The branch of analytical chemistry known as quantitative analysis concerns itself with the amounts of the various components within a sample, and it is often separated into three categories: gravimetric, volumetric, and instrumental. Earlier in the semester instrumental analyses were performed utilitzing the sophisticated device called a spectrometer. In this experiment a gravimetric analysis will be performed, and it will rely on traditional laboratory equipment: balances, beakers, Büchner funnels, and filter flasks.

In gravimetric analysis, a substance is treated so that the component of interest is separated either in its pure form or as a constituent in a compound of known composition, which can be weighed. The separation is often accomplished by first dissolving a sample of the substance in a suitable solvent and then adding a reagent that reacts with the desired component to form an insoluble solid.

A gravimetric precipitation method must fulfill certain basic requirements in order to provide an accurate analysis.

1. The precipitation reaction should be quantitative so that only a negligible fraction on the component of interest remains in solution after the precipitate is isolated. A moderate excess of the precipitating agent is commonly employed to help achieve this condition.

2. Other constituents in the sample solution should not interfere with the precipitation of the component of interest.

3. The precipitation should be as free of contaminants as possible.

4. The particles of precipitate should be large enough to filter easily and to facilitate the removal of soluble impurities during washing operations.

5. The precipitate should easily be converted to a form suitable for weighing. The conversion may require only a drying operation to remove residual moisture; or, if the precipitate has an indefinite chemical composition, an ignition to produce a solid with a definite composition.

6. In addition to a definite composition, the weighing form should have: stability at the relatively high temperatures required for the drying or ignition operations; little or no tendency to react with substances in the air, and a molar mass significantly larger than that of the compound of interest.

The quantity of substance being analyzed may be anywhere from a few micrograms to several thousand kilograms. In the majority of cases, a sample, rather than the entire mass, is selected for analysis. Sampling a homogeneous material is relatively simple since the composition of the system is uniform throughout. In heterogeneous substances, samples must be taken from different sites within the substance.

Solid materials must be dried to remove moisture before they are weighed. This operation is usually performed in an oven set at 110C. Once a sample is weighed, it is dispersed in an appropriate solvent system. The solution volume is selected to give the component of interest a concentration suitable for a successful precipitation. Temperature is important because it affects solubility.

179

The following are the major techniques that are used in a gravimetric analysis.

1. DESICCATION. Solid reagents, which must be kept dry, are stored in the low humidity environment of a desiccator. A layer of material, which readily absorbs moisture (a desiccant), maintains the low humidity. Popular desiccants include granular anhydrous calcium chloride, anhydrous calcium sulfate, anhydrous magnesium perchlorate, phosphorus pentachloride, and silica gel. A desiccator made from a plastic container with a top is popular since it is lightweight, easily handled, and inexpensive. Obviously, the cover of the desiccator should be kept in place as much as possible. A desiccant should be replaced at infrequent intervals, or whenever it is apparently caked.

2. PRECIPITATION. The heart of any gravimetric analysis is the precipitation reaction. In most cases the reaction involves the formation of an ionic solid due to cation-anion combination during the mixing of precipitating agent and sample solutions.

3. DIGESTION. A precipitate is seldom ready for filtration immediately after it is formed, because its particles are generally small and retain an unnecessarily large amount of impurities. In order to minimize both these problems, the precipitate is allowed to remain in contact with the liquid phase for a period of time prior to being filtered. The process is known as digestion. An increase in particle size is observed during a digestion, and is attributed to two processes: the dissolution of the very small, more soluble particles to yield ions that then reprecipitate on the surface of the larger crystals; and the coagulation of small particles to form aggregates. As digestion takes place, impurities adsorbed on the surface of the precipitate particles tend to dissolve. Although the impurities may eventually be readsorbed, the decrease in precipitate surface area, which goes along with larger particles, lessens the chance of adsorption. Thus, digestion yields purer as well as larger, more easily filtered particles.

4. TESTING FOR COMPLETE PRECIPITATION. After the precipitate has settled, a drop of the precipitating agent is added to the clear supernatant liquid. If the drop produces a cloud of new precipitate, additional precipitating agent must be added, and digestion continued. If the drop produces no visible precipitate, it may be assumed that the precipitation is complete.

