Chapter 4  Measurements, Solutions and Calibration

 

 

          Similar to the production of high quality goods by master craftsmen, the analyst must use measurement tools of the highest quality, in order to prove an answer to a laboratory test that is indicative of the actual amount of the analyte in the sample.  The tools the analyst uses are volumetric glassware, analytical balances and analytical instruments.  To a large extent the accuracy of these tools is directly related to the initial cost and the time spent on maintenance and calibration.  Each of these categories of tools and their care are the topics of this chapter.

Reading scales and displays generally involve seeing and recording numbers. Please, please remember that 'numbers by themselves mean nothing'. The engineering units are vital to knowing what the numbers mean. Always, always append the engineering unit [inches, kilos, kps]. Use appropriate notations [standard, fixed or scientific] and calculate according to significant numbers.

          Erlenmeyer flasks and beakers are not volumetric measuring tools.  They are, in many cases, marked with approximate volume indication. However, even in the most reliable flasks and beakers, there is a ±5 % uncertainty in where the volume line actually belongs.  There are only five volumetric measuring devices recognized as suitable for accurate and precise analytical work.  They are:  burets, volumetric flasks, volumetric (transfer) pipets, glass measuring pipets and graduated cylinders.  Produced and calibrated in accordance with ASTM standards.¹  They are available in either of two grades, Class A and Class B. Class B is sometimes called student or economy grade, although in certain cases these designators indicate containers of even lower quality than Class B.

          The ASTM standards define the tolerances within which the markings are placed on the glass, with Class A glassware having the smallest tolerances.  The Class B tolerances are, in general, twice the acceptance range of the Class A values (see Tables 4-1 through 4-4).  All plastic (Teflon®, polypropylene, polymethylpentene and polyethylene) volumetric containers are Class B.  Class A volumetric glassware will always have a large “A” prominent near the label on the piece.  Glassware without an obvious “A” is Class B or of lesser accuracy.

          Some of the glassware manufacturers have been offering two types of Class A calibrated volumetric ware.  The first is a generic Class A line of glassware.  The second type is a certified/serialized Class A and comes complete with documentation and traceability to NIST, which is required for certification to ISO 9000 standards.

Table 4-1.  Comparison of Class A and Class B tolerances for Volumetric Flasks.  Tolerances are in mL.			Table 4-2.  Comparison of Class A and Class B tolerances for Pipets.  Tolerances are in mL.			Table 4-3.  Comparison of Class A and Class B tolerances for Graduated Cylinders.  Tolerances are in mL.			Table 4-4.  Comparison of Class A and Class B tolerances for Burets.  Tolerances are in mL.
Nominal Volume mL	Class A tolerance	Class B tolerance	Nominal Volume mL	Class A tolerance	Class B tolerance	Nominal Volume mL	Class A tolerance	Class B tolerance	Nominal Volume mL	Class A tolerance	Class B tolerance
10	±0.02	±0.04	1	±0.006	±0.012	10	±0.08	±0.1	10	±0.02	±0.04
25	±0.03	±0.06	5	±0.01	±0.02	25	±0.14	±0.3	25	±0.03	±0.06
50	±0.05	±0.10	10	±0.02	±0.04	50	±0.20	±0.4	50	±0.05	±0.10
100	±0.08	±0.16	25	±0.03	±0.06	100	±0.35	±0.6	100	±0.10	±0.20
250	±0.12	±0.24	50	±0.05	±0.10	250	±0.65	±1.4
500	±0.20	±0.40	100	±0.08	±0.16	500	±1.10	±2.6
1000	±0.30	±0.60				1000	±2.00	±5.0
2000	±0.50	±1.00				2000	----	±10.0

                         Pipets are used for accurate volume measurements and transfer.  There are three types of pipets commonly used in the laboratory:  volumetric pipets, graduated or Mohr pipets, and serological pipets.  Volumetric pipets are used to deliver a single volume.  Measuring pipets (graduated) will deliver fractions of the total volume.

                 Pipets come in a variety of shapes and sizes.  Measuring pipets can be differentiated from volumetric pipets by the presence of a graduated volume scale on the side of the measuring pipet.  There are two types of graduated pipets commonly found in the laboratory.  The measuring pipet (Mohr) is graduated from a zero mark near the top of the pipet to a baseline near the tip of the pipet.  Mohr pipets are intended to indicate the delivered volume of liquid by the difference between the initial and final liquid position, with delivery of the maximum calibrated volume leaving the tip of the pipet full of liquid.  Mohr pipets come in calibrations with Class A and Class B tolerances, which are the same as those of the volumetric pipets.  A serological pipet is graduated from a zero mark near the top of the pipet to the very tip of the pipet.  It can be used to indicate the difference between the initial and final liquid levels similar to the Mohr pipet, however to deliver the whole calibrated amount, the pipet is blown out with a pipet bulb such that no liquid remains in the tip.  The best serological pipets are available only with Class B tolerances.  Pipets with wide tips for measuring sludges and other viscous liquids are serological pipets.  Disposable serological pipets made of glass or plastic are available and calibrated to Class B or lesser accuracy.

