Analytical Chemistry Manual PDF 2002

Summary

This is an analytical chemistry manual for undergraduate students, focusing on volumetric glassware calibration. It provides tolerances and details the use of various pieces of volumetric equipment.

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Al –alBayt Univesity Analytical Chemistry Manual Prepared by Dr. Hutaf M. Baker 2002 1 2 Experiment (1) Calibration of Volumetric Glassware ______________________________________________...

Al –alBayt Univesity Analytical Chemistry Manual Prepared by Dr. Hutaf M. Baker 2002 1 2 Experiment (1) Calibration of Volumetric Glassware _________________________________________________________________________________________________ Introduction For very accurate volumetric analysis, it is advisable to calibrate the volumetric glassware. Though a volumetric pipet may be labeled 25 mL, it will not deliver exactly that volume. There are allowed tolerances in manufacture. For example, a 100 mL volumetric flask is anufactured to a tolerance of ±0.08 mL, and since liquids and glass expand or contract as temperature rises and falls, the tolerance applies at the temperature indicated on the flask, usually 2 0°C. The tolerance values established for volumetric glassware by the National Institute of Standards and Technology (NIST) are listed below in Table I. It should be noted that glassware meeting these specifications is termed "class-A" glassware, and it is adequate for all but the most exacting work, for which calibrated glassware is a necessity. Table I Tolerances for Volumetric Glassware Volume Volumetric Transfer Burets Capacity Flasks Pipets mL ± 0.02 mL 1 ± 0.02 mL ± 0.006 mL 2 ± 0.02 mL ± 0.01 mL ± 0.01mL 5 ± 0.02mL ± 0.02 mL ± 0.02mL 10 ± 0.03 mL ± 0.03 mL ± 0.03mL 25 ± 0.05 mL ± 0.05 mL ± 0.05mL 50 ± 0.08 mL ± 0.08 mL ± 0.1mL 100 ± 0.10 mL ± 0.10 mL 200 ± 0.12mL 250 ± 0.20 mL 500 1000 3 Volumetric glassware that commonly require calibration if very exact work is to be done would be the volumetric flask, the volumet-ric pipet and the buret. These three items are described further in the following paragraphs. Volumetric Flask: A volumetric flask is calibrated to contain (TC) the indicated volume of water at 20 o C when the bottom of the meniscus is adjusted to just rest on the center of the line marked on the neck of the flask. Most flasks bear the label "TC 20 o C" indicating that the flask is calibrated to contain the indicated volume at 20 o C. Other types of glassware, such as pipets and burets, may be cali-brated to deliver (TD) the indicated volume. Volumetric flasks are normally manufactured with capacities from 5 mL to 5 L. They are used in the preparation of standard solutions and in the dilution of solutions to fixed volumes prior to taking aliquots (with a transfer pipet) in an analysis. Though temperature must be considered when dealing with the accurate measurement of ® volumes, modern laboratory glasswaremade of Pyrex or other low expansion borosilicate glass can be safely heated without fear of breakage in an oven to at least 320 o C without harm. Glassware is normally dried at 110-150 o C. Burets: Burets are used to deliver accurately known, but variable, volumes up to its maximum capacity. The precision attainable with a buret is substantially greater than with a pipet. A buret equipped with a glass stopcock valve requires a layer of lubricant between the ground- glass surfaces of the stopcock for a liquid-tight seal. Because this lubricant can get into the tip and on the inner wall of the buret, thorough cleaning is needed after use. Silicone lubricants are especially difficult to remove, and often require hot alkali solutions, which can also attack glass. For this reason, Teflon ® is used to form the rotating part of a stopcock. It is resistant to chemical attack, acts as its own lubricant and is soft enough to form a liquid-tight seal. Pipets: Pipets permit the transfer of accurately known volumes from one container to another. Volumetric pipets are typically available between 0.5 and 200 mL. Because an attraction exists between most liquids and glass, a small amount of liquid tends to remain in the tip of the pipet after the pipet is emptied. This residual liquid is never blown out of a volumetric pipet; but with other pipet types it is proper to blow out the last drop. CLEANING GLASSWARE Clean glassware is imperative for accurate and precise volumetric applications. It is therefore necessary to thoroughly clean all glassware before use. A brief soaking in a warm detergent solution is usually sufficient to remove the grease and dirt responsible for water breaks. If detergent is ineffective, treatment with cleaning solution usually helps. The following solutions are commonly used. 4 1-Dilute Nitric Acid 2-Dichromate-Sulfuric Acid Cleaning Solution 3-Aqua Regia Cleaning solution METHODS OF CALIBRATION There are three general methods commonly employed to calibrate glassware. These are as follows: 1. Direct, absolute calibration 2. Indirect, absolute calibration 3. Relative calibration In this experiment you will make cleaning of you 50. mL buret and your 10. pipet by using a suitable cleaning solution, the you will make calibratiofor your glassware Experimental Procedure a-`Cleaning of Volumetric glassware with Dichromate-Sulfuric Acid Cleaning Solution 1- Cleaned your glassware with a detergent and rinsed carefully with distilled water. 2- Pour a small quantity of the chromate solution into the glassware, allowing it to flow down all parts of the glass surface. 3-Pour the solution back into its stock bottle. 4-Rinse the glassware well. The cleaning solution may be reused until it acquires the green color of the chromium(III) ion. Once this happens, it should be discarded. b- Calibration of a 50 mL Buret 1-Ensure the buret you desire to calibrate is clean. If small droplets of water adhere to the inner surface of the buret after delivering deionized water, the buret is dirty and must be cleaned before proceeding further. 2-Fill the buret completely full with deionized water and make sure that air bubbles are not trapped in the stopcock or tip. Draining water from the buret very slowly, lower the liquid level until the bottom of the meniscus just rests on the 0.00 mL mark. Touch the tip to the wall of a beaker to remove any adhering drop. 5 3-Wait 10 min and recheck the volume. If the stopcock is tight, there should be no perceptible change in the meniscus. During this interval, weigh (to the nearest milligram) a weighing bottle recording its mass on the Report sheet. 4- Slowly transfer (at a rate of about 10 mL/min) approximately 10 mL of water to the flask. Wait one minute, then record the apparent volume delivered from the buret to the second place after the decimal. 