procedure (s 2) : a
Additivity of variance: s 2 = s 2 + s 2 osa
If either the sampling or the analytical standard deviation is much larger than the other, then the
overall variance is dominated by the larger variance. For example, if ss three time larger than sa, then
90% of the overall variance comes from s (because s 2 = s 2 + s 2 = 32 + 12 = 10). sosa
In this experiment, you will measure the content of strong base (mainly NaOH) in the household drain cleaner Drano. This product consists of solid pellets of NaOH, some aluminum shavings, some
insoluble material, and undoubtedly, some Na2CO3 from the reaction of NaOH with atmospheric CO2. If you weigh out replicate portions of Drano, the quantity of NaOH varies substantially form protion
to portion. In the experiment, you will evaluate the analytical variance and the sampling variance. A possible class project is to find out how the sampling variance depends on the sample size.
Bromocresol green indicator: dissolve 100 mg in 14.3 mL of 0.01 M NaOH and dilute to 250 mL
with distilled water.
Phenolphthalein indicator: Dissolve 50 mg in 50 mL of ethanol and dilute to 100 mL with distilled
Standard hydrochloric acid: ~0.1 M HCl. Prepare by diluting ~ 8.2 mL of 37% (w/w) HCl to 1.0
L with distilled water. [Standardize with primary standard “tris” (tris(hydroxymethyl)- aminomethane), using the green end point of bromocresol green indicator. Repeat three times.]
Solid Drano: (~4g per student) We recommend having severaltightly capped cans of the commercial product in the lab. Students can weigh solid directly out of the can.
Measuring the Analytical Variance
1. Weigh out 1.9 – 2.1g of solid Drano in a 50 mL beaker on a balance accurate to 0.001 g. add 20 mL of distilled water to the beaker and swirl to dissolve the solid. Any aluminum shavings or other
insoluble material will not dissolve. Decant the liquid into a 100 mL volumetric flask, leaving behind the solid shavings in the beaker. Add ~10 mL of water to he beaker, swirl to rinse the inside
of the beaker well, and decant the liquid in the volumetric flask. Repeat this process with several 10 mL portions of water to complete a quantitative transfer of the Drano (minus the insoluble
portion) into the volumetric flask finally, dilute to the mark, cap the flask, and mix well by inverting 20 times. There may be small particles of undissolved solid suspended in the liquid.
2. Dip a clean, dry 10 mL transfer pipet into the volumetric flask and take up ~ 5 mL of solution. Be extremely careful not to suck liquid into the rubber pipet bulb. Tip the pipet to rinse it with
the liquid and discard the liquid.
3. Use the pipet from step 2 to transfer 10.00 mL of Drano solution from the volumetric flask into a 125 mL erlenmeyer flask with a magnetic stir bar. Add several drops of phenolphthalein
indicator. Titrate with standard 0.1 M HCl from a 50 mL buret to the colorless endpoint. The flask should be magnetically stirred throughout the titration. A sheet of white paper placed under the
erlenmeyer will help you to see the color change better. The phenolphthalein color may gradually fade to become nearly imperceptible during the titration prior to the end point. If so, add one more
drop of indicator and continue the titration. If you add indicator and it turns pink, you have not yet passed the end point.
4. Repeat the previous step at least three times to obtain several accurate measurements to the end point. If the equivalence point is at less then 15 mL of HCl, titrate 20.00 ml of Drano solution
instead of 10.00 mL. In each case add 90-95 % of the required HCl rapidly, and then titrate slowly to find the end point.
5. From each equivalence volume of HCl, compute the wt % of NaOH in the solid Drano, assuming that the only base present is NaOH. Calculate standard deviation in wt % NaOH. As an example, your
result might be 35.33 ± 0.42 wt % NaOH. The relative standard deviation is 0.42/35.33 = 0.1119. This number is the relative analytical standard deviation, sa, in the weight percent of NaOH in the
Drano sample that you used. The relative analytical variance is sa2 = 0.0119 = 1.4 ×1034. The term “relative”means that each stand deviation os divided by the mean to which it applies.
Measuring the Sampling Variance
1. Weigh0.28 – 0.32 g (measured accurately to 0.001 g) of solid drano in to a 125 mL erlenmeyer flask with a magnetic stir bar. Record the level of titrant in your buret and add ~5 mL rapidly. Stir
to dissolve the Drano. (Metal shavings will remain undissolved.) Add several drops of phenolphthalein indicator and titrate to the colorless endpoint. Because you do not know where the endpoint
will be, try titrating at a constant rate of ~ 2 mL/min (~1.5 s/drop). You will need to pay careful attention to the color to try to find the endpoint to within ~ 2 to3 drops. If you need to add
more indicator because it fades, stop the titration while you add another drop of indicator. From the equivalence volume of HCl, compute the wt % of NaOH in the Drano. It is likely that your answer
will differ substantially from what you observed in the first part of this experiment.
2. Repeat the previous step at three times with fresh 0.27-0.33 g masses of solid Drano.
3. From the four titrations of solid Drano, determine the mean and the relative standard deviation for wt % of NaOH in Drano. This standard deviation is the relative overall standard deviation, so,
because it includes contributions form from both the sampling operation and the analytical titration. The square of so is the overall variance.
4. Compute the relative sampling variance s 2. Express your result with the appropriate number of s
procedure (s 2) : a