                 Volumetric pipets have a bubble in the shaft of the pipet and, in general, a single calibration mark.  Volumetric pipets come in “To Contain” (TC) and “To Deliver” (TD) calibrations.  There is a special volumetric pipet called a Dual Purpose pipet which has calibration marks with Class A tolerances for both TC and TD use.  The recommended procedure for emptying volumetric pipets is:  held in the vertical position;  unrestricted outflow;  tip touched to wet surface or receiving vessel and kept in contact until the emptying is complete;  Under no circumstances should the small amount remaining in the tip be blown out.

 

Proper use of volumetric glassware

                 The first consideration in the use of volumetric glassware is the temperature.  Glass more closely resembles a very viscous solution than it does a crystalline solid.  The properties of glass can be varied greatly by varying the additives.  For example, addition of B₂O₃ produces a glass (called borosilicate glass) that expands and contracts little under large temperature changes.  Thus it is useful for labware and cooking utensils.  Glass is an amorphous solid containing a good deal of disorder.  Not only do different types of glass have different rates of expansion but different areas of the same piece of glass have different rates of expansion, so, there is no universal correction factor for temperature variation.  Instead, the temperature at the time of calibration is normally etched on the piece.  When none is etched, 20^º C is assumed.

                 Furthermore, the solutions change volumes, most expanding when raising the temperature.  Water is significantly unique in its behavior, shrinking in volume from 0 to 4^º C, thereafter expanding with temperature rise.  This volume variation affects the reagent concentration.  Diluting most acids and bases in water is exothermic, whereas dissolving ammonium chloride is endothermic.  Therefore, final volume adjustments should always be delayed until the solution’s temperature has stabilized at the initial temperature.

                 ‘Dilute to the mark’ and ‘read the meniscus’ are common instructions for preparation of solutions or titrating.  Most calibration marks on volumetric glassware extend all the way around, aiding orientation of the eye and the container in order to see a single straight line just intersecting with the bottom curve of the liquid.

                 If the container is a TC device, the entire contents are the correct volume.  Then transferring the contents to another container, a quantitative transfer must be made.  This entails blowing out the pipet with a pipet bulb and rinsing the inside of the pipet with additional solvent from a squeeze bottle, or rinsing the flask or cylinder with additional solvent.

                 For TD containers, a flowtime must be observed.  Proper dispensing of solution from a TD pipet requires touching the pipet tip to the inside wall of the receiving container and maintaining contact for at least the time determined by Table 4-5.  The reason is to allow all of the water film on the inside of the pipet to drain off, so you get the full accuracy the pipet is capable of.  If you watch, you can see that takes a while.  Really accurate pipets, like class A, should be designed with narrow enough holes in the tip to make them drain so slowly that the film draining would keep up with the bulk draining, and the timing could take care of itself.

Table 4-5.  Flowtimes for TD pipets

Nominal Volume mL	Class A Flowtime (sec)	Class B Flowtime (sec)
1	10	3
10	15	8
25	25	15
50	25	15
100	30	30

                 For solutions which have a different density or viscosity than pure water, the flowtimes are not correct, and the analyst should consider using a TC pipet because the error associated with the retained solution in the tip of the TD pipet generally exceeds the manufacturing tolerance of the TC pipet.  Similar consideration apply to the use of pipet pumps and pipet bulbs.  Certainly the analyst should never pipet by mouth, especially in a wastewater laboratory, therefore pipetting aids are necessary.  However the calibration of the pipet is performed assuming only gravity is affecting the liquid flow and it is not being pushed out of the pipet rapidly by air pressure.

                 A solution consists of a dissolved substance, the solute, and a dissolving medium, the solvent.  A solution is a homogeneous mixture and has a constant composition throughout.  A solute need not be a solid.  If the solution contains two liquids, the liquid that is in excess is conventionally called the solvent.  The most common solvent is water.

                 Titration is an experimental procedure in which the unknown concentration of a known volume of solution is determined by measuring the volume of a solution of known concentration required to react completely with it.