5-Refill the buret again to the 0.00 mL mark. Weigh the weighing bottle and its contents to the nearest milligram. Determine the mass of water delivered by difference. Use the data in Table II to convert this mass to the true volume deliv-ered. 6-Subtract the apparent volume from the true volume. This difference is the correction that should be applied to the apparent volume to give the true volume. Repeat the 10 mL calibration until agreement between subsequent true values is within ±0.02 mL. Table II Volume Occupied by 1.0000 g of Water Weighed in Air Against Stainless Steel Weights volume in mL Temperature, volume of corrected to °C 1.0000 g H2O at T T 20°C 16 1.0021 mL/g 1.0022 mL/g 17 1.0022 mL/g 1.0023 mL/g 18 1.0024 mL/g 1.0025 mL/g 19 1.0026 mL/g 1.0026 mL/g 20 1.0028 mL/g 1.0028 mL/g 21 1.0030 mL/g 1.0030 mL/g 22 1.0033 mL/g 1.0032 mL/g 23 1.0035 mL/g 1.0034 mL/g 24 1.0037 mL/g 1.0036 mL/g 25 1.0040 mL/g 1.0037 mL/g 26 1.0043 mL/g 1.0041 mL/g 27 1.0045 mL/g 1.0043 mL/g 28 1.0048 mL/g 1.0046 mL/g 6 Data Sheet Calibration of a 50 mL buret 1 2 3 4 Trial: mass of flask (with sample) mass of flask (empty): mass of water: apparent volume (from buret): true volume (corrected): volume difference: (true - apparent) Temperature oC mean difference: _____________ mean true volume ± s.d.: ___________ Instructor's Signature ------------------------------ 7 Experiment (2) THE Gravimetric Determination of Chloride _________________________________________________________________________________________________ Introduction In most reactions the reactants and products remain soluble. This is not the case for the association of many common anions with a number of transition metal ions. yMn+(aq) + nXy-(aq) (MyXn) (s) M is the metal ion, X is the anion and the resulting salt is insoluble and drops out of solution (precipitates). The equilibrium constant for the above reaction (which is generally very large) is most commonly written as: 1 K= n [M ] [ X y  ]n y However we are more familiar in discussing this type of equilibrium in terms of the Ksp or solubility product. (MyXn)(s)  yMn+ + nXy- Ksp = [Mn+]y [Xy-]n The Ksp is simply the inverse of the K for the formation of the salt and correspondingly is usually a small number. Most transition metals form insoluble salts with sulfate, phosphate, carbonate, and hydroxide anions. For the most part halide and nitrate salts are soluble. Silver is one exception, in that it forms insoluble salts with halides. Any of these insoluble products can provide a basis for the quantitative analysis of one of the component ions of the salt. It is possible to find a counter ion which will precipitate just about any of the most common cations and anions. Gravimetric analysis is a long standing technique (and in some instances can give more accurate results than some more modern methods) utilizing the precipitation of salts to determine the concentration of an analyte. Several aliquots of the precipitating agent is added to a solution of the analyte. This is the method we are using for determining chloride; based on the precipitation, collection, and weighing of insoluble silver chloride. 8 Ag+(aq) + Cl-(aq) AgCl(s) The precipitation is carried out in acidic solution to avoid any interference from 2- 3- anions of weak acids such as CO3 and PO4 that form insoluble salts with silver ion in neutral or alkaline solution. Silver chloride forms initially as a colloid, which is coagulated by heating in the presence of a high concentration of added electrolyte. Silver chloride in suspension is susceptible to photodecomposition when exposed to sunlight and should not be allowed to stand in direct sunlight longer than absolutely necessary. Some decomposition is inevitable and the deposited elemental silver will give the precipitate a faint purple hue. Silver is an expensive reagent and it is common practice to save the precipitate and precipitating reagent for later recovery of the metal. Consult your instructor for directions concerning disposal of these reagents. Experimental Procedure a-` Forming the precipitate Silver chloride - Transfer the unknown of cholride solution to a marked 400 ml cleaned beaker or larger beaker.  - Prepare 6 molar of nitric acid.  - Add 90 ml of distilled water to the 400 ml beaker. 4- Add 6M HNO3. Add 1 mL of 6M HNO3 in excess. 5- Add, drop wise, 20.00 mL of 0.1M AgNO3. Allow the solution to stand a minute and test for complete precipitation by adding one drop of 0.1M AgNO3 to the solution near the edge of the beaker. Observe carefully, and if more AgCl forms, add an additional 3 mL of 0.1M AgNO3 and retest for complete precipitation.  9 - Heat the solutions to boiling and let stand in the dark until the precipitate coagulates (at least 1 hour or the next laboratory period). Meanwhile obtain 4 filter papers. Number and record the weight (to 0.1mg) of each, into your notebook.  - Decant the first supernatant liquid onto the first filter paper using a gentle suction. This is done using the sidearm filtering flask. The apparatus can be used to vacuum filter the sample using the vacuum on the lab bench. Wash the remaining precipitate in the beaker three times with small portions of deionized water containing 1 mL of concentrated HNO3 per liter, and decant the washings onto the filter.  - Transfer the precipitate to the filter, loosening any particles sticking to the wall with a stirring rod, rubber policeman or a stream of deionized water from your wash bottle.  - Wash the precipitate on the filter, with the 6M HNO 3, three times.The nitric acid wash replaces the silver nitrate adsorbed on the surface of the precipitate. Wash the precipitate three more times with 5 mL of deionized water to remove traces of HNO 3.  - Place the filter papers in on watch glasses and place them inside your lab drawer until the next lab period. Weigh them at your convenience during that lab period. Discard all waste in accordance with instructions provided by the TA or Instructor. 11- Calculate actual weight of AgCl collected. From this calculate grams of Cl- in your AgCl and use this to report the amount of chloride in the original sample as %Cl-. Report the results on the datasheet. Be sure to show the formulas you have used for these calculations on the datasheet. 10 Data Sheet Gravimetric Analysis Determination of chloride Volume of unknown solution________________ Weight of filter paper________________ Weight of filter paper and weight of precipitate (AgCl) _____________ Weight of (AgCl) ________________ Weight of (Cl-) _________________ The concentration of (Cl-) in mg per liter _______________ 11 Instructor's Signature ------------------------------ Questions: 1-Would the presence of iodide ion in this solution affect the precipitation of AgCl? If so, why? 2-What is the maximum concentration of silver ion in a saturated solution of silver chloride under standard conditions? 