5. SUCTION FILTRATION. To hasten the separation of a solid and a liquid, a filtration can be performed with the use of a vacuum. The funnel used in this filtration is called a Büchner funnel. Fitted with a piece of filter paper, the funnel sits on a filter flask, which is just an Erlenmeyer flask with a sidearm that can be connected to a vacuum with rubber tubing.

6. WASHING THE PRECIPITATE. After the removal of the supernatant liquid, the small amount of solution that remains along with a precipitate may serve as a source of contamination in later operations. In addition, foreign ions are likely to be absorbed by a precipitate as it forms. To remove these contaminants, the precipitate is washed. Although the wash liquid is often deionized water, occasionally a very dilute solution of the original precipitating agent is used. A precipitate can also be washed with acetone to remove water from the precipitate in order to decrease the drying time. The liquid is added directly to the precipitate container and is removed by suction filtration.

7. DRYING. Solid materials must be dried to remove moisture before they are weighed. This operation is usually performed in an oven set at 110C, and the solid is dried from several hours to overnight.

180

A traditional gravimetric analysis for iodide ion features the use of the reagent lead (II) nitrate to bring about the precipitation of lead (II) iodide from an aqueous solution containing a known mass of sample. The precipitate reaction is

- 2+ 2I (aq) + Pb (aq)  PbI2 (s)

This reaction satisfies the important criteria for a satisfactory gravimetric method: namely, a quantitative reaction yielding a product of definite composition, essentially free from impurities. After a period of digestion, the lead (II) iodide is isolated by filtration, washed and dried to a constant mass.

Since the composition of lead (II) iodide is known, a comparison of the precipitate mass with the mass of the original sample yields a value for the mass percentage of iodide in the substance being analyzed.

STATISTICAL ANALYSIS

In this experiment up to seven students will be analyzing the same unknown phosphate ion sample. The students with the same unknown will compile their data and summarize it in a useful manor. A complete summary of a data set must include a measurement of central tendency, and a measurement of dispersion.

1. CENTRAL TENDENCY. The prediction of a central or typical value for a measurement in a data set is called central tendency. The three most common measurements of central tendency are mean, median, and mode. The most familiar measurement of central tendency is the average, or mean. We usually denote the mean value of some variable by placing a bar over its symbol:

x =  x ____ n

where x is the mean of n observations of x.

As an example, if four students determined the percentage of phosphate ion in the sample to be 51.3%, 55.6%, 49.9%, and 52.0%, the mean percentage of phosphate ion in the sample would be:

x = 51.3% + 55.6% + 49.9% + 52.0% = 52.2% ______4

Although we will not calculate them in this experiment, the other measurements of central tendency are median, the middle value of a data set, and mode, the value that appears most often in a data set.

181

2. DISPERSION. The prediction of a spread or distribution of measurements in a data set is called central tendency. The three most common measurements of dispersion are range, variance, and standard deviation. Range is the difference between the highest and lowest values in the data set. However, it is a poor indicator of the distribution of all the data points because it only depends on the highest and lowest values.

This leads to a measurement of dispersion called the variance. The variance is the mean square deviation of all data points:

2 Vx =  (x - x) ______n - 1

where Vx is the variance of the n observations of x, and the deviation is the difference between an individual data point and the mean: x - x. The demoninator in the definition is of some interest. Because x is calculated from the n individual x values, only n – 1 deviation calculations are independent, so the sum of the square deviations is divided by n – 1, not n. Consider a sample with 5 data points. First, we calculate x and then we begin to calculate the 5 deviations from the mean, (x - x). When we reach the fifth data point, the deviation is no longer independent, because the value of the fifth data point could be calculated from the mean and the four other data points before we even saw it! Therefore, Vx is the variance of the n – 1 independent calculations. The number of independent deviation calculations is called the degrees of freedom.

The units of the variance are the units of x2, which does not convey any physical meaning. Thus, standard deviation, or root-mean-square deviation, is a more useful measurement to indicate dispersion. It is assigned the symbol sx, and is defined by taking the square root of the above equation. Therefore, to make a complete summary of a data set must, we will include the mean to indicate central tendency and the standard deviation to indicate dispersion.