                 The three types of titration reactions are:

• (1) an acid with a base to give a soluble salt and water,
• (2) a soluble salt with a second soluble salt (or complexing agent)  to give a precipitate, and
• (3) an oxidizing material with a reducing material.

  The four general steps used during a chemical titration are:

• (1) Record level in buret (titrant),
• (2) Record volume of sample,
• (3) Add titrant until end point is reached,
• (4) Record level of titrant.

  When using a buret for dispensing solutions, such as in a titration, the correct procedure is to fill the buret to the very top, then open the stopcock and allow liquid to drain out until the air bubble in the tip of the buret is flushed.  Refill the buret, drain until the meniscus matches the zero mark and record the volume.  Perform the titration by adding drops from the buret to the rapidly stirred solution until the permanent endpoint is close (very near), indicated by the color change first occurring on addition of the drop, then rapidly fading back to the initial state.  Very accurate work can be performed by opening the stopcock a little until a partial drop appears, closing the stopcock and the using a squeeze bottle to air wash the liquid off the tip of the buret and into the titration solution.  Remember to wash the sides of the titration flask down with a little water to insure that all the reagent delivered to the flask has reacted with the solution.  Before pouring the titrant into the buret, be sure mix it so that any condensed water vapor on the upper surfaces of the inside of the bottle is recombined with the rest of the solution.  Otherwise the titrant will be too strong.  this is important when pipetting standard solutions out of bottles.  Record the end volume off the buret onto the benchsheet (lab data book).  The fastest work with a buret is achieved by performing a rough titration on an aliquot of sample to give an idea of the volume required, then taking a second aliquot of sample, rapidly adding a little less than the volume needed from the buret, then carefully finishing the titration in a dropwise fashion.  The most accurate results are obtained by performing careful titrations in duplicate, then averaging the values.

                 Documentation:  Running all these tests will be effective only when properly documented.  Neat, legible and complete information written (or recorded) will communicate to others, less is unacceptable.  Document the raw data as soon as possible.  Verify.  The information is useful only if accurate and complete.  Schedule time for transferring data to files for legal requirements and process control analysis.  The lab technician will have completed the task ONLY when the results of the sample analysis are properly documented.

                 There is no standard laboratory form (Benchsheets).  Most operators usually develop their own data sheets for recording test results and other important data.  These data sheets should be prepared in a manner that makes it easy for you to record results, review them, and recover these results when it is necessary.  Each facility will have different needs for collecting and recording data and may require several different data or worksheets or benchsheets.

                            Volumetric glassware should never be placed in an oven.  The etched markings on the glassware weaken the piece at that point and the stresses from the heating are sufficient to cause a crack.  Sterilization in an autoclave is permissible but allow a long slow cool down on the order of one to two hours.  Likewise, graduated cylinders should never be used for mixing solutions.  The exothermic reactions are sufficient to crack the container where etching identifies volumes.

Calibration of nonstandard volumetric measuring devices

                 There are numerous tools used in the laboratory for fluid measuring and transfer which one would like to calibrate to the maximum accuracy possible.  Examples include BOD bottles, colorimetric tubes, syringes, diluters, bottle-top dispensers and disposable tip adjustable and fixed volume pipetters.  These can easily be calibrated.  All one needs is an analytical balance, a source of reagent water, a standardized thermometer, a calibration logbook and a table of water densities (or specific gravity) such as that found in the Handbook of Chemistry and Physics.

                 First, let everything equalize to room temperature and place the thermometer in the container of reagent water.  Dispense (measure) a volume of water from the device to be calibrated onto the analytical balance.  Record the weight in grams of water dispensed.  Repeat this at least two more times, then determine the average weight.  Record the temperature.  Look up the density of water in the table and divide the average weight of water dispensed by the density (g/mL).  The resulting number is the actual volume dispensed in mL.

                 Calibration of bottles and other containers is performed by calculating the weight of water at the ambient temperature corresponding to the desired volume, then adding water to the container while on the balance until the proper weight is obtained.  The meniscus position is permanently marked by etching a line on the bottle with a diamond point pen or file.  Once a glass container is etched with a volume marking it should never be subjected to thermal stress.