12 Experiment (3) The Gravimetric Determination of Sulfate _________________________________________________________________________________________________ Introduction Determining the concentration of a particular ion can be based upon the limited solubility of that ion in the presence of an oppositely charged ion forming an "insoluble" salt. After quantitatively precipitating the compound in question, BaSO 4 for this lab, one collects it, dries it, and uses the mass to determine the amount of sulfate in the sample. BaSO4 solubility is lowest in neutral solution. However, analysis here will be done in acidic solution because crystals that form in acid solution are larger and more easily collected than in neutral solution. 2 - In addition, any CO3 present will be converted to HCO3- and PO43- to HPO42-. These reactions will reduce the possibility of BaCO3 or Ba3(PO4)2 from coprecipitating, keeping the acidity low and having excess Ba2+ , no appreciable error will occur. In this experiment, you will dissolve a know quantity of a solid containing sulfate in distilled water. Addition of BaCl2 will occur to the boiling, acidified solution, resulting in a precipitate, BaSO4, Filtering, washing with distilled water and igniting at red heat in a porcelain crucible should yield solid BaSO4. From this, you will be able to calculate the present sulfate in the unknown sample. Experimental Procedure a-` Forming the precipitate Barium Sulfate 13 1- Pipet 10.00 ml of an unknown sample containing sulfate and transfer to it a clean 400 mL beaker. 2- Record the unknown number. 3- Add 200 mL of distilled water to the beaker. 4- Add 2 mL of conc. HCl to the solution. Stir. Cover with a watch glass. 5- Now: turn on the flame on a low setting. Bring the solution to a gentle boil. 6- Carefully remove the watch glass. Rinse the underside of the watch glass with a smaller spray of distilled water. 7- Maintain a gentle boil. 8- Using a graduated buret, add 30.00 mL of 0.1 M BaCl2 dropwise to the boiling solution. 9- Replace the watch glass and reduce the heat slightly (below boiling). Continue heating for 15 minutes. 10-Remove the beaker from the hot plate and allow the precipitate to settle. Test for completeness of precipitation by adding a few drops of BaCl2 solution. If cloudiness occurs when the drops enter the solution add an additional 5 mL of BaCl2 solution, allow the precipitate to settle and test for completeness again. 11- Allow the solution to cool to room temperature. b- Getting Ready to Filter 1- Weigh the ashless filter paper. 2. Fold and place the paper in the funnel. 3. Set up the filter paper with the funnel. 4. Pour the solution with the precipitate into the funnel. 5. Wash the precipitate in the filter paper with several portions ( 5 mL) of distilled water. 14 6. Test the removal of all the chloride ion by adding a drop of silver nitrate solution to a new sample of the wash (from the filter funnel). If there is turbidity (solid AgCl) wash with additional distilled water. Discard the filtrate (the solution that passed through the filter paper). Wash also with 0.1 M of nitric acid ( nearly 2 ml). 7. Fold the filter paper into the shape of a boat and place into the weighed crucible. Place the crucible in the nicrome triangle and heat in the crucible until gases are no longer given off. Do not allow the paper to flame. 8. When the paper becomes charred, remove the crucible cover and incline the crucible in the triangle. Allow the flame to touch only the lower half of the crucible and heat the crucible to a red heat. It is the hope that the filter paper will burn away, leaving a pure white (hopefully) residue and no black carbon adhering to the crucible. Continue heating at red heat for 5 minutes. Remove the heat and allow to cool for about 3 minutes. Transfer to the desiccator and allow to cool to room temperature. 9- Record the mass. 10- Reheat for 5 minutes. Allow to cool as before. Reweigh. Mass should be within 2 mg (0.002 g). 11-Determine the percent of sulfate (in the form of barium sulfate) in your original sample. Write up your results as a formal laboratory experiment report. Record all data and observations directly at your data sheet. 15 Data Sheet Gravimetric Analysis Determination of Sulfate Volume of unknown solution________________ Weight of empty crucible________________ Weight of empty crucible and weight of precipitate (BaSO 4) _____________ Weight of (BaSO4) ________________ Weight of (SO42-) _________________ The concentration of (SO42-) in mg per liter _______________ 16 Instructor's Signature ------------------------------ Experiment (4) THE Gravimetric Determination of Nickel _________________________________________________________________________________________________ Introduction The gravimetric determination of nickel is an example of the precipitation of inorganic ions with the aid of organic reagents, with which they form sparingly soluble and often coloured compounds. The nickel is precipitated by the addition of an ethanolic solution of dimethylglyoxime [CH3.C(:NOH).C(:NOH).C(:NOH).CH3] to a hot, faintly acidic solution of the nickel salt, then adding a slight excess of aqueous ammonia (free from carbonate). The precipitate is washed with cold water and weighed as nickel dimethylglyoximate, after drying at 110 - 120oC. Ni2+ + 2H2DMG  Ni(HDMG)2 + 2H+ Organic precipitants usually have high molecular weights, so that a small amount of the inorganic ion will yield a relatively large amount of the precipitate (small gravimetric factor). The precipitates are crystalline and can be produced with good characteristics of filterability and washability. Organic reagents often react with more than one metal ion; adequate specification can often be achieved by control of concentration and pH. The most important reagents are those which form chelate complexes, which involve the formation of one or more (usually five or six-membered) rings incorporating the metal ion. Dimethylglyoxime gives a bright red precipitate of Ni(C4H7O2N2)2 with nickel(II) solutions. 17 The precipitate is soluble in free mineral acids (even as little as is liberated by reaction in neutral solutions) in solutions containing more than 50% of ethanol by volume, and in hot water, but is insoluble in dilute ammonia solution. The reagent is almost insoluble in water, and is added in the form of a 1% solution in ethanol; 1mL of this solution is sufficient for the precipitation of 2.5mg of nickel. A slight excess of the reagent shall have no effect on the precipitate, but a large excess should be avoided because (a) of the possible precipitation of the H2DMG itself due to its low solubility in water, and (b) the increased solubility of the precipitate in ethanol/water mixtures. The precipitate is of definite composition and can be isolated by filtration on a sintered-glass crucible; it has little affinity for water and can be dried at 110 - 120oC. The precipitate remains unchanged in composition up to 170oC. Under these conditions of precipitation, palladium and gold would be partially precipitated, and iron(III) would yield a red-coloured soluble complex. Experimental Procedure a-` Forming the precipitate Nickel dimethylglyoxime 1- Pipette a sample (10 mL) of the solution containing the nickel salt into a 400 mL beaker, provided with a watch-glass cover and stirring rod. 2- Add dilute hydrochloric acid (5mL) and dilute to 200mL with deionised water. Heat to 70 - 80oC. Add 30 mL of the dimethylglyoxime reagent to give a slight excess of reagent. 