To calculate the standard deviation for the above example:

s = (51.3% - 52.2%)2 + (55.6% - 52.2%)2 + (49.9% - 52.2%)2 + (52.0%-52.2%)2 = 2.4% ______4 - 1

In academics the standard deviation is reported with the mean. In industry the standard deviation is commonly expressed in a percentage form called the relative standard deviation, or RSD:

RSD = sx (100) ___ n

To calculate the RSD in the previous example:

RSD = 2.4% (100) = 4.6% ______52.2%

182

Finally, before calculating a mean, you will want to make sure that all of the data points should be included in the calculation of the mean. Occasionally in a set of data there is one data point that is significantly different from the rest, called an outlier. This is usually caused by a gross error, which is a careless error due to a mistake that is not likely to be repeated in similar determinations. This would include the spilling of a sample, reading the weight incorrectly, a volume reading incorrectly, etc. The data set may not have an outlier, but if it does, there are statistical tests that can be done to determine if an outlier exists. The statistical test we will use for identification and rejection of an outlier is the Q-test. A Q value is calculated by determining the gap between the suspected outlier, xoutlier, and its nearest data point, xnearest, then dividing that by the range of the data points (the difference between the highest and lowest data points:

Q = gap = xoutlier – xnearest ______

range xhighest – xlowest

The Q is then compared to the Q95% , a reference value corresponding to the number of data points in the data set, given in the table below. For the number of data points in the data set, the Q95% is the minimum Q value that would indicate, to a 95% confidence level, that the suspected outlier is actually an outlier. Therefore, if the Q exceeds the Q95%, then statistically to a 95% confidence level, the suspected outlier can be rejected from the calculation of the mean.

Number of Data Points : 3 4 5 6 7 8 9 10

Q95% : 0.970 0.829 0.710 0.625 0.568 0.526 0.493 0.466

In the previous example, the 55.6 s data point is the furthest from its nearset neighbor, so it is the most likely to be an outlier. The calculation for the Q value would be:

Q = 55.6% - 52.0% = 0.632 ______55.6% - 49.9%

From the table on the previous page, the Q95% value corresponding to four data points in the data set is 0.829. Because Q does not exceed the Q95%, then statistically to a 95% confidence level, the suspected outlier is not an outlier, and should not be rejected from the calculation of the mean.

183

PROCEDURE

1. Students will work individually for this experiment. Except for the laboratory handout, remove all books, purses, and such items from the laboratory bench top, and placed them in the storage area by the front door. For laboratory experiments you should be wearing closed-toe shoes. Tie back long hair, and do not wear long, dangling jewelry or clothes with loose and baggy sleeves. Open you lab locker. Put on your safety goggles, your lab coat, and gloves.

2. Plug in your hot plate and turn it on. Depending on the model of the hot plate, adjust it to a setting of 125°C or a setting of 5 out of 10.

3. Obtain an unknown mixture that contains iodide ions from your instructor. Write down the number of your unknown (found on the unknown’s container) in your Data Table. Do not remove the number label from the unknown container. Using an analytical balance, accurately weigh out between 0.8 and 1.0 grams of the unknown in a tared 400-mL beaker.

NOTE: If any crystals are spilled on the balance or on the lab bench, clean them up immediately, and dispose of it in the waste bottle in fume hood A. If there are any crystals left on the balance or the lab bench at the end of the lab period, the instructor will deduct one point from everyone’s lab score as a charge for cleaning up after you.

4. Dissolve the crystals in approximately 100 mL of deionized water.

5. To the unheated solution, slowly and while stirring, add 50 mL of 0.2 M lead (II) nitrate, which should be sufficient to bring about an essentially complete precipitation of the iodide ion and also provide a slight excess of lead (II) ion. The precipitation is carried out at room temperature because the solubility of lead (II) iodide in water at room temperature is negligible.