                 For devices which have moving parts and require preventative maintenance such as the diluters, dispensers and pipetters, this procedure should be repeated at regular intervals, such as weekly.  The reason for this is that it serves as a check on the state of the seals and lubricants inside the devices.  For example, one lab checks the calibrations on their disposable tip pipetters weekly and calculates the relative variation on the mean of three determinations from the true volume, and the relative standard deviations of the three determinations.  For a 1,000 mL adjustable pipetter the first week gave 1.0141 mL (±1.59% variation) and 0.15% RSD, the second week gave 1.0170 mL (±1.86%) and 0.65 RSD and the third week gave 1.0454 mL (±4.8%) and 5.1% RSD indicating the seals/lubricant were failing.  After cleaning/repair and relubrication, the calibration of the pipetter gave 1.0066 mL (±0.9%) and 0.28% RSD.  Other than checking, the calibration on a regular basis, there was no indication that the device was in a failing mode.  For adjustable volume pipetters, at least two volumes, one high and one low, should be checked.  Some have found that these types of devices are irregular in their failures, but generally require major cleaning or replacement every one to three months.

 

Analytical balances

                 The weighing of solids in the laboratory is essential for preparing reagents and it is the final determinative instrument for solids analyses.  It is quite rare to see the old chain and arm balances in the wide glass and wood cabinets still in use in analytical labs, however these are just as usable as modern electronic balances.  In fact, some new instruments work on the same principle.  Most analytical balances are reproducibly sensitive to the ten thousandth of a gram (0.00001 g)(1 mg = .001 g, 0.01 mg = 0.00001 g) if situated on a vibration free platform in an area not subject to stray air currents or temperature variation.  Analytical balances have limited working ranges, often only to 100 or 200 grams.  The more sensitive the balance, the smaller the range.  Less sensitive balances such as top-loaders and mechanical triple beam scales should be used in situations where greater range is needed.

                 Just as with all mechanical devices the accuracy of a balance depends on the frequency of calibration.  The calibration of an analytical balance should be performed by a professional service technician and it should be performed at least once each year.  “Self-calibration” is always doubtful and the analyst must note the status.  Analytical balances must be checked for accuracy against an independent standard at least once a month.  The professional analyst will check the balance calibration every time it is used.  The calibration is checked by placing a calibration weight on the balance and verifying that the balance indicates a weight within the manufacturer’s tolerances of the balance.  Repeatable out-of-tolerance results indicate the need for a qualified service technician. 

Calibration weight sets are available in a wide variety of grades.  The NIST Class S weights have been the standard for checking the calibration of analytical balances for many years, however these are no longer commercially available.  An equivalent standard is the ANSI/ASTM Class 2 weights which have identical tolerances to the Class S series for the 1 mg to 10 g range.  ANSI/ASTM Class 1 weights are designed with even tighter tolerances, but the higher cost is justified only by the professional balance service technician.

                 Analytical balances and the work area around the balance must be kept clean at all times to provide reliable data.  Dirt is the most common cause for balance inaccuracy.  A dirty environment will result in more frequent visits by the service technician.

                 The tare function on an analytical balance is convenient to use but can hide problems and inaccuracies in the measurement.  Maximum confidence in the use of the analytical balance requires first setting the balance to zero with nothing on the weigh pan, checking the calibration with a test weight, then obtaining the weight of the empty sample container and writing it down on the benchsheet.  When the sample is ready for weighing, the procedure is repeated.  The tare function does not change the maximum range of the balance and it can result in errors in the case where another analyst has re-zeroed the balance while you are waiting for your sample to cool.

                 The maximum accuracy of the balance is obtained at the low end of the scale.  The maximum accuracy weight determination is obtained when the weight difference of the sample is large in comparison to the sample container.  For example, a solids analysis is being performed and the analyst has a choice of a value based on the difference between the following weights:

                 Tare              Final         % Weight Difference

                 35.0231       35.0256               0.0071

                 0.1231          0.1256                 2.03

the second situation represents about 500 times greater confidence in the result.  This is a specific example of the generalization that measurement of a small difference on a large background is a much poorer analytical situation than measurement of a large difference on a small background.

 

1080 C.  Reagent Water Quality

1.  Quality Guidelines

    Several guidelines for reagent water quality, based on contaminant levels, are available, but the final test is the appropriateness for the analysis.  Table 1080: II lists some characteristics of various qualities of reagent water.

Table 1080:II Reagent Water Specifications 

Quality Parameter	High	Medium	Low
Resistivity, megohm-cm at 25 º C	>10	>1	0.1
Conductivity, umho/cm at 25 º C	<0.1	<1	10
SiO2, mg/L	<0.05	<0.1	<1

    High-quality reagent water, having a minimum resistivity of 10 megohms-cm, 25^º C (in line), typically is prepared by distillation, deionization, or reverse osmosis treatment of feedwater followed by polishing with a mixed-bed deionizer and passage through a 0.2 um pore membrane filter.  Alternatively treat by reverse osmosis followed by carbon adsorption and deionization.  Determine quality at the time of production.  Mixed-bed deionizers typically add small amounts of organic matter to water, especially if the beds are fresh.  Resistivity should be >10 megohm-cm at 25^º C, measured in-line.  Resistivity measurements will not detect organics or nonionized contaminants, nor will they provide an accurate assessment of ionic contaminants at the microgram-per-liter level.

