator color as a function of pH (pKa=5.0).

Titration of strong acids and base The hydronium ions in an aqueous solution of a strong acid have two sources: (1) the reaction of the acid with water. (2) the dissociation of water itself. In most dilute solutions, the contribution from the strong acid far exceeds that from the solvent. Thus, for a solution of HCl with a concentration greater than about 10-6M.

Where [OH-] represents the contribution of hydronium ions from the dissociation of water. An analogous relationship applies for a solution of a strong base, such as sodium hydroxide.

Titrating a Strong Acid with a Strong Base Three types of calculations must be done in order to construct the hypothetical curve for titrating a solution of a strong acid with a strong base. Each of these types corresponds to a distinct stage in the titration: (1) pre-equivalence, (2) equivalence, and (3) post-equivalence.  In the pre-equivalence stage, we compute the concentration of the acid from its starting concentration and the amount of base added.  At the equivalence point, the hydronium and hydroxide ions are present in equal concentrations, and the hydronium ion concentration can be calculated directly from the ion-product constant for water, Kw.  In the post-equivalence stage, the analytical concentration of the excess base is computed, and the hydroxide ion concentration is assumed to be equal to or a multiple of the analytical concentration.

Titrating a Strong Acid with a Strong Base

The Effect of Concentration With 0.1 M NaOH as the titrant, the change in pH in the equivalence-point region is large. With 0.001 M NaOH, the change is much smaller, but still pronounced.

Choosing an Indicator The selection of an indicator is not critical when the reagent concentration is approximately 0.1 M. Bromothymol blue provides a satisfactory end point with a minimal systematic error in the titration of 0.001 M NaOH.

Titrating a Strong Base with a Strong Acid Titration curves for strong bases are calculated in a similar way to those for strong acids. Short of the equivalence point, the solution is basic, and the hydroxide ion concentration is numerically related to the analytical concentration of the base. The solution is neutral at the equivalence point and becomes acidic in the region beyond the equivalence point. After the equivalence point, the hydronium ion concentration is equal to the analytical concentration of the excess strong acid.

Titration curves for weak acids Four different types of calculations are needed to compute values for a weak acid (or a weak base) titration curve: 1. At the beginning, the solution contains only a weak acid or a weak base, and the pH is calculated from the concentration of that solute and its dissociation constant. 2. After various increments of titrant have been added (up to, but not including, the equivalence point), the solution consists of a series of buffers. The pH of each buffer can be calculated from the analytical concentrations of the conjugate base or acid and the concentrations of the weak acid or base that remains. 3. At the equivalence point, the solution contains only the conjugate of the weak acid or base being titrated (that is, a salt), and the pH is calculated from the concentration of this product. 4. Beyond the equivalence point, the excess of strong acid or base titrant suppresses the acidic or basic character of the reaction product to such an extent that the pH is governed largely by the concentration of the excess titrant.

Con… Question 2. Generate a curve for the titration of 50.00 mL of 0.1000 M acetic acid (HOAc) with 0.1000 M sodium hydroxide at 25°C.

The Effect of Concentration Initial pH values are higher and the equivalence-point pH is lower for the more dilute solution (Curve B). At intermediate titrant volumes, however, the pH values differ only slightly because of the buffering action of the acetic acid/sodium acetate system that is present in this region. (pH of buffers is largely independent of dilution)

Con… The Effect of Reaction Completeness: Titration curves for 0.1000 M solutions of acids with different dissociation constants are shown in Figure. The pH change in the equivalence-point region becomes smaller as the acid becomes weaker—that is, as the reaction between the acid and the base becomes less complete. Suitable indicator

Unsuited for titration

Indicator exhibiting a color change in the basic region, such as phenolphthalein, provides a sharp end point with a minimal titration error.

Titration curves for weak bases The calculations needed to draw the titration curve for a weak base are analogous to those of a weak acid

Questions 1. Generate the hypothetical titration curve for the titration of 50.00 mL of 0.0500 M HCl with 0.1000 M NaOH at 25°C. 2. Calculate the pH during the titration of 50.00 mL of 0.0500 M NaOH with 0.1000 M HCl at 25°C after the addition of the following volumes of reagent: (a) 24.50 mL, (b) 25.00 mL, (c) 25.50 mL. 3. Generate a curve for the titration of 50.00 mL of 0.1000 M acetic acid (HOAc) with 0.1000 M sodium hydroxide at 25°C. 4. A 50.00-mL aliquot of 0.0500 M NaCN (Ka for HCN 5 6.2 X 10-10) is titrated 5. with 0.1000 M HCl. The reaction is: Calculate the pH after the addition of (a) 0.00, (b) 10.00, (c) 25.00, and (d) 26.00 mL of acid.

Questions 1. What is the pH of the solution that results when 0.093 g of Mg(OH)2 is mixed with (a) 75.0 mL of 0.0500 M HCl? (b) 100.0 mL of 0.0500 M HCl? (c) 15.0 mL of 0.0500 M HCl? (d) 30.0 mL of 0.0500 M MgCl2? 2. Calculate the pH of an aqueous solution that is (a) 1.00 X 10-1 M in HOCl. (b) 1.00 X10-2 M in HOCl. (c) 1.00 X10-4 M HOCl. 3. Calculate the pH of an ammonia solution that is (a) 1.00 X10-1 M NH3.(b) 1.00 X10-2 M NH3. (c) 1.00 X10-4 M NH3. 4. Calculate the pH of the solution that results when 20.0 mL of 0.1750 M formic acid is: (a) diluted to 45.0 mL with distilled water. (b) mixed with 25.0 mL of 0.140 M NaOH solution. (c) mixed with 25.0 mL of 0.200 M NaOH solution. (d) mixed with 25.0 mL of 0.200 sodium formate soultion. 5. In a titration of 50.00 mL of 0.05000 M formic acid with 0.1000 M KOH, the titration error must be smaller than 0.05 mL. What indicator can be chosen to realize this goal?