3- Immediately add dilute ammonia solution dropwise, directly to the solution, not down the side of the beaker, with constant stirring until precipitation takes place, and then in slight excess. Allow to stand on the steam bath for 20 - 30 minutes, and test the solution for complete precipitation when the red precipitate has settled out. Allow the precipitate to stand for 1 hour, cooling at the same time. 4- Filter the cold solution through a sintered glass crucible, previously heated to 110 - 120oC, and weighed after cooling in a desiccator. Wash the precipitate with cold water until free from chloride, and dry it at 110 - 120oC for 45 - 50 minutes. 5- Allow to cool in a desiccator and weigh. Dry to constant weight. Carry out a duplicate determination. Calculate the w/v percentage of nickel in the solution. 18 Data Sheet Gravimetric Analysis Determination of Nickel ion Volume of unknown solution________________ Weight of empty crucible________________ Weight of empty crucible and weight of precipitate (Ni(DMG)2) _____________ Weight of (Ni(DMG)2) ________________ Weight of (Ni2+) _________________ The concentration of (Ni2+) in mg per liter _______________ 19 Instructor's Signature ------------------------------ Questions 1- Why is the precipitate washed until it is chloride free? How can chloride ion in the filtrate be tested for? 2- If the precipitate with an organic reagent did not have a definite composition, how could a weighable form of precipitate be produced? 3- What is a chelate complex? 4- Through which atoms is the dimethylglyoxime bonded to the nickel(II) ion? 20 Experiment (5) An Introduction to Acid - Base Titrations (Neutralization Titration in Aqueous Medium) _____________________________________________________________________ Introduction This experiment will introduce you to the analytical method of volumetric titration. Volumetric titration is one of the two important classical or wet analytical methods, the other being gravimetric analysis. Titrimetric methods are based on the ability to prepare a standard solution, that is, a solution where the concentration is accurately known. The standard solution is then used to determine, either directly or indirectly, the analyte in a sample. Standard solutions may be prepared by two methods. One method involves the direct weighing and dissolution of a high purity "standard material" to form a solution of known concentration. A primary standard is a substance that is used to standardize a solution. A good primary standard must be: (1) Available in very pure form. (2) Reasonably soluble. (3) Stable in the pure form and in solution. (4) Non-hygroscopic and easily dried. (5) A compound with molecular mass above 100. The solution added from the buret is called the titrant. For every titration, there must be a way to determine when the titration reaction is complete. In acid-base titrations, this is 21 accomplished by adding a small amount of an organic dye, called an indicator, to the solution to be titrated. If the indicator is chosen correctly, a color change, called the end point, occurs when the moles of acid equal the moles of base. Alternatively, a known amount of "standard material" is titrated by a previously prepared solution. The concentration of the previously prepared solution is then determined by the volume that reacts with a given amount of standard material. In this experiment you will prepare a standard solution from standard material this solution will be used to standardize an HCl solution by titration, this standard solution of HCl will be Used to make standardization of NaOH also by titration. An unknown acid sample of phosphoric acid (H3PO4) will be taken; a titration of phosphoric acid with standard solution of sodium hydroxide will be done by choosing the appropriate indicator. The BrØnsted-Lowry theory is the most useful and widely accepted description of the ionization of both acids and bases. In this theory the definition of an acid is any substance that can ionize to give a hydrogen ion. On the other hand, a base is a substance which can accept a hydrogen ion. Most salts are completely ionized in aqueous solution, but some acids and bases are not ionized 100%. The Ka values for phosphoric acid (weak acid) are shown in this table Phosphoric Acid Ka Ka1 7.50E-03 Ka2 6.20E-08 Ka3 4.80E-13 f For H3PO4 there will be three dissociation steps, each step has a specific value of pH. In this neutralization titration, addition of hydroxide ions will not significantly increase the pH of the solution until most of the H3PO4 has been changed to H2PO4- (dihydrogen phosphate. pH  4.6). The addition of more hydroxide ions will increase the pH of the solution. More of the hydroxide ions will then react with the second hydrogen of sodium phosphoric acid converting H2PO4- to H1PO42- ( monohydrogen phosphate the pH  9.7). The third hydrogen ion reacts partially with OH- ions yielding PO43- ( tri phosphate pH  12.6). 22 Burets The principal use of the buret is for titrations. Precise titrations require burets that drain freely, are very clean, and do not leak around the stopcock. Teflon stopcocks can usually be prevented from leakage by tightening the tension nut, which seats the stopcock more firmly. A clean, properly operating buret should be held in place by a buret clamp, which is attached to a ring stand. Before you fill the buret, you should rinse it several times with the solution that will eventually be in it. To rinse it, first check to make sure that the stopcock is closed. Take the buret from the clamp and use a beaker to pour about 3 to 5 mL of the solution into the buret. Carefully tip the buret on its side while holding it with your hand. Do not allow the solution to spill, but tip the buret until the solution comes in contact with almost the entire length. Rotate the buret in your hand so that the inner walls are rinsed completely with the solution. Drain the buret through the stopcock, discard this portion of the solution, and repeat the entire rinsing procedure two more times. If you are using the buret for the first time, examine its markings before you fill it. The lines that span the entire circumference occur for each milliliter, starting with zero at the top and reaching the maximum volume of 50 ml at the bottom of the buret. As a consequence, the buret