    Medium quality water typically is produced by distillation or deionization.  Resistivity should be >1 megohm-cm at 25^º C.

 

    

    Low-quality water should have a minimum resistivity of 0.1 megohm-cm, and may be used for glassware washing, preliminary rinsing of glassware, and as feedwater for production of higher-grade waters.

    The pH of high or medium quality water cannot be measured accurately without contaminating the water. Measure other constituents as required for individual tests.

    High-quality water cannot be stored without significant degradation; produce it continuously and use it immediately after processing.  Medium-quality water may be stored, but keep storage to a minimum and provide quality consistent with the intended use.  Store only in materials that protect the water from contamination, such as TFE and glass for organics analysis or plastics for metals.  Store low quality water in materials that protect the water from contamination.

 

Concentration

                 Concentration is a way of expressing how much of the stuff of interest is in the solution.  Most of the results from the laboratory are reported in terms of a concentration, for example:  milligrams per liter or parts per million parts.  Most reagents are prepared to a certain concentration which depends on the molecular weight of the reagent and the intended use.  So, an exposition on molecular weight follows.

                 Compounds are collections of elements in fixed numerical and weight (mass) proportions.  An example of a compound is common table salt, sodium chloride.  For each sodium atom in the compound there is one chlorine atom.  All samples of sodium chloride will have equal numbers of sodium and chlorine atoms.  Looking on a Periodic Chart one will find that the mass of a sodium atom is 22.990 atomic mass units (amu) and a chlorine atom is 35.453 amu.  If the amu unit is replaced with an equal number of grams, then one has defined the mass of a mole of sodium chloride, in this case 58.443 g.  In general, to find the molecular (or formula) mass of a compound the exact number and types of elements in the compound must be known.  Multiplying the mass of each element by the number of atoms of that element in the compound and summing the results for all the elements will give the molecular (or formula) mass.

 

Sodium Chloride NaCl
element	mass (amu)	number of atoms in compound		total
Sodium	22.990	1	=	22.990
Chlorine	35.453	1	=	±35.453
			total	58.443 amu

Calcium Chloride   CaCl2
element	mass (amu)	number of atoms in compound		total
Calcium	40.080	1	=	40.080
Chlorine	35.453	2	=	±70.906
			total	110.986 amu

Calcium Carbonate   CaC03
element	mass (amu)	number of atoms in compound		total
Calcium	40.080	1	=	40.080
Carbon	12.011	1	=	12.011
Oxygen	15.999	3	=	±47.997
			total	100.088 amu

                     Hydrates are compounds which have a definite number of water molecules associated with each molecular unit of the compound.  Examples of frequently encountered hydrates are bluestone (copper sulfate pentahydrate) and potassium hydrogen phosphate trihydrate.  The first compound has five molecules of water for every unit of copper sulfate, the second has three molecules of water for every unit of potassium hydrogen phosphate.

Water  H2O
element	mass (amu)	number of atoms in compound		total
Hydrogen	1.008	2	=	2.016
Oxygen	15.999	1	=	±15.999
			total	18.015 amu

Copper Sulfate   CuS04
element	mass (amu)	number of atoms in compound		total
Copper	63.456	1	=	63.456
Sulfur	32.06	1	=	32.060
Oxygen	15.999	4	=	±63.9960
			total	159.602 amu

   

Copper Sulfate Pentahydrate  CuS04• 5H2O
element	mass (amu)	number of atoms in compound		total
Copper	63.456	1	=	63.456
Sulfur	32.06	1	=	32.060
Oxygen	15.999	4	=	±63.9960
			total	159.602 amu
Water	18.015	5		±90.0750
			total	249.677 amu

Potassium Hydrogen Phosphate   K2HPO4
element	mass (amu)	number of atoms in compound		total
Potassium	39.098	2	=	78.196
Hydrogen	1.008	1	=	1.008
Phosphorous	30.974	1	=	30.974
Oxygen	15.999	4	=	±63.996
			total	174.174 amu

 

                            A key point is that  228.219 g of  potassium hydrogen phosphate trihydrate contains exactly 174.174 g of potassium hydrogen phosphate.  The only difference is that the first compound contains water and the second does not.  For example, a procedure calls for dissolving 5.00 g potassium hydrogen phosphate in 1000 mL of water, and only the trihydrate form is available on the chemical shelf.  The appropriate amount of the trihydrate to use is determined by mathematical calculation.