6. In order to prepare the precipitate for filtration, it must be digested. The digestion may be carried out at room temperature by allowing the solid-liquid mixture to stand for several hours with a covered beaker located on the lab bench. Alternatively, the mixture, with frequent stirring, can be heated for about 20 minutes just under its boiling point using a hot plate. Therefore, place the beaker on your hot plate (adjusted to a setting of 125°C or a setting of 5 out of 10), and heat the solution with frequent stirring. Before you remove the stirring rod from the solution, rinse any solid that is adhering to the stirring rod back into the solution with deionized water. Do not let any of the solid or liquid leave the solution on your stirring rod! While digesting, the solution should be heated to just below its boiling point. If the solution shows any signs that it is starting to boil, turn down the setting on the hot plate.

CAUTION: Boiling may cause the mixture to "bump".

7. At the end of the digestion period remove the 400-mL beaker from the hot plate and set it on a hot pad to cool. When the solid has settled, test the system for completeness of precipitation by adding one drop of 0.2 M lead (II) nitrate solution. If no precipitate forms when the drop contacts the liquid, it can be assumed that all of the iodide has been precipitated out as lead (II) iodide. If more precipitate appears when the drop contacts the liquid, 10 mL of additional lead (II) nitrate solution must be added, digestion continued, and the solution tested again until precipitation is complete.

8. Prior to filtration, the system must cool to room temperature so that the solubility losses are minimized. Half-fill a plastic container with ice. After several minutes on the hot pad, transfer the 400-mL beaker to the ice bath and let your solution cool for ten minutes.

184

9. Set up a ring stand with a three-pronged clamp attached to it. Obtain a Büchner funnel, a gray, conical funnel-support, and a filter flask from the side of the room.

CAUTION: Immediately clamp your filter flask to the ring stand with the three-pronged clamp. If you do not, the weight of the rubber tubing will knock over the filter flask and it may break.

Obtain a piece of Whatman Grade No. 1 filter paper (medium porosity, medium flow rate, 11 μm particle retention) from the back of the lab room, and determine its mass on the same balance you used in step 3.

10. Set up a suction filtration apparatus by attaching the rubber tubing from the filter flask to the vacuum line. Next, place the gray, conical funnel-support on the top of the filter flask, and set the Büchner funnel on the funnel-support. One side of the filter paper has a microlip that you can feel when you run your fingertip along its circular edge. With the microlip side of the filter paper face down, place it in the Büchner funnel. Turn on the vacuum and completely wet the filter paper with deionized water from your wash bottle. The sound of air passing into the filter flask indicates that the Büchner funnel and filter support are not making a complete seal with the filter flask. Push down slightly on the Büchner funnel to make a complete seal, and the sound should subside.

11. With the vacuum still on, decant a majority of the supernatant liquid into the Büchner funnel as shown below to the left. Next, pour as much of the precipitate into the Büchner funnel as possible. Transfer the rest of the precipitate using a stream of deionized water projected from a wash bottle, as shown below to the right. If this does not completely transfer the precipitate to the Büchner funnel, any remaining particles adhering to the beaker walls should be removed with a rubber policeman. Rinse any precipitate adhering to the rubber policeman into the Büchner funnel with deionized water from your wash bottle. The filtrate collected in the filter flask should be clear.

185

12. If the filtrate in the filter flask contains solid particles, turn off the vacuum and detach the filter flask from the Büchner funnel. Pour the filtrate into a clean beaker. Reattach the filter flask, turn on the vacuum, and pour the filtrate through the Büchner funnel a second time. Once the filtrate in the filter flask is clear, continue with step 13.

13. With the vacuum still on, wash the solid in the funnel with three 10-mL portions of deionized water, and allow the vacuum to air dry the precipitate for about 5 minutes.

14. With the vacuum still on, wash the solid in the funnel with 3 10-mL portions of acetone from an acetone bottle found in Fume Hood A, and allow the vacuum to air dry the precipitate for about 2 minutes.

15. Label a 250-mL beaker with your name, determine its mass, and record it in the Data Table. Turn off the vacuum and, using your microspatula, lift the filter paper and the lead (II) iodie precipitate from the funnel, and place the filter paper in the 250-mL beaker. Remove any of the lead (II) iodide precipitate that is adhering to the Büchner funnel with your rubber policeman, and wipe the precipitate onto the inside of the 250-mL beaker. All of the precipitate should be transferred to the 250-mL beaker, do not leave any of the precipitate in the Büchner funnel.