will show the volume of a liquid that has been delivered rather than the volume that remains. The smaller lines indicate each tenth of a milliliter. Fill the buret to above the zero mark with the stopcock closed. Open the stopcock fully so that the liquid drains rapidly to flush out air bubbles in the tip of the buret. Drain the buret until the meniscus rests between the zero and 1 ml marks. Do not waste time trying to align the bottom of the meniscus with the zero mark. Read the buret with your eye on the same level as the meniscus. To obtain the volume of the liquid that you use in a titration, subtract this reading from the final reading. The left hand is used to open and close the stopcock. With a bit of practice, you will be able to adjust the stopcock so that as little as half a drop will form on the capillary tip. The right hand is used to swirl the flask. A left handed student may turn the buret 180°, then open and close the stopcock with the right hand. Unfortunately, the markings on the buret will sometimes be away from the student and will not be as easy to read. Experimental Procedure a- Standardization of 0.1 M Hydrochloride Acid (HCl) Solution 23 1- Accurately weight 0.5 g (to the nearest 0.1 mg) of pure sodium carbonate which has been previously dried in an oven at 110 oC for 1½ hours, in a weighing bottle Dissolve in distilled water then transfer quantitatively into 100 mL volumetric flask, make shore that all the solid is dissolved by shaking well then complete to the mark. Calculate the molarity of this solution 2- Using a 10 mL pipet, transfer exactly 10.00 mL of the standard solution ( carbonate solution) into an 250 mL Erlenmeyer flask. 3- Add about 30 mL of deionized or distilled water and add 4 drops of bromocresol green indicator. It changes from blue to green and then yellow. The proper end-point however is green. If you titrate to the yellow color, you have gone to far. 4- Titrate against standard 0.1M HCl to an intermediate blue-yellow color. Repeat the titration another two times 5- Calculate a molarity for the hydrochloric acid solution from data obtained in titration. b- Standardization of the 0.1 M Sodium Hydroxide (NaOH) Solution 1- Using a 10 mL pipet, transfer exactly 10.00 mL of NaOH solution into 250 mL Erlenmeyer flask. 2- Add 30 mL of deionized or distilled water and add 4 drops of phenolphthalein indicator pink color will appear. 3- Titrate against the standard HCl solution until the solution color change from pink to colorless. Repeat the titration another two times 4- Calculate the molarity of NaOH solution. c- Determination of the concentration of phosphoric acid solution 1- Pipet 10 mL of unknown H3PO4 solution into 250 mL conical flask. Record your unknown number. 24 2- Add about 30 mL of deionized or distilled water and add 4 drops of bromocresol green or methyl orange indicator. 3- Titrate against standard NaOH solution until reaching the end point record the volume, repeat this titration another two times. 4. Calculate the concentration of H3PO4 in the unknown solution in gram per liter. 5- Repeat the steps 1-3 but instead of adding bromocresol green or methyl orange indicator, add 4 drops of phenolphthalein indicator. Calculate the concentration of H 3PO4 in the unknown solution in gram per liter. Data Sheet a- Standardization of 0.1 M Hydrochloride Acid (HCl) Solution Weight of Na2CO3---------------------------g Volume of Na2CO3solution Volume of HCl 1- mL mL 2- mL mL 3- mL mL b- Standardization of the 0.1 M Sodium Hydroxide (NaOH) Solution Volume of NaOH solution Volume of HClsolution 1- mL mL 2- mL mL 3- mL mL c- Determination of the concentration of phosphoric acid solution Volume of unknown solution H3PO4 Volume of NaOH solution 25 Bromocresol green or methyl orange indicator 1- mL mL 2- mL mL 3- mL mL Volume of unknown solution H3PO4 Volume of NaOH solution phenolphthalein indicator 1- mL mL 2- mL mL 3- mL mL Instructor's Signature ----------------------------- Questions 1. For each of the following errors, indicate whether the calculated molarity of HCl would be higher or lower than the real value or unaffected. Briefly explain your answer using the calculating equation for the molarity of HCl. The calculating equation for the molarity of HCl is: M = 2(mass of Na2CO3)/(106)(Vol. of HCl) a. The sodium carbonate was not dried before use. b. The sodium carbonate was dissolved in 50 mL of water instead of 100 mL. c. The buret was wet with water and wasn't rinsed with HCl before filling. 2- The green solution at the endpoint of the titration will gradually change to yellow if allowed to sit for a period of time. What would be the possible cause for this color change? 3- Why in the first step of dissociation of phosphoric acid you do not use phenolphthalein indicator ? 26 Experiment (6) Determination of a Carbonate mixture _________________________________________________________________________________________________ Introduction It is relatively simple to determine the composition of a mixture by titrating separate aliquots to a phenolphthalein endpoint and to a methyl orange endpoint. In this experiment you can have a mixture of Na2CO3, and NaHCO3 but in solution a maximum of two of these species can co-exist at one time. Experimental Procedure a- Phenolphthalein runs. 1- By means of pipet take 10 mL of the carbonate and bicarbonate unknown mixture. Record your unknown number. 2- Add a few drops of phenolphthalein indicator. 3- Slowly titrate the solution with previously standardized HCl solution. The volume of the titrant corresponds to half the carbonate. 27 a- Methyl orange runs. 1- Take another 10 mL of the carbonate and bicarbonate unknown mixture; add a few drops of methyl orange as an indicator. 2- Titrate with the HCl solution; the volume of acid used corresponds to carbonate mixture. Calculate the amount of each of the carbonate and bicarbonate present in 10 mL mixture expressed in mg per L. Data Sheet Determination of carbonate mixture a- Phenolphthalein runs Volume of unkown solution Volume of HCl 1- mL mL 2- mL mL 3- mL mL b- Methyl orange runs Volume of unkown solution Volume of HCl 1- mL mL 2- mL mL 3- mL mL 28 Instructor's Signature ----------------------------- Experiment (7) Precipitation Titrations (Argentometric Titrations) _________________________________________________________________________________ Introduction A special type of titrimetric procedures involves the formation of precipitates during the course of a titration. The titrant react with the analyte forming an insoluble material and the titration continues till the very last amount of analyte is consumed. The first drop of titrant in excess will react with an indicator resulting in a color change and announcing the termination of the titration. Argentometric Titrations: It is the most famous example for precipitation titration and it is the most widely applicable precipitation titrations involve the use of silver nitrate with chlorides, bromides, iodides, and thiocyanate. Since silver is always there, precipitation titrations are referred to as Argentometric titrations. This implies that this type of titration is relatively limited. According to end point detection method, three main procedures are widely used depending on the type of application. These are: a. Mohr Method 29 This method utilizes chromate as an indicator. Chromate forms a precipitate with Ag + but this precipitate has a greater solubility than that of AgCl, for example. Therefore, AgCl is formed first and after all Cl- is consumed, the first drop of Ag+ in excess will react with the chromate indicator giving a reddish precipitate. 