                      = 6.55 g

                 There is just one compound which contains only the elements sodium and chlorine:  sodium chloride (where the ratio of atoms is 1: 1).  Calcium chloride has two chlorine atoms for every calcium and the ratio is 1:2 of calcium to chlorine.  Other elements will combine in a variety of different ratios.  Iron and chlorine can combine 1: 2 or 1: 3 (FeCl₂, FeCl₃).  If a procedure calls for ferric chloride and ferrous chloride is substituted, the procedure probably will not work.

                 All the previous examples used inorganic compounds.  Organic compounds are very similar in that the chemical formula must be known to calculate the molecular weight (Mwt).  Organic compounds contain carbon and hydrogen with assorted amounts of other elements.  A few exceptions of organic compounds without hydrogen are known, such as CCl₄, carbon tetrachloride.

      Glucose C₆H₁₂O₆

Glucose C6H12O6
element	mass (amu)	number of atoms in compound		total
Carbon	12.011	6	=	72.066
Hydrogen	1.008	12	=	12.096
Oxygen	15.999	6	=	±95.994
			total	180.156 amu

Carbon Tetrachloride CCl4
element	mass (amu)	number of atoms in compound		total
Carbon	12.011	1	=	12.011
Chlorine	35.453	4	=	±141.812
			total	153.823 amu

                 Regardless of whether an inorganic or an organic compound is under consideration, the formula weight, formula mass, molecular mass, molecular weight, gram atomic weight, equivalent mass, or other terms for the same calculation represent the same number of molecules or formula units, which is called a “mole”.  153.823 g of carbon tetrachloride, 180.156 g of glucose and 228.219 g of potassium hydrogen phosphate trihydrate all contain the same number of compound units.

                 A frequently used concept in the environmental laboratory industry is to report differing forms of an element in terms of that element alone.  An example is reporting ammonia, organic nitrogen, nitrite and nitrate, all in terms of nitrogen.  The formula weight of each of these is :

 

Ammonia  NH3
element	mass (amu)	number of atoms in compound		total
Nitrogen	14.007	1	=	14.007
Hydrogen	1.008	3	=	±3.024
			total	17.031 amu

  

Nitrite  NO2-
element	mass (amu)	number of atoms in compound		total
Nitrogen	14.007	1	=	14.007
Oxygen	15.999	2	=	±31.998
			total	46.005 amu

  

                 The percent of nitrogen in each compound is different:

                 Ammonia     82.2 %  of the mass is Nitrogen      %       

                 Nitrite           30.4 %  of the mass is Nitrogen       %

                 Nitrate          22.6 %  of the mass is Nitrogen      %.

 

   Measure ammonia as mg/L NH₃ and you are asked to report it as ammonia-N, you must multiply by 0.822 to convert it.  And you must convert all measurements to N basis in order to add them together to get total inorganic nitrogen.

 

 

Quantitative solution chemistry

                 Manipulation and weighing of solid reagents, standards, and samples is tedious and messy.  A further limitation is placed upon weighing by the physical range of the scales and balances.  Many analytical determinations are in the low ppb [parts per billion] range, which is micrograms per liter and few analytical balances will weigh below 100 micrograms.  For these reasons, most of the chemistry in the water and wastewater laboratory is performed in solution.  The ability to manipulate solutions with a high degree of accuracy and obtain known concentrations of chemicals at very low levels is the strongest argument for the widespread use of solution chemistry.

                 Quantitative solution chemistry is based upon the mole concept.  Molarity is the number of moles of a substance in a liter of solution.  The molarity of the solution is symbolized by a number followed by an italicized capital M.                                     Other quantitative conventions are in existence, however, molarity is the most widely used concept used in the analytical laboratory.  A 1.00 M solution of sodium chloride (NaCl) contains 1 mole (58.443 g ) of sodium chloride dissolved in water to a final volume of 1000 mL.  1.00 mL of this solution contains 1/1000th of a mole (0.058443 g) of sodium chloride.  The analytical balance can accurately weigh 58.443 g  but not 0.058443 g.  The 1000 mL volumetric flask and the 1.00 mL volumetric pipet are used to achieve the desired accuracy from the initial weighing of 58.443 grams of sodium chloride.