16. Place the labled 250-mL beaker in the drying oven for 75 minutes.

17. Empty the contents from the filter flask into a large waste beaker on your bench top. Empty any remaining unknown into the waste container also. All liquids from today’s experiment will be discarded in the liquid waste container in the Fume Hood A. Clean and dry the unknown container, and return it to the back of the lab. To clean the filter flask, rinse it three times with deionized water, then once with acetone from the Fume Hood A, collecting all washing in the waste beaker on your bench top. Hang the filter flask on a drying rack, with the hose suspended over the sink. Return the funnel-support and unknown container to the back of the lab. The washings in the large beaker are to be discarded in the liquid waste container in Fume Hood A.

18. To clean the Büchner funnel, scrub it with soap and a test tube brush, and then rinse it thoroughly with deionized water. Dry the Büchner funnel, and return to the back of the lab.

19. After the 75 minutes in the drying oven, remove the beaker from the oven with beaker tongs, allow the filter paper to cool, and determine the mass of the filter paper and precipitate. Place your filter paper and precipitate in the wide-mouth solid waste bottle in the Fume Hood A.

20. Calculate the Mass % of Iodide in Unknown Sample and record it in your Data Table. Find your unknown number on the white board, and write your calculated mass percentage underneath it. Record all of the calculated mass percentages for your unknown in your Data Table. List the mass percentages from lowest to highest, then apply a Q-Test to the highest and lowest mass perecentages to determine if one of them should be rejected because it is an outlier.

21. The statistical analysis can be done on a TI-30 calculator. Clear the calculator by pressing . If Error appears, press . Enter the first mass percentage, then press . Enter the second mass percentage, press , and continue this until all of the mass percentages have been entered. At this point you will see n = x, where x is the number of data points you have entered. To find the mean of the entered data, press , and you will see the mean displayed. To find the standard deviation, press , and you will see the standard deviation displayed. You will need to calculate the relative standard deviation on your own. Record each of these calculated values in your Data Table.

21. Clean and wipe dry your laboratory work area and all apparatus. When you have completed your lab report have the instructor inspect your working area. Once your working area has been checked your lab report can then be turned in to the instructor.

186

EXPERIMENT 18 LAB REPORT

Name: ______Student Lab Score: ______

Date/Lab Start Time: ______Lab Station Number: ______

DATA TABLE

Unknown Code Number ______

Mass of Unknown Sample . g

Mass of Filter Paper . g

Mass of 250-mL Beaker . g

Mass of Dried 250-mL Beaker, Filter Paper, PbI2 . g

1 Mass of PbI2 . g

2 Mass of Iodide from PbI2 . g

3 Mass % of Iodide in Unknown Sample . %

Mass % of Iodide from 2nd Experimentor . %

Mass % of Iodide from 3rd Experimentor . %

Mass % of Iodide from 4th Experimentor . %

Mass % of Iodide from 5th Experimentor . %

Mass % of Iodide from 6th Experimentor . %

Mass % of Iodide from 7th Experimentor . %

4 Mean Mass % of Iodide in Unknown Sample . %

Standard Deviation . %

5 Relative Standard Deviation . %

187

CALCULATIONS

188

5. 4. (Q-test)

5. 5.

QUESTIONS

1. If all of the iodide ions were not precipitated out by the addition of the lead (II) nitrate, would the calculated percentage of iodide in the unknown sample be greater or less than the actual percentage? Explain based upon your calculations in Box 2 and Box 3.

______

2. If the lead (II) iodide was not completely dry before weighing, would the calculated percentage of iodide in the unknown sample be greater or less than the actual percentage? Explain based upon your calculations in Box 2 and Box 3.

______

189

3. What precipitating agent could be used to analyze an unknown sample for:

(a) sulfate ions ______

(b) magnesium ions ______

4. A toothpaste sample was analyzed for fluoride by gravimetric analysis. A 34.067 g sample of the toothpaste was dissolved in water, treated with calcium nitrate, and 0.105 g of precipitate was collected. Calculate the percentage of fluoride in the toothpaste.

190