2 Ag+ + CrO42-  Ag2CrO4 (s) In this method, neutral medium should be used since, in alkaline solutions, silver will react with the hydroxide ions forming AgOH. In acidic solutions, chromate will be converted to dichromate. Therefore, the pH of solution should be kept at about 7. There is always some error in this method because a dilute chromate solution is used due to the intense color of the indicator. This will require additional amount of Ag + for the Ag2CrO4 to form.. b. Volhard Method + The Volhard method of Ag determination is associated with argentometric titrations even though the titrating agent is actually SCN- : Volhard titration reaction Ag + + SCN-  AgSCN(s) Analyte titrant 3+ The indicator in Volhard titrations is Fe , which reacts with titrant to form a red colored complex: Volhard titration reaction Fe 3+ + SCN-  Fe(SCN)2+ (aq) indicator titrant red complex This is an indirect method for chloride determination where an excess amount of standard Ag+ is added to the chloride solution containing Fe3+ as an indicator. The excess Ag+ is then titrated with standard SCN- solution until a red color is obtained this procedure known as back-titration. The indicator system is very sensitive and usually good results are obtained. The medium should be acidic to avoid the formation of Fe(OH) 3. However, the use of acidic medium together with added SCN- titrant increase the solubility of the precipitate leading to significant errors. This problem had been overcome by two main procedures: 30 The first includes addition of some nitrobenzene, which surrounds the precipitate and shields it from the aqueous medium. The second procedure involves filtration of the precipitate directly after precipitation, which protects the precipitate from coming in contact with the added SCN- solution. C. Fajans Method Fluorescein and its derivatives are adsorbed to the surface of colloidal AgCl. After all chloride is used, the first drop of Ag+ will react with fluorescein (FI-) forming a reddish color. Ag+ + FI-  AgF Since fluorescein and its derivatives are weak acids, the pH of the solution should be slightly alkaline to keep the indicator in the anion form but, at the same time, is not alkaline enough to convert Ag+ into AgOH. Fluorescein derivatives that are stronger acids than fluorescien (like eosin) can be used at acidic pH without problems. This method is simple and results obtained are reproducible. If the reaction is run in neutral or basic solution some of the indicator will dissolve to form the dichlorofluorescinate anion, which is represented as (FI-). Before the + equivalence point, with Ag as titrant, excess Cl - is present in solution. The excess - Cl is adsorbed onto the precipitate particles formed and the indicator anion is repelled by the negatively-charged precipitate. Ag + (aq) + 2Cl - (aq)  AgCl:Cl - (s) - At the equivalence point, there is little or no excess Cl , and just beyond the + equivalence point Ag is in excess and becomes the primary adsorbed ion. The charge on the precipitate changes from negative to positive and the indicator anion is adsorbed. AgCl:Cl - (s) + Ag + (aq)  AgCl:Ag + (s) + Cl - (aq) AgCl:Ag + (s) + FI- (aq)  AgCl:Ag + FI- (s) yellow rose-pink 31 The color change is: yellow rose-pink + It is believed that the indicator anion (yellow) forms a complex ion with Ag , adsorbed on the silver chloride precipitate, which alters its light-absorbing properties, and hence its color. The indicator function is critically dependent on the availability of a large precipitate surface area to allow adsorption. The greatest surface area results from a precipitate comprised of very small particles (colloidal). Stabilization of these colloidal particles (recall that a colloid has a very high surface- to-volume ratio) is accomplished by adding a protective colloid, such as dextrin. Since fluorescein and its derivatives are weak acids, the pH of the solution should be slightly alkaline to keep the indicator in the anion form but, at the same time, is not alkaline enough to convert Ag+ into AgOH. Fluorescein derivatives that are stronger acids than fluorescien (like eosin) can be used at acidic pH without problems. This method is simple and results obtained are reproducible. In this experiment, we will be using dichlorofluorescein, a Fajans (adsorption) indicator, and Ferric, a Volhard to make determination of Cl-. silver chloride is light sensitive and excessive photodecomposition will produce erroneous results, according to the reaction: AgCl(s) + hv Ag (s)+ ½ Cl2 The precipitate becomes violet-purple, due to the presence of finely divided silver metal, and results will be low. Experimental Procedure a-`Standardization of ca. 0.1 M of silver nitrate by Fajan's metod 1- Dry the sample and NaCl primary standard for at least one hour at 110 °C. Cool in a desiccators. 2- Weigh accurately 0.5 g sample of the pure NaCl (to the nearest 0.1 mg) in a weighing bottle Dissolve in distilled water then transfer quantitatively into 100 mL volumetric flask, make shore that all the solid is dissolved by shaking well then complete to the mark. 32 3- Using a 10 mL pipet, transfer exactly 10.00 mL of the standard solution ( chloride solution) into an 250 mL Erlenmeyer flask. 4- Add 5 mL of 2% dextrin solution and 10 drops of 0.1% dichlorofluorescein solution to the first flask. The purpose of the dextrin solution is to stabilize the colloidal suspension of AgCl(s) formed. 5- Titrate against standard AgNO3 solution at a rapid rate, using continuous swirling until a permanent change in the color of indicator is observed. Record the volume of AgNO 3 solution consumed. Repeat the titration another two times 6- Calculate the molarity and the weight per liter of silver nitrate. After completing your titrations, dispose of the AgCl(s) and titrating solutions by pouring them into the waste bottles in the hood that are marked “AgCl(s)Waste.” Also return any unused titrant solution to the instructor. Anything that contained AgNO3 should be rinsed thoroughly before being put away. b- Standardization of ca. 0.1 M of potassium thiocyanate by Volhard's method 1- Using a 10 mL pipet, transfer exactly 10.00 mL of silver solution into 250 mL Erlenmeyer flask. 