                 A 0.100  M solution is prepared by dissolving 0.100 moles of a substance in water and diluting to a final volume of 1000 mL.  An alternate preparation is to dissolve 0.010 moles in 100 mL.  This allows preparation of a known concentration solution in an amount appropriate for the laboratory needs, without wasting reagents and taking up valuable storage space.  Note, however, that the accuracy of the knowledge of the solution concentration has decreased by a decimal place because of the limited accuracy of the analytical balance.

                                           

                 By knowing the chemical formula of the compound, the desired molarity and the desired volume any solution of known concentration can be prepared.  For example, 75.0 mL of a 0.247 M ferrous ammonium sulfate solution is needed and the only material on hand is ferrous ammonium sulfate hexahydrate (Fe[NH₄]₂[SO₄]₂ • 6H₂O).  The first step is to calculate the number of moles needed.

                 .       

The second step:  calculate the Mwt of the (Fe[NH₄]₂[SO₄]₂ • 6H₂O).

Fe[NH4]2[SO4]2 • 6H2O ferrous ammonium sulfate
element	mass (amu)	number of atoms in compound		total
Fe	55.847	1	=	55.847
N	14.007	2	=	28.014
H	1.008	8	=	8.064
S	32.06	2	=	64.12
O	15.999	8	=	±127.992
			total	284.037 amu
Water	18.015	6	=	±108.090
			total	392.13 amu

The third step:  calculate the mass required.

                

All that remains to be done is to dissolve this mass in water and dilute to a final volume of 75 mL.

                 The real power of solution chemistry  comes from the ability to make a concentrated solution from a highly accurate determination on an analytical balance and the prepare more dilute solutions of known concentration with a high degree of accuracy.   A 0.0010  M NaCl solution could be made directly by dissolving 0.058 g sodium chloride to 1000 mL in water, but if 1.00 mL of a 1.00 M NaCl solution is diluted to 1000 mL in a volumetric flask the final concentration can be calculated using a dilution equation thereby increasing the accuracy of the final concentration by a factor of 100.

.

                

                 A series of dilutions can be used to develop an intriguing paradox.  A mole contains 6.02 x 10²³ molecules (Avogadro’s Number) and a molecule is the smallest unit of a compound.  Suppose 180.156 g (1 mole) of glucose is dissolved in water and diluted to 1000 mL.  The resulting solution is 1.00 M and contains 6.02 x 10²³ molecules of glucose.  1.00 mL of this solution is then diluted to 1000 mL to give a 0.001000 M solution which contains 0.180156 g and 6.02 x 10²⁰ molecules of glucose.  1.00 mL of this solution is then diluted to 1000 mL giving a 0.000001000 M solution containing 0.000100156 g and 6.02 x 10¹⁷ molecules of glucose.  The ninth iteration calculates 0.602 molecules in the solution.  Clearly, taking things too far without all the facts present a paradox, a lie.  When you make that last transfer, there is about a 60% chance that you got a molecule of glucose in your 1 mL pipet, when you took 1 mL out of the 1 L flask containing 602 molecules of glucose.  So the final dilution either contains a glucose molecule (~60.2% chance), or it doesn't.  Of course, as they say, "there are lies, there are damn lies, and then there are statistics."

 

                 Example:  4.5060 g of NaOH is added to a 250.0 ml volumetric flask.  10.00 ml of this solution is then diluted to 500.00 ml in a second volumetric flask.  What is the final concentration?

GIVEN:

MASS OF SOLUTE = 4.5060 g

MOLECULAR WEIGHT OF SOLUTE = 39.99707 (22.98977±1.0079±15.9994)

VOLUME =.250 L

INITIAL VOLUME = 10.00 mL

FINAL VOLUME = 500 mL

                       

    

 

                 The concentration of a solute in a solution is often given in molarity (mol/L), molality (mol/kg), mole fraction (no units), and parts-per million [ppm] (no units).  In the case of a solute “a” dissolved in a solvent “b”, the following equations relate these concentrations to various parameters of the solution.

1) 

2)     3)

4)   5)

6)7)

8)

9) 

 

                 Normality  is an archaic but frequently encountered measure of the concentration of a solution.  Normality is based upon the reactions for which a solution is intended.  When acid-base reactions are considered the concept of Normality is straight forward.  A 1.00 Normal solution has one equivalent of acid or base per liter.  A 1 M solution of a monoacidic material is also 1 N.  (N is the symbol for Normality).  However, a 1 M solution of a di-acidic material such as sulfuric acid contains 2 moles of acidity per liter and is thus 2 N.  The idea is that 1.0 mL of a 1 N  solution always has the same amount of acidity regardless of whether a monoacidic or a di-acidic acid is used.  Base solutions can be dealt with in the same fashion.

                 The problem with Normality arises when reactions other than acid-base reactions are considered.  A common application is redox reactions.  Consider these two examples:

   acidic conditions  5Fe^2± ± MnO₄^- ± 8H^± t 5Fe^3± ± Mn^2± ± 4H₂O

   basic conditions    3Fe^2± ± MnO₄^- ± 2H₂O  t  3Fe^3± ± Mn^4±O₂ ± 4OH^-

In the first example there is a 5:1 ratio of iron to permanganate.  A 1 N  iron solution would be 1 M, and a 1 N  permanganate solution would be 0.2 M.  In the second reaction, which is conducted under alkaline conditions, there is a 3:1 relationship and a  1 N  permanganate solution would be 0.33 M.  Needless to say, the labeling of a 1 N  permanganate solution and placing it on the shelf can lead to a great deal of confusion, particularly when there are a large number of different procedures being performed in the lab.  Standard Methods  is currently moving away from the Normality notation, however its use will probably linger around like the English system of measure instead of the Metric. 

                 When the exact concentration of a chemical or compound in a solution is known, it is referred to as a “standard solution.”  Many time standard solutions can be ordered already prepared.  Once a standard has been prepared, it can then be used to standardize other solutions.  To standardize a solution means to determine its concentration accurately, thereby making it a standard solution.  “Standardization” is the process of using one solution of known concentration to determine the concentration of another solution and often involves a procedure called a “titration.”

 

Calibration

                 The imaginary tricorder used in the Star Trek series is becoming a reality as do many science fiction ideas.  Even so, it will also have to be calibrated routinely even if by a robot.  Chemical laboratories are now being manufactured on microchips.  They, too, will have to be proven to give accurate and reliable analyses (probably calibrated with each use).  There is no procedure in any of the EPA method manuals or Standard Methods which lack steps for preparing standard solutions and calibrating the test.  To report results from tests where the analyst has not performed a calibration on the instrument is a serious violation of federal and state regulations.

                 Calibration consists of establishing a relationship between the analytical response of a test and the concentration of target analyte in the sample.  This is done by testing samples of known concentration of the analyte and recording the analytical response.  The analytical response may consist of a voltage, resistance or amperage difference from an electrode or a decrease in the amount of light of a specific wavelength passed through a solution (absorbance).  The most common procedure for calibrating an instrument is to perform the test on standards (at least three if another number is not specified in the method) and then create a graph of the response versus the concentration.  When data points are connected, the resulting line is called a calibration curve.  Maybe the analyst reading this for the first time does not realize that for most colorimetric determinations, it is desirable to work in the linear range.      

                 Most bench top meters and spectrophotometers require at least a 2 standard check.  Verify the standard curve daily by analyzing one or more standards within the linear range.  Reportable analytical results are those within the range of the standard dilutions used.  Do not report values above the highest standard unless an initial demonstration of greater linear range has been made, no instrument parameters have been changed, and the value is less than 1.5 times the highest standard.  The lowest reportable value is the MDL (method detection limit), provided that the lowest standard is less than 10 times the MDL.

                 The scale of spectrophotometers is generally graduated in two ways:  percent transmittance and units of absorbance (the converse of transmittance).  Beer’s Law states that the concentration of a light absorbing colored solution is directly proportional to absorbance over a given range of concentrations. 

 Questions for Chapter 4

 

1.  70% nitric acid (HNO₃) has a density of 1.41 g/mL.  How many grams and mL of 70% nitric acid need to be diluted to 1000 mL to give a 1.00 N solution?

 

2.  5.00 mL of 0.241 M hydrochloric acid is diluted to 250 mL.  What is the final concentration?

 

3.  What is the formula weight of MgSO₄ • 10H₂O?

 

4.  How many grams of sulfur are in 50 grams of sulfuric acid?

 

5.  What is the formula weight of lime, slaked lime and limestone?

 

6.  Which of the following formulas is potassium phosphate dibasic?

H₃PO₃   KHSO₄    KH₂PO₄    K₂HPO₄    K₃PO₄    KH₂PO₃

 

7.  An amount of solid is dissolved into 50.0 gallons of water.  The water had an initial density of 1.00 g/mL.  The final density of the solution is 1.08.  How many pounds of solid was dissolved in the water?

 

8.  8.40 # of calcium hydroxide, Ca(OH)₂ was dissolved in 100.0 gal of water.  What is the percent concentration, Molarity and Normality of the resulting solution?