2- Add 50 mL of distilled water, 2.5 mL of 6 M of HNO 3 solution provided, 1 mL of ferric indicator solution and 2 mL of nitrobenzene and shake vigorously. (you may need to seal the flask with parafilm) 3- Titrate against KSCN solution until the red brown color of Fe(SCN)2+ is permenant for one minute. Record the volume of KSCN solution consumed. Repeat the titration another two times 4- Calculate the molarity and the weight per liter of potassium thiocyanate. c- Determination of a mixture of halides (NaCl+KCl) according to Volhard's method 1- Pipet 10 mL of unknown mixture solution into 250 mL conical flask. 33 2- Add 50 mL of distilled water, 2.5 mL of 6 M of HNO 3 solution provided, 1 mL of ferric indicator solution and 2 mL of nitrobenzene and shake vigorously. Add exactly 20.0 mL of standard solution of silver nitrate ( part a). 3- Titrate against standard KSCN solution record the volume, repeat this titration another two times. 5. Calculate the concentration of chloride in the unknown mixture according to the following equations Let W1 (g) is the weight of the mixture in 10.0 mL which contains x g of NaCl and y g of KCl then x  y  W1 eq (1) x y   MV eq ( 2 ) 58.5 74.5 Where M is the molarity of AgNO3 and V is the volume of AgNO3 required for the titration x + y = 6.5 g/ L in unknown solution Data Sheet a- `Standardization of ca. 0.1 M of silver nitrate by Fajan's metod Weight of NaCl---------------------------g Volume of NaCl solution Volume of AgNO3 1- mL mL 2- mL mL 3- mL mL b- Standardization of ca. 0.1 M of potassium thiocyanate by Volhard's method 34 Volume of AgNO3 solution Volume of KSCN solution 1- mL mL 2- mL mL 3- mL mL c- Determination of a mixture of halides (NaCl+KCl) according to Volhard's method Volume of unknown solution mixture Volume of KSCN solution 1- mL mL 2- mL mL 3- mL mL Instructor's Signature ----------------------------- Questions 1- In Fajan's method what is the function of dextrine ? 2- Why you use 1 mL of indicator not for example 3-4 drops of indictor? 3- Write all the chemical equations for the adsorption indicator (FI-) with AgCl precipitate. 4- In Volhard's method what is the function of adding nitrobenzene and HNO 3? 35 Oxidation-Reduction Reactions (Redox Titration) Experiment (8) Determination of the Volume of Strength of Hydrogen Peroxide solution by using Potassium Permanganate solution. _________________________________________________________________________________________________ Introduction Solutions of permanganate ion are strong oxidizing reagent; the aqueous solutions of permanganate are not entirely stable because the ion tends to oxidize water 4MnO4+ 2H2O 2MnO2(s) + 3O2(g) + 4OH- 36 Standardized solutions of permanganate should be stored in the dark. Filtration and restandardization are required if any solid (MnO2) is detected in the solution or the walls of the storage bottle. The volume strength of H2O2 solution is the number of ml of oxygen that can be obtained by complete thermal decomposition of the solution. Under these conditions, decomposition occurs according to the equation:- 2H2O2 2H2O + O2 The volume strength of H2O2 can be determined by using standard solution permanganate. The reaction is 2MnO4+ 5H2O2 + 6H + 2Mn2+ + 5O2 + 8H2O The potassium permanganate is previously standardized against sodium oxalate in acid solution. The reaction is: 2MnO4+ 5H2C2O4 + 6H + 2Mn2+ + 10CO2 + 8H2O Potassium permanganate acts as its own indicator both in the standardization and in the determination of the volume strength. Experimental Procedure a-`Standardization of 0.02 M of potassium permanganate solution. 1- Weigh about 0.2- 0.3 g of primary-standard sodium oxalate (Na2C2O4) sample (to the nearest 0.1 mg) that is previously dried at 110oC for at least 1 hr. 2- Transfer this sample quantitatively into 100 mL volumetric flask. 3- Pipette 10.00 mL the oxalate solution and put into a conical flask. 4- Add about 80 mL of 1M of H2SO4. Heat each solution to 80 - 90 °C. 37 5- Titrate slowly with permanganate whilst or stirring with a thermometer. If the solution remains pink after adding the first drop or two, wait until it clears before continuing the titration. 6- Continue the titration slowly until a faint permanent pink tinge is obtained. The temperature should not be less than 60oC at the end-point. If it falls below this during the titration, the solution must be reheated. The end point is marked by the appearance of a faint pink color that persists at least 30 s. 7- Repeat this process to obtain a mean value for the molar concentration of the permanganate. 8- Determine a blank by titrating an equal volume of the 1 M H 2SO4. Correct the titration data for the blank, and calculate the concentration of the permanganate solution b- Determination of the volume strength of an unknown sample 1- Pipette 10 mL of H2O2 solution into 100 mL volumetric flask and adjust to volume with water. 2- Transfer by means of a pipette a 20 mL portion of the above solution. 3- Add to it 10 mL of 50 % v/v sulfuric acid. Titrate with KMnO 4 standard solution until reaching the end point. Repeat the titration for another time. Calculate the % w/v of H2O2 by using the balance equation and also by using the following relationship: 0.001701 g H2O2 is equivalent of 1 mL of 0.1 N of KMnO4 Compare between the two results. Calculate the volume of strength of the solution if given that: 68.04 g H2O2 = 22400 mL O2 1 g H2O2 = 329.2 mL O2 38 Data Sheet a- Standardization of KMnO4 Weight of sodium oxalate---------------------------g Volume of Na2C2O4 solution Volume of KMnO4 1- ml ml 2- ml ml 3- ml ml b- Determination of the volume strength 39 Volume of H2O2 solution Volume of KMnO4 1- ml ml 2- ml ml 3- ml ml Instructor's Signature ------------------------------ Oxidation-Reduction Reactions (Redox Titration) Experiment (9) The Determination of Iron (III) in a Given Sample by Titration with Potassium Dichromate solution _________________________________________________________________________________________________ Introduction Numerous oxidants are used to determine reducing agents by titration. Among the most important are permanganate (MnO4-), dichromate (Cr2O72-) and iodine (I2). Strong oxidants (MnO4- and Cr2O72-) can be employed for determination of iron (II) by oxidizing it to iron ( III). Various other compounds can be determined in a similar fashion. In this experiment you will use a standard solution of potassium dichromate (K 2Cr2O7) to determine the percent by 40 weight of iron (as Fe2+) in an unknown sample. Dichromate ion reduces to two chromium (III) ions. This reaction requires 6 electrons and 14 hydrogen ions: Cr2O72+ 14H+ + 6e- 2Cr3+ + 7H2O Only one electron is necessary to reduce Fe (III) to Fe(II) Fe3+ + e- Fe2+ Therefore, 1 mole of Cr2O72(the oxidizing agent) reacts with 6 moles of Fe2+ (the reducing agent) to form 6 moles of Fe3+ and 2 moles of Cr3+. Thus, in net ionic form: Cr2O72+ 6Fe2+ + 14H+ 6Fe3+ + 2Cr3+ + 7H2O The molecular form of the reaction equation can be written as: K2Cr2O7 + 6Fe(NH4)2(SO4)2 + 7H2SO4 3Fe2(SO4)3 + Cr2(SO4)3 + K2SO4 + 6(NH4)2SO4 + 7H2O The 1:6 mole ratio with respect to the amounts of Cr2O72and Fe2+ consumed will provide the stoichiometric basis for all of the calculations in this experiment. In this experiment a mixture of Fe (II) and Fe(III) will be analyzed by using a standard of K2Cr2O7. The K2Cr2O7 can not react with the oxidized form of iron for that prereduction to Fe (II) must precede titration with the oxidant. The most satisfactory prereductant for iron is tin (II) chloride (SnCl2): 2Fe3+ + Sn2+ 2Fe2+ + Sn4+ The excess reducing agent is eliminated by the addition of mercury(II) chloride (HgCl2): Sn2+ + 2HgCl2 Hg2Cl2(s) + Sn4+ + 2Cl- Experimental Procedure 41 a-`Standardization of 0.02 M of potassium dichromate solution. 1- Precisely weigh by difference from a weighing bottle, between 0.2-0.3 g of the refried, primary standard Fe (NH4)2(SO4)2. 2-Transfer this sample quantitatively into 100 ml volumetric flask. Carefully dilute the Fe(NH4)2(SO4)2 solution with deionized water up to the calibration mark of the 100 ml volumetric flask. 3- Using a 10 mL pipet, transfer exactly 10.00 mL of the standard solution into an Erlenmeyer flask. 4. Using a graduated cylinder, add 25 mL of 1 M H2SO4 to flask. Then add 10 mL of syrupy phosphoric acid (H3PO4) and 8 drops of sodium diphenylamine sulfonate indicator to the flask. Swirl the flask gently to mix the contents. 5. Fill your buret with the solution and drain out enough so that the liquid level is just below the upper calibration mark and the buret tip is full. Read the initial volume from the calibration scale on the buret. This reading and all other buret readings should be estimated to the nearest 0.01 mL. 6. Titrate the iron (II) solution in the flask with K 2Cr2O7 solution from a blue-green, through a grayish tinge to the first permanent intense purple ( Blue-violet) color produced by the first drop of excess K2Cr2O7 signals the end point for the titration. The titration should be conducted dropwise when the grey tinge is noted because the oxidation of the indicator is somewhat slow at this point. Obtain the final volume reading from the calibration scale on the buret. 7. Repeat step 6 twice. The volume of K 2Cr2O7 solution used should agree with the first titration within 0.20 mL. In addition, obtain a mean value for the molar concentration of the dichromate solution. b- Determination of an unknown of Fe(II) and Fe(III) mixture. 42 1- Using a 10 mL pipet, transfer exactly 10.00 mL of an unknown mixture into an Erlenmeyer flask. 2- Using a graduated cylinder, add 25 mL of 1 M H 2SO4 to flask. Then add 10 mL of syrupy phosphoric acid (H3PO4) and 8 drops of sodium diphenylamine sulfonate indicator to the flask. Swirl the flask gently to mix the contents. Titrate with the standard solution of K 2Cr2O7 until reaching the end point, repeat the titration and calculate the amount of Fe (II) in the mixture in g/L. Reduction of Fe(III) to Fe(II) and Titration of Fe(II) The reduction step must be done one trial at a time and the titration of that sample must be done immediately after the reduction. This is because the reduced Fe2+ is readily oxidized in air to Fe3+. Note the oxidized form of the iron does not react with K 2Cr2O7. The reduction of iron (III) to iron (II) can be established as follows:- 1- Pipette another 10 mL of the unknown mixture into an Erlenmeyer flask. 2- Heat this solution containing the iron sample almost to boiling. Stop heating and carefully add tin(II) chloride (SnCl2) solution dropwise with stirring until the yellow Fe(III) color just disappears. Then add only 2 drops excess of SnCl2 solution. 3- Cool by running the outside of the flask under the tap cold water (until the flask can be comfortably held, Ag > Cs > Rb > K > NH4 > Na > H > Li 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ 2+ Divalent: Ba > Pb > Sr > Ca > Ni > Cd > Cu > Co > Zn > Mg > UO2 2- 2- - - - - - - - - Anions: SO4 > C2O4 > I > NO3 > Br > Cl > HCO2 > CH3CO2 > OH > F + - Once ions are introduced to column, more H or OH is added, replacing ions on exchanger, causing the ions to migrate to end / be eluted from column. Experimental Procedure a-Preparation of Ion-Exchange Columns 1- Get a typical ion-exchange column which is a cylinder of 25 to 40 cm in length and 1-1.5 cm in diameter. A buret makes a convenient column. 2- Insert a plug of glass wool to retain the resin particles and fill it with distilled water. 3- Take about 15 mL (40 g) from the cation exchange resin and put it in 400 mL beaker and cover this resin with distilled water. 4- Transfer about 10 mL of 4M of HCl to this 400 mL beaker , mix the contents of the beaker with stirring glass-rod then let the beaker to stand for few minutes then make an occasional stirring. This treatment of acid is useful to get red of any cations that may attach to the resin (impurities) and make replacement by hydrogen ions. 5- Make decantation for the solution and start washing of this resin several times with distilled water until the wash solution shows the alkaline color of the methyl orange. 6- After washing with distilled water, begin to transfer the slurry to the column while opening the stopcock until the settled resin reaches to about the 40 mL mark, the add sufficient distilled water to cover the resin. 55 Remark: Do not allow the level of water in the column to fall below the surface of the resin bed and make sure that there are no air bubbles while packing of the column. b- Determination of the concentration an unknown of Ca2+ 1- Pipette 10.00 mL of an unknown sample and transfer it onto column and pass it through the resin bed let the unknown solution stand for five mints. 2- Open the stopcock of the column and begin to collect the effluents in slowly drain in 250 mL conical flask while washing of the resin in the same flask until the last washing shows the basic color of the indicator. 3- Take the collected solution which, is present in the flask and titrate it with 0.05M of NaOH until reaching the end point by using phenolphthalein indicator. Calculate the amount of the calcium by ppm concentration. Data Sheet Volume of 0.05M of NaOH solution Volume of unknown 1- mL mL 2- mL mL 3- mL mL 56 Instructor's Signature ------------------------------ Questions 1- What do we mean by regeneration of resin? 2- The synthetic ion-exchanger resin are made from polymers, name these polymers. 3- Did these polymers dissolved in water explain your answer? 4- How you could calculate the concentration of your unknown by unit called milliequivalents per